---
title: "The solver said it had converged. The agent checked."
url: "https://tryreynolds.com/studies/converging-diverging-nozzle"
description: "A nozzle with a shock standing inside it, found where theory says it should be. The reason to read this one is what happened first: a solver reported success, and the agent tested the claim against physics before believing it."
---

**[Reynolds](https://tryreynolds.com)** is agentic CFD, built by
**[InviscidAI](https://inviscidai.com)** and backed by Y Combinator, Winter 2026 batch.
The agent is open source under the MIT licence at
[github.com/InviscidAI/OpenReynolds](https://github.com/InviscidAI/OpenReynolds).
Using it requires no OpenFOAM knowledge.

This is the agent-readable Markdown twin of https://tryreynolds.com/studies/converging-diverging-nozzle. It lives at https://tryreynolds.com/studies/converging-diverging-nozzle.md, and
[tryreynolds.com/llms.txt](https://tryreynolds.com/llms.txt) indexes every one of them.

# The solver said it had converged. The agent checked.

A nozzle with a shock standing inside it, found where theory says it should be. The reason to read this one is what happened first: a solver reported success, and the agent tested the claim against physics before believing it.

RUN 03APPLIEDCOMPRESSIBLEAPRIL 202620260409-072030-97ab

- **Asked**: “Compressible flow through a converging-diverging nozzle designed for about Mach 2, air. Show me the shock structure if it is over- or under-expanded, and compare the exit Mach number.”
- **Run**: rhoPimpleFoam with local time stepping · 4,800 cells
- **Result**: Overexpanded: a normal shock inside the duct at x ≈ 0.18–0.20 m
- **Answer**: Overexpanded. Normal shock inside the duct at x ≈ 0.18 to 0.20 m of 0.30 m
- **Peak Mach**: 1.51 on the centreline, ahead of the shock
- **Exit Mach**: 0.52, against 0.43 from quasi-1D shock theory at the same shock position
- **Verification**: Inlet and outlet mass flow reconciled before the result was reported

![Mach field through a converging-diverging nozzle with a normal shock](https://tryreynolds.com/assets/nozzle-mach-Bey4ucvC.png)

Figure 1 Subsonic inlet, sonic throat, a supersonic pocket, a sharp normal shock, then subsonic to the exit.

## The question behind the question

A converging-diverging nozzle only reaches its design Mach number if the pressure it exhausts into is low enough. Give it more back pressure than that and the supersonic flow in the divergent section cannot reach the exit: it slams back to subsonic through a normal shock partway down the duct. That is what overexpanded means, and it is the regime the question was really about.

Reynolds set the geometry from theory rather than by eye. A throat-to-exit area ratio of 1.6875 is the one-dimensional isentropic value for a design Mach of exactly 2.0, so the duct is a real Mach 2 nozzle. Then it picked the back pressure to land in the interesting regime: 75 kPa static against 101,325 Pa stagnation, which 1D theory places squarely in the shock-inside-the-duct band. A shock-free run at this area ratio would have needed about 13 kPa.

## Testing the claim

The first attempt used rhoSimpleFoam, the natural steady choice. Under heavy under-relaxation it settled into a state with flat residuals, which is what most people and nearly every automated pipeline would record as a converged solution and ship.

Reynolds tested it instead. It measured the mass flow entering the duct against the mass flow leaving it, and they disagreed by a factor of three. A steady compressible solution that does not conserve mass has not solved the equations: the residuals had flattened because under-relaxation had frozen the solution in place, not because anything was satisfied.

It switched to rhoPimpleFoam with local time stepping, marching a transient scheme toward a pseudo-steady state, which stays stable in the presence of a shock where the SIMPLE scheme did not. That run conserves mass, and it is the one reported.

This is what a workspace buys you. Nothing in the harness told it to check mass conservation, and nothing told it that flat residuals can lie. It had a machine, it could run whatever it liked against the output, and it went looking for a reason to disbelieve its own first answer.

> rhoSimpleFoam (steady SIMPLE) diverged, and after heavy under-relaxation it reached a numerically “converged” state that actually violated mass conservation by 3×: a false convergence, discarded.

## Reading the gap

Quasi-1D shock theory, applied at the shock position the CFD found, predicts an exit Mach number of about 0.43. The simulation gives 0.52. The agent explained the difference rather than presenting the number bare.

On a 4,800-cell mesh the shock is resolved as a ramp a few cells wide rather than a discontinuity, and a smeared shock is a weaker shock: it destroys less stagnation pressure than a sharp one, so the flow behind it moves faster than one-dimensional theory expects. The direction and the rough size of the difference are both what that mechanism predicts, which is what makes it an explanation rather than an excuse. An error you can attribute to a specific mechanism is a different object entirely from one you cannot.

![A structured block mesh of the converging-diverging duct, symmetry-plane half model](https://tryreynolds.com/assets/nozzle-mesh-DOWGHda4.png)

Figure 2 A structured block mesh of the duct, run as a symmetry-plane half model.

![Centreline profiles of Mach number and static pressure with the nozzle contour beneath](https://tryreynolds.com/assets/nozzle-centerline-CDNfmX5V.png)

Figure 3 Centreline Mach and static pressure, with the nozzle contour beneath for reference.

## The whole session, exactly as it happened.

One prompt in, and everything the agent said and ran on the way to the answer. Open a step to see the command it sent and what came back. Nothing here is rewritten.

26 messages, 80 tool calls

### you

Compressible flow through a converging-diverging nozzle designed for about Mach 2, air, 2D or axisymmetric. Show me the shock structure if it is over- or under-expanded, and compare the exit Mach number with 1D isentropic theory.

### tool: bash

`ls /work/.toolbox; echo ---; cat /work/.toolbox/notes/*.md 2>/dev/null | head ...` exit 0

**input**

```
{
  "cmd": "ls /work/.toolbox; echo ---; cat /work/.toolbox/notes/*.md 2>/dev/null | head -100; echo ---; find $FOAM_TUTORIALS -iname \"*nozzle*\" -o -iname \"*laval*\" 2>/dev/null"
}
```

### tool: bash

`find $FOAM_TUTORIALS -iname "*rhoSimpleFoam*" -maxdepth 1; ls $FOAM_TUTORIALS/...` exit 0

**input**

```
{
  "cmd": "find $FOAM_TUTORIALS -iname \"*rhoSimpleFoam*\" -maxdepth 1; ls $FOAM_TUTORIALS/compressible/; ls $FOAM_TUTORIALS/compressible/rhoSimpleFoam/ 2>/dev/null; ls $FOAM_TUTORIALS/compressible/rhoCentralFoam/ 2>/dev/null"
}
```

**output**

```
exit_code: 0

acousticFoam
overRhoPimpleDyMFoam
overRhoSimpleFoam
rhoCentralFoam
rhoPimpleAdiabaticFoam
rhoPimpleFoam
rhoPorousSimpleFoam
rhoSimpleFoam
sonicDyMFoam
sonicFoam
sonicLiquidFoam
aerofoilNACA0012
angledDuctExplicitFixedCoeff
gasMixing
squareBend
squareBendLiq
squareBendLiqNoNewtonian
LadenburgJet60psi
biconic25-55Run35
forwardStep
movingCone
obliqueShock
shockTube
wedge15Ma5
```

### tool: bash

`find $FOAM_TUTORIALS -iname "*nozzle*"; find / -iname "*lavalNozzle*" 2>/dev/n...` exit 0

**input**

```
{
  "cmd": "find $FOAM_TUTORIALS -iname \"*nozzle*\"; find / -iname \"*lavalNozzle*\" 2>/dev/null; find / -iname \"*cdNozzle*\" 2>/dev/null; cat $FOAM_TUTORIALS/compressible/rhoCentralFoam/obliqueShock/system/controlDict 2>/dev/null | head -30"
}
```

**output**

```
exit_code: 0

/usr/lib/openfoam/openfoam2512/tutorials/combustion/reactingFoam/RAS/chokedNozzle
/usr/lib/openfoam/openfoam2512/tutorials/discreteMethods/molecularDynamics/mdFoam/nanoNozzle
/usr/lib/openfoam/openfoam2512/tutorials/multiphase/interFoam/LES/nozzleFlow2D
/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  v2512                                 |
|   \\  /    A nd           | Website:  www.openfoam.com                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    object      controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

application     rhoCentralFoam;

startFrom       startTime;

startTime       0;

stopAt          endTime;

endTime         10;

deltaT          0.0025;

writeControl    adjustable;
```

### tool: bash

`cd $FOAM_TUTORIALS/compressible/rhoSimpleFoam/aerofoilNACA0012 && for f in 0/p...` exit 0

**input**

```
{
  "cmd": "cd $FOAM_TUTORIALS/compressible/rhoSimpleFoam/aerofoilNACA0012 && for f in 0/p 0/T 0/U 0/nuTilda constant/*; do echo ==$f==; cat $f 2>/dev/null | sed -n '1,40p'; done 2>&1 | head -200"
}
```

**output**

```
exit_code: 0

==0/p==
==0/T==
==0/U==
==0/nuTilda==
==constant/thermophysicalProperties==
/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  v2512                                 |
|   \\  /    A nd           | Website:  www.openfoam.com                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    object      thermophysicalProperties;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

thermoType
{
    type            hePsiThermo;
    mixture         pureMixture;
    transport       const;
    thermo          hConst;
    equationOfState perfectGas;
    specie          specie;
    energy          sensibleInternalEnergy;
}

mixture // air at room temperature (293 K)
{
    specie
    {
        molWeight   28.9;
    }
    thermodynamics
    {
        Cp          1005;
        Hf          0;
    }
    transport
    {
==constant/turbulenceProperties==
/*--------------------------------*- C++ -*------------------------------
```

### tool: bash

`cd $FOAM_TUTORIALS/compressible/rhoSimpleFoam/aerofoilNACA0012 && ls 0.orig 2>...` exit 0

**input**

```
{
  "cmd": "cd $FOAM_TUTORIALS/compressible/rhoSimpleFoam/aerofoilNACA0012 && ls 0.orig 2>/dev/null; for f in 0.orig/p 0.orig/T 0.orig/U; do echo ==$f==; sed -n '18,60p' $f; done\necho ---squareBend---\nfind $FOAM_TUTORIALS/compressible/rhoSimpleFoam -maxdepth 1\n"
}
```

**output**

```
exit_code: 0

T
U
alphat
k
nut
omega
p
==0.orig/p==

dimensions      [1 -1 -2 0 0 0 0];

internalField   uniform $pOut;

boundaryField
{
    freestream
    {
        type            freestreamPressure;
        freestreamValue uniform $pOut;
    }

    wall
    {
        type            zeroGradient;
    }

    #includeEtc "caseDicts/setConstraintTypes"
}

// ************************************************************************* //
==0.orig/T==

dimensions      [0 0 0 1 0 0 0];

internalField   uniform $Tinlet;

boundaryField
{
    freestream
    {
        type            inletOutlet;
        inletValue      uniform $Tinlet;
        value           $inletValue;
    }

    wall
    {
        type            zeroGradient;
    }

    #includeEtc "caseDicts/setConstraintTypes"
}

// ************************************************************************* //
==0.orig/U==

dimensions      [0 1 -1 0 0 0 0];

internalField   uniform $Uinlet;

boundaryField
{
    freestream
    {
        type            freestreamVelocity;
        freestreamValue uniform $Uinlet;
        value           uniform $Uinlet;
    }

    wall
    {
        type            noSlip;
    }

    #includeEtc "caseDicts/setConstraintTypes"
}

// ************************************************************************* //
---squareBend---
/usr/lib/openfoam/openfoam2512/tutorials/compressible/rhoSimpleFoam
/usr/l
```

### tool: bash

`cd $FOAM_TUTORIALS/compressible/rhoSimpleFoam/squareBend && for f in 0/p 0/T 0...` exit 0

**input**

```
{
  "cmd": "cd $FOAM_TUTORIALS/compressible/rhoSimpleFoam/squareBend && for f in 0/p 0/T 0/U; do echo ==$f==; sed -n '18,80p' $f; done; echo ---; cat system/fvSolution | sed -n '1,60p'; echo ---controlDict---; cat system/controlDict"
}
```

**output**

```
exit_code: 0

==0/p==
sed: can't read 0/p: No such file or directory
==0/T==
sed: can't read 0/T: No such file or directory
==0/U==
sed: can't read 0/U: No such file or directory
---
/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  v2512                                 |
|   \\  /    A nd           | Website:  www.openfoam.com                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    object      fvSolution;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

solvers
{
    p
    {
        solver          GAMG;
        tolerance       1e-08;
        relTol          0.1;
        smoother        GaussSeidel;
        nCellsInCoarsestLevel 20;
    }

    "(U|e|k|epsilon)"
    {
        solver          GAMG;
        tolerance       1e-08;
        relTol          0.1;
        smoother        GaussSeidel;
        nCellsInCoarsestLevel 20;
    }
}

SIMPLE
{
    nNonOrthogonalCorrectors 0;
    pMinFactor      0.1;
    pMaxF
```

### agent

Good — SIMPLE with `transonic yes; consistent yes;` is exactly the setting for transonic/supersonic duct flow. Let's see squareBend's 0.orig BCs (inlet/outlet duct with subsonic conditions, likely not supersonic though). Let's check.

### tool: bash

`cd $FOAM_TUTORIALS/compressible/rhoSimpleFoam/squareBend && for f in 0.orig/p ...` exit 0

**input**

```
{
  "cmd": "cd $FOAM_TUTORIALS/compressible/rhoSimpleFoam/squareBend && for f in 0.orig/p 0.orig/T 0.orig/U; do echo ==$f==; sed -n '18,80p' $f; done; echo ---; cat constant/thermophysicalProperties | sed -n '18,60p'"
}
```

**output**

```
exit_code: 0

==0.orig/p==

internalField   uniform 110000;

boundaryField
{
    inlet
    {
        type            zeroGradient;
    }

    outlet
    {
        type            fixedValue;
        value           $internalField;
    }

    "(?i).*walls"
    {
        type            zeroGradient;
    }
}

// ************************************************************************* //
==0.orig/T==

internalField   uniform 1000;

boundaryField
{
    inlet
    {
        type            fixedValue;
        value           $internalField;
    }

    outlet
    {
        type            inletOutlet;
        value           $internalField;
        inletValue      $internalField;
    }

    "(?i).*walls"
    {
        type            zeroGradient;
    }
}

// ************************************************************************* //
==0.orig/U==

internalField   uniform (0 0 0);

boundaryField
{
    inlet
    {
        type            flowRateInletVelocity;
        massFlowRate    constant 0.5;
        rhoInlet        0.5;    // Guess for rho
    }

    outlet
    {
        type            inletOutlet;
        value           $internalField;
        inletValue      $internalField;
    }

    "(?i).*walls"
    {
        type            noSlip;
    }
}

// ************************************************************************* //
---
{
    type            heRhoThermo;
    mixtur
```

### tool: bash

`find /usr/lib/openfoam/openfoam2512/src -iname "*totalPressure*" -o -iname "*t...` exit 0

**input**

```
{
  "cmd": "find /usr/lib/openfoam/openfoam2512/src -iname \"*totalPressure*\" -o -iname \"*totalTemperature*\" 2>/dev/null | grep -v Doxygen; find /usr/lib/openfoam/openfoam2512/tutorials -path \"*rhoPimpleFoam*\" -name \"p\" | xargs grep -l totalPressure 2>/dev/null | head"
}
```

**output**

```
exit_code: 0

/usr/lib/openfoam/openfoam2512/src/finiteVolume/fields/fvPatchFields/derived/inletOutletTotalTemperature
/usr/lib/openfoam/openfoam2512/src/finiteVolume/fields/fvPatchFields/derived/inletOutletTotalTemperature/inletOutletTotalTemperatureFvPatchScalarField.C
/usr/lib/openfoam/openfoam2512/src/finiteVolume/fields/fvPatchFields/derived/inletOutletTotalTemperature/inletOutletTotalTemperatureFvPatchScalarField.H
/usr/lib/openfoam/openfoam2512/src/finiteVolume/fields/fvPatchFields/derived/prghPermeableAlphaTotalPressure
/usr/lib/openfoam/openfoam2512/src/finiteVolume/fields/fvPatchFields/derived/prghPermeableAlphaTotalPressure/prghPermeableAlphaTotalPressureFvPatchScalarField.C
/usr/lib/openfoam/openfoam2512/src/finiteVolume/fields/fvPatchFields/derived/prghPermeableAlphaTotalPressure/prghPermeableAlphaTotalPressureFvPatchScalarField.H
/usr/lib/openfoam/openfoam2512/src/finiteVolume/fields/fvPatchFields/derived/prghTotalPressure
/usr/lib/openfoam/openfoam2512/src/finiteVolume/fields/fvPatchFields/derived/prghTotalPressure/prghTotalPressureFvPatchScalarField.C
/usr/lib/openfoam/openfoam2512/src/finiteVolume/fields/fvPatchFields/derived/prghTotalPressure/prghTotalPressureFvPatchScalarField.H
/usr/lib/openfoam/openfoam2512/src/finiteVolume/fields/fvPatchFields/derived/rotatingTotalPressure
/usr/lib/openfoam/openfoam2512/src/finiteVolume/fields/fvPatchFields/derived/rotatin
```

### agent

Good, `totalPressure` and `totalTemperature` BCs exist. Let's check header docs for required entries.

### tool: bash

`sed -n '1,80p' /usr/lib/openfoam/openfoam2512/src/finiteVolume/fields/fvPatchF...` exit 0

**input**

```
{
  "cmd": "sed -n '1,80p' /usr/lib/openfoam/openfoam2512/src/finiteVolume/fields/fvPatchFields/derived/totalPressure/totalPressureFvPatchScalarField.H | sed -n '30,80p'\necho ---T---\nsed -n '30,80p' /usr/lib/openfoam/openfoam2512/src/finiteVolume/fields/fvPatchFields/derived/totalTemperature/totalTemperatureFvPatchScalarField.H"
}
```

**output**

```
exit_code: 0

    grpInletBoundaryConditions grpOutletBoundaryConditions

Description
    This boundary condition provides a total pressure condition.  Four
    variants are possible:

    1. incompressible subsonic:
        \f[
            p_p = p_0 - 0.5 |U|^2
        \f]
        where
        \vartable
            p_p     | incompressible pressure at patch [m2/s2]
            p_0     | incompressible total pressure [m2/s2]
            U       | velocity
        \endvartable

    2. compressible subsonic:
        \f[
            p_p = p_0 - 0.5 \rho |U|^2
        \f]
        where
        \vartable
            p_p     | pressure at patch [Pa]
            p_0     | total pressure [Pa]
            \rho    | density [kg/m3]
            U       | velocity
        \endvartable

    3. compressible transonic (\f$\gamma = 1\f$):
        \f[
            p_p = \frac{p_0}{1 + 0.5 \psi |U|^2}
        \f]
        where
        \vartable
            p_p     | pressure at patch [Pa]
            p_0     | total pressure [Pa]
            G       | coefficient given by \f$\frac{\gamma}{1-\gamma}\f$
        \endvartable

    4. compressible supersonic (\f$\gamma > 1\f$):
        \f[
            p_p = \frac{p_0}{(1 + 0.5 \psi G |U|^2)^{\frac{1}{G}}}
        \f]
        where
        \vartable
            p_p     | pressure at patch [Pa]
            p_0     | total pressure [Pa]
            \gam
```

### tool: bash

`mkdir -p /work/20260409-072030-97ab/case` exit 0

**input**

```
{
  "cmd": "mkdir -p /work/20260409-072030-97ab/case\ncat << 'PYEOF' > /work/20260409-072030-97ab/gen_blockMesh.py\nimport numpy as np\n\ngamma=1.4\n# geometry params\nh_in, h_th, h_ex = 0.15, 0.05, 0.084375\nLc, Ld = 0.10, 0.20\nzt = 0.01   # thickness (2D slab)\n\ndef wall_y(x):\n    if x <= Lc:\n        return h_th + (h_in-h_th)*0.5*(1+np.cos(np.pi*x/Lc))\n    else:\n        s = (x-Lc)/Ld\n        return h_th + (h_ex-h_th)*0.5*(1-np.cos(np.pi*s))\n\n# block layout: 8 conv blocks (nx=5 each ->40), 8 div blocks (nx=10 each ->80)\nnconv, ndiv = 8, 8\nnx_conv, nx_div = 5, 10\nx_conv = np.linspace(0, Lc, nconv+1)\nx_div  = np.linspace(Lc, Lc+Ld, ndiv+1)[1:]\nxs = np.concatenate([x_conv, x_div])   # station x's, len = nconv+ndiv+1 = 17\nny = 40\n\nN = len(xs)-1  # number of blocks\nnx_list = [nx_conv]*nconv + [nx_div]*ndiv\n\nys = np.array([wall_y(x) for x in xs])\n\n# vertices: per station...
```

**output**

```
exit_code: 0

N blocks: 16 total nx: 120 ny: 40 cells: 4800
h_in 0.15 h_th 0.05 h_ex 0.084375 area ratio 1.6875
```

### agent

Now let's check blockMesh accepts this dict.

### tool: bash

`cd /work/20260409-072030-97ab/case && mkdir -p constant 0 && blockMesh 2>&1 | ...` exit 0

**input**

```
{
  "cmd": "cd /work/20260409-072030-97ab/case && mkdir -p constant 0 && blockMesh 2>&1 | tail -60"
}
```

**output**

```
exit_code: 0

/*---------------------------------------------------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  2512                                  |
|   \\  /    A nd           | Website:  www.openfoam.com                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
Build  : _87ed40d2-20251219 OPENFOAM=2512 version=2512
Arch   : "LSB;label=32;scalar=64"
Exec   : blockMesh
Date   : Aug 28 2026
Time   : 23:24:56
Host   : modal
PID    : 41431
I/O    : uncollated
Case   : /work/20260409-072030-97ab/case
nProcs : 1
trapFpe: Floating point exception trapping enabled (FOAM_SIGFPE).
memory pool : not available
fileModificationChecking : Monitoring run-time modified files using timeStampMaster (fileModificationSkew 5, maxFileModificationPolls 20)
allowSystemOperations : Allowing user-supplied system call operations

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
Create time

--> FOAM FATAL ERROR: (openfoam-2512)
cannot find file "/work/20260409-072030-97ab/case/system/controlDict"

    From virtual Foam::autoPtr<Foam::ISstream> Foam::fileOperations::u
```

### agent

Good, blockMeshDict parsed fine (needs controlDict now). Let's set up full case files.

### tool: write_file

`/work/20260409-072030-97ab/case/system/controlDict`

**input**

```
{
  "path": "/work/20260409-072030-97ab/case/system/controlDict",
  "content": "FoamFile\n{\n    version 2.0;\n    format  ascii;\n    class   dictionary;\n    object  controlDict;\n}\n\napplication     rhoSimpleFoam;\n\nstartFrom       latestTime;\n\nstartTime       0;\n\nstopAt          endTime;\n\nendTime         2000;\n\ndeltaT          1;\n\nwriteControl    timeStep;\n\nwriteInterval   200;\n\npurgeWrite      2;\n\nwriteFormat     ascii;\n\nwritePrecision  6;\n\nwriteCompression off;\n\ntimeFormat      general;\n\ntimePrecision   6;\n\nrunTimeModifiable true;\n"
}
```

**output**

```
wrote 455 bytes to /work/20260409-072030-97ab/case/system/controlDict
```

### tool: write_file

`/work/20260409-072030-97ab/case/system/fvSchemes`

**input**

```
{
  "path": "/work/20260409-072030-97ab/case/system/fvSchemes",
  "content": "FoamFile\n{\n    version 2.0;\n    format  ascii;\n    class   dictionary;\n    object  fvSchemes;\n}\n\nddtSchemes\n{\n    default         steadyState;\n}\n\ngradSchemes\n{\n    default         Gauss linear;\n}\n\ndivSchemes\n{\n    default         none;\n    div(phi,U)      bounded Gauss linearUpwind grad(U);\n    div(phi,e)      bounded Gauss upwind;\n    div(phi,K)      bounded Gauss upwind;\n    div(phid,p)     bounded Gauss upwind;\n    div(phi,Ekp)    bounded Gauss upwind;\n    div((phi*interpolate(rho)),p) bounded Gauss upwind;\n    div(phi,epsilon) bounded Gauss upwind;\n    div(phi,k)      bounded Gauss upwind;\n    div((muEff*dev2(T(grad(U))))) Gauss linear;\n}\n\nlaplacianSchemes\n{\n    default         Gauss linear corrected;\n}\n\ninterpolationSchemes\n{\n    default         linear;\n}\n\nsnGradSc...
```

**output**

```
wrote 856 bytes to /work/20260409-072030-97ab/case/system/fvSchemes
```

### tool: write_file

`/work/20260409-072030-97ab/case/system/fvSolution`

**input**

```
{
  "path": "/work/20260409-072030-97ab/case/system/fvSolution",
  "content": "FoamFile\n{\n    version 2.0;\n    format  ascii;\n    class   dictionary;\n    object  fvSolution;\n}\n\nsolvers\n{\n    p\n    {\n        solver          GAMG;\n        tolerance       1e-08;\n        relTol          0.1;\n        smoother        GaussSeidel;\n        nCellsInCoarsestLevel 20;\n    }\n\n    \"(U|e|k|epsilon)\"\n    {\n        solver          GAMG;\n        tolerance       1e-08;\n        relTol          0.1;\n        smoother        GaussSeidel;\n        nCellsInCoarsestLevel 20;\n    }\n}\n\nSIMPLE\n{\n    nNonOrthogonalCorrectors 1;\n    pMinFactor      0.1;\n    pMaxFactor      2;\n    transonic       yes;\n    consistent      yes;\n\n    residualControl\n    {\n        p               1e-4;\n        U               1e-5;\n        e               1e-5;\n    }\n}\n\nrelaxationFactors\n{\n...
```

**output**

```
wrote 963 bytes to /work/20260409-072030-97ab/case/system/fvSolution
```

### tool: write_file

`/work/20260409-072030-97ab/case/constant/thermophysicalProperties`

**input**

```
{
  "path": "/work/20260409-072030-97ab/case/constant/thermophysicalProperties",
  "content": "FoamFile\n{\n    version 2.0;\n    format  ascii;\n    class   dictionary;\n    object  thermophysicalProperties;\n}\n\nthermoType\n{\n    type            hePsiThermo;\n    mixture         pureMixture;\n    transport       sutherland;\n    thermo          hConst;\n    equationOfState perfectGas;\n    specie          specie;\n    energy          sensibleInternalEnergy;\n}\n\nmixture\n{\n    specie\n    {\n        molWeight   28.9;\n    }\n    thermodynamics\n    {\n        Cp          1005;\n        Hf          0;\n    }\n    transport\n    {\n        As          1.4792e-06;\n        Ts          116;\n    }\n}\n"
}
```

**output**

```
wrote 582 bytes to /work/20260409-072030-97ab/case/constant/thermophysicalProperties
```

### tool: write_file

`/work/20260409-072030-97ab/case/constant/turbulenceProperties`

**input**

```
{
  "path": "/work/20260409-072030-97ab/case/constant/turbulenceProperties",
  "content": "FoamFile\n{\n    version 2.0;\n    format  ascii;\n    class   dictionary;\n    object  turbulenceProperties;\n}\n\nsimulationType  laminar;\n"
}
```

**output**

```
wrote 133 bytes to /work/20260409-072030-97ab/case/constant/turbulenceProperties
```

### agent

Now the 0/ fields: p, T, U.

### tool: write_file

`/work/20260409-072030-97ab/case/0/p`

**input**

```
{
  "path": "/work/20260409-072030-97ab/case/0/p",
  "content": "FoamFile\n{\n    version 2.0;\n    format  ascii;\n    class   volScalarField;\n    object  p;\n}\n\ndimensions      [1 -1 -2 0 0 0 0];\n\ninternalField   uniform 75000;\n\nboundaryField\n{\n    inlet\n    {\n        type            totalPressure;\n        p0              uniform 101325;\n        gamma           1.4;\n        value           uniform 101325;\n    }\n\n    outlet\n    {\n        type            fixedValue;\n        value           uniform 75000;\n    }\n\n    wall\n    {\n        type            zeroGradient;\n    }\n\n    symmetry\n    {\n        type            symmetryPlane;\n    }\n\n    front\n    {\n        type            empty;\n    }\n\n    back\n    {\n        type            empty;\n    }\n}\n"
}
```

**output**

```
wrote 680 bytes to /work/20260409-072030-97ab/case/0/p
```

### tool: write_file

`/work/20260409-072030-97ab/case/0/T`

**input**

```
{
  "path": "/work/20260409-072030-97ab/case/0/T",
  "content": "FoamFile\n{\n    version 2.0;\n    format  ascii;\n    class   volScalarField;\n    object  T;\n}\n\ndimensions      [0 0 0 1 0 0 0];\n\ninternalField   uniform 290;\n\nboundaryField\n{\n    inlet\n    {\n        type            totalTemperature;\n        T0              uniform 300;\n        gamma           1.4;\n        value           uniform 300;\n    }\n\n    outlet\n    {\n        type            inletOutlet;\n        inletValue      uniform 290;\n        value           uniform 290;\n    }\n\n    wall\n    {\n        type            zeroGradient;\n    }\n\n    symmetry\n    {\n        type            symmetryPlane;\n    }\n\n    front\n    {\n        type            empty;\n    }\n\n    back\n    {\n        type            empty;\n    }\n}\n"
}
```

**output**

```
wrote 709 bytes to /work/20260409-072030-97ab/case/0/T
```

### tool: bash

`find /usr/lib/openfoam/openfoam2512/src -iname "*pressureInletOutletVelocity*"...` exit 0

**input**

```
{
  "cmd": "find /usr/lib/openfoam/openfoam2512/src -iname \"*pressureInletOutletVelocity*\" | grep '\\.H$'; sed -n '1,50p' /usr/lib/openfoam/openfoam2512/src/finiteVolume/fields/fvPatchFields/derived/pressureInletOutletVelocity/pressureInletOutletVelocityFvPatchVectorField.H | sed -n '25,55p'"
}
```

**output**

```
exit_code: 0

/usr/lib/openfoam/openfoam2512/src/finiteVolume/fields/fvPatchFields/derived/pressureInletOutletVelocity/pressureInletOutletVelocityFvPatchVectorField.H
/usr/lib/openfoam/openfoam2512/src/finiteVolume/fields/fvPatchFields/derived/rotatingPressureInletOutletVelocity/rotatingPressureInletOutletVelocityFvPatchVectorField.H
/usr/lib/openfoam/openfoam2512/src/finiteVolume/lnInclude/pressureInletOutletVelocityFvPatchVectorField.H
/usr/lib/openfoam/openfoam2512/src/finiteVolume/lnInclude/rotatingPressureInletOutletVelocityFvPatchVectorField.H

Class
    Foam::pressureInletOutletVelocityFvPatchVectorField

Group
    grpInletBoundaryConditions grpOutletBoundaryConditions

Description
    This velocity inlet/outlet boundary condition is applied to velocity
    boundaries where the pressure is specified.  A zero-gradient condition is
    applied for outflow (as defined by the flux); for inflow, the velocity is
    obtained from the patch-face normal component of the internal-cell value.

    The tangential patch velocity can be optionally specified.

Usage
    \table
        Property     | Description             | Required    | Default value
        phi          | flux field name         | no          | phi
        tangentialVelocity | tangential velocity field | no  |
    \endtable

    Example of the boundary condition specification:
    \verbatim
    <patchName>
    {
```

### agent

Good — that works for both inlet and outlet velocity boundaries.

### tool: write_file

`/work/20260409-072030-97ab/case/0/U`

**input**

```
{
  "path": "/work/20260409-072030-97ab/case/0/U",
  "content": "FoamFile\n{\n    version 2.0;\n    format  ascii;\n    class   volVectorField;\n    object  U;\n}\n\ndimensions      [0 1 -1 0 0 0 0];\n\ninternalField   uniform (100 0 0);\n\nboundaryField\n{\n    inlet\n    {\n        type            pressureInletOutletVelocity;\n        value           uniform (100 0 0);\n    }\n\n    outlet\n    {\n        type            pressureInletOutletVelocity;\n        value           uniform (0 0 0);\n    }\n\n    wall\n    {\n        type            noSlip;\n    }\n\n    symmetry\n    {\n        type            symmetryPlane;\n    }\n\n    front\n    {\n        type            empty;\n    }\n\n    back\n    {\n        type            empty;\n    }\n}\n"
}
```

**output**

```
wrote 644 bytes to /work/20260409-072030-97ab/case/0/U
```

### agent

Now let's build the mesh, check it, and render before solving.

### tool: bash

`cd /work/20260409-072030-97ab/case && blockMesh 2>&1 | tail -40` exit 0

**input**

```
{
  "cmd": "cd /work/20260409-072030-97ab/case && blockMesh 2>&1 | tail -40"
}
```

**output**

```
exit_code: 0

        k : 0.01 .. 0.01

    Block 13 cell size :
        i : 0.0025 .. 0.0025
        j : 0.00184413 .. 0.00184413
        k : 0.01 .. 0.01

    Block 14 cell size :
        i : 0.0025 .. 0.0025
        j : 0.00198352 .. 0.00198352
        k : 0.01 .. 0.01

    Block 15 cell size :
        i : 0.0025 .. 0.0025
        j : 0.00207668 .. 0.00207668
        k : 0.01 .. 0.01

No patch pairs to merge

Writing polyMesh with 0 cellZones
----------------
Mesh Information
----------------
  boundingBox: (0 0 0) (0.3 0.15 0.01)
  nPoints: 9922
  nCells: 4800
  nFaces: 19360
  nInternalFaces: 9440
----------------
Patches
----------------
  patch 0 (start: 9440 size: 40) name: inlet
  patch 1 (start: 9480 size: 40) name: outlet
  patch 2 (start: 9520 size: 120) name: symmetry
  patch 3 (start: 9640 size: 120) name: wall
  patch 4 (start: 9760 size: 4800) name: front
  patch 5 (start: 14560 size: 4800) name: back

End
```

### agent

Mesh built cleanly: 4800 cells, 120×40 in x/y, matches the design. Now checkMesh and geometry/mesh renders.

### tool: bash

`cd /work/20260409-072030-97ab/case && checkMesh 2>&1 | tail -60` exit 0

**input**

```
{
  "cmd": "cd /work/20260409-072030-97ab/case && checkMesh 2>&1 | tail -60"
}
```

**output**

```
exit_code: 0

    face zones:       0
    cell zones:       0

Overall number of cells of each type:
    hexahedra:     4800
    prisms:        0
    wedges:        0
    pyramids:      0
    tet wedges:    0
    tetrahedra:    0
    polyhedra:     0

Checking topology...
    Boundary definition OK.
    Cell to face addressing OK.
    Point usage OK.
    Upper triangular ordering OK.
    Face vertices OK.
    Number of regions: 1 (OK).

Checking patch topology for multiply connected surfaces...
    Patch               Faces    Points     Surface topology
    inlet               40       82       ok (non-closed singly connected)  
    outlet              40       82       ok (non-closed singly connected)  
    symmetry            120      242      ok (non-closed singly connected)  
    wall                120      242      ok (non-closed singly connected)  
    front               4800     4961     ok (non-closed singly connected)  
    back                4800     4961     ok (non-closed singly connected)  
    ".*"                9920     9922     ok (closed singly connected)      

Checking faceZone topology for multiply connected surfaces...
    No faceZones found.

Checking basic cellZone addressing...
    No cellZones found.

Checking basic pointZone addressing...
    No pointZones found.

Checking geometry...
    Overall domain bounding box (0 0 0) (0.3 0.15 0.01)
    Me
```

### tool: bash

`cat /work/.toolbox/geometry_view.py | head -30; echo ---; cat /work/.toolbox/r...` exit 0

**input**

```
{
  "cmd": "cat /work/.toolbox/geometry_view.py | head -30; echo ---; cat /work/.toolbox/render.py | head -40"
}
```

**output**

```
exit_code: 0

#!/usr/bin/env python3
"""Surface geometry -> pictures of it, plus the numbers that describe it.

Meshing decisions are made against geometry nobody has looked at, and a surface that
is 1000x too large, inside-out, or full of holes looks exactly like a good one from
the shell. This draws it -- four fixed views, every facet edge visible -- and prints
what is measurable about it. It attaches no verdicts: whether 40 open edges matter
depends on where they are and what you are about to run.

    python3 geometry_view.py wing.stl
    python3 geometry_view.py constant/triSurface/            # every surface in a dir
    python3 geometry_view.py a.stl b.stl --per-part --out /work/case/renders
    python3 geometry_view.py wing.stl --check               # numbers only, no render

Reads anything VTK reads: .stl, .obj, .ply, .vtk, .vtp, .vtu.
"""

from __future__ import annotations

import argparse
import sys
from pathlib import Path

import numpy as np
import pyvista as pv

pv.OFF_SCREEN = True

SUFFIXES = (".stl", ".obj", ".ply", ".vtk", ".vtp", ".vtu")

---
#!/usr/bin/env python3
"""A few fixed pyvista scenes: mesh cuts and field slices, saved as PNGs.

Headless via OSMesa. Fixed cameras so two runs of the same case are a visual diff
rather than two unrelated pictures.

    python3 render.py /work/case                      # latest time, all default scenes
    python3 rend
```

### agent

No STL geometry here (blockMesh-generated), so geometry_view isn't directly applicable; I'll use render.py --scene mesh for the mesh view.

### tool: bash

`cd /work/20260409-072030-97ab/case && python3 /work/.toolbox/render.py . --sce...` exit 0

**input**

```
{
  "cmd": "cd /work/20260409-072030-97ab/case && python3 /work/.toolbox/render.py . --scene mesh --out /work/20260409-072030-97ab/renders 2>&1 | tail -40"
}
```

**output**

```
exit_code: 0

2026-08-28 23:26:43.825 (   0.633s) [    2AC917E2A540]        vtkRenderer.cxx:1161  WARN| vtkOpenGLRenderer (0x24f9400): Resetting view-up since view plane normal is parallel
time 0  (available: 0)
cells 4,800  points 9,922
/work/20260409-072030-97ab/renders/mesh_z.png
```

### tool: read_file

`/work/20260409-072030-97ab/renders/mesh_z.png`

**input**

```
{
  "path": "/work/20260409-072030-97ab/renders/mesh_z.png"
}
```

**output**

```
[image/png, 269175 bytes]
/work/20260409-072030-97ab/renders/mesh_z.png — 1100x800 image/png, 269173 bytes
```

### agent

The mesh looks clean and well-formed — it correctly captures the converging-diverging contour with cells conforming smoothly to the curved wall (the image is just rotated 90°: flow direction is the long axis here, inlet at the wide end, throat at the neck, diverging section flaring out toward the exit). checkMesh reports no errors, good aspect ratio, acceptable non-orthogonality/skewness for a coarse block-structured mesh.

Now running the steady solve.

### tool: job_start

`cd /work/20260409-072030-97ab/case && rhoSimpleFoam 2>&1 | tee log.rhoSimpleFo...`

**input**

```
{
  "name": "nozzle-simple",
  "cmd": "cd /work/20260409-072030-97ab/case && rhoSimpleFoam 2>&1 | tee log.rhoSimpleFoam"
}
```

**output**

```
started job 249acf73-dd87-4b86-839a-c718c670b1fe (nozzle-simple)
```

### tool: job_check

`job_id=249acf73-dd87-4b86-839a-c718c670b1fe wait_s=60`

**input**

```
{
  "job_id": "249acf73-dd87-4b86-839a-c718c670b1fe",
  "wait_s": 60
}
```

**output**

```
job 249acf73-dd87-4b86-839a-c718c670b1fe name=nozzle-simple status=exited exit_code=0 end_reason=completed log_size=2324 ran_for=7s
log: bytes 0–2324, eof=True

/*---------------------------------------------------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  2512                                  |
|   \\  /    A nd           | Website:  www.openfoam.com                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
Build  : _87ed40d2-20251219 OPENFOAM=2512 version=2512
Arch   : "LSB;label=32;scalar=64"
Exec   : rhoSimpleFoam
Date   : Aug 28 2026
Time   : 23:27:18
Host   : modal
PID    : 48499
I/O    : uncollated
Case   : /work/20260409-072030-97ab/case
nProcs : 1
trapFpe: Floating point exception trapping enabled (FOAM_SIGFPE).
memory pool : not available
fileModificationChecking : Monitoring run-time modified files using timeStampMaster (fileModificationSkew 5, maxFileModificationPolls 20)
allowSystemOperations : Allowing user-supplied system call operations

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
Create time

Create mesh for time = 0

SIM
```

### agent

Need the correct div scheme name for rhoSimpleFoam.

### tool: bash

`sed -i 's#div((muEff\*dev2(T(grad(U))))) Gauss linear;#div(((rho*nuEff)*dev2(T...` exit 0

**input**

```
{
  "cmd": "sed -i 's#div((muEff\\*dev2(T(grad(U))))) Gauss linear;#div(((rho*nuEff)*dev2(T(grad(U))))) Gauss linear;#' /work/20260409-072030-97ab/case/system/fvSchemes\ncat /work/20260409-072030-97ab/case/system/fvSchemes"
}
```

**output**

```
exit_code: 0

FoamFile
{
    version 2.0;
    format  ascii;
    class   dictionary;
    object  fvSchemes;
}

ddtSchemes
{
    default         steadyState;
}

gradSchemes
{
    default         Gauss linear;
}

divSchemes
{
    default         none;
    div(phi,U)      bounded Gauss linearUpwind grad(U);
    div(phi,e)      bounded Gauss upwind;
    div(phi,K)      bounded Gauss upwind;
    div(phid,p)     bounded Gauss upwind;
    div(phi,Ekp)    bounded Gauss upwind;
    div((phi*interpolate(rho)),p) bounded Gauss upwind;
    div(phi,epsilon) bounded Gauss upwind;
    div(phi,k)      bounded Gauss upwind;
    div(((rho*nuEff)*dev2(T(grad(U))))) Gauss linear;
}

laplacianSchemes
{
    default         Gauss linear corrected;
}

interpolationSchemes
{
    default         linear;
}

snGradSchemes
{
    default         corrected;
}

wallDist
{
    method meshWave;
}
```

### tool: bash

`cd /work/20260409-072030-97ab/case && rm -rf 1 2 3 log.rhoSimpleFoam; ls` exit 0

**input**

```
{
  "cmd": "cd /work/20260409-072030-97ab/case && rm -rf 1 2 3 log.rhoSimpleFoam; ls"
}
```

**output**

```
exit_code: 0

0
constant
system
```

### tool: job_start

`cd /work/20260409-072030-97ab/case && rhoSimpleFoam 2>&1 | tee log.rhoSimpleFo...`

**input**

```
{
  "name": "nozzle-simple2",
  "cmd": "cd /work/20260409-072030-97ab/case && rhoSimpleFoam 2>&1 | tee log.rhoSimpleFoam"
}
```

**output**

```
started job c2fd4ced-ddeb-4fcf-8c1b-8dcf841536d4 (nozzle-simple2)
```

### tool: job_check

`job_id=c2fd4ced-ddeb-4fcf-8c1b-8dcf841536d4 wait_s=60`

**input**

```
{
  "job_id": "c2fd4ced-ddeb-4fcf-8c1b-8dcf841536d4",
  "wait_s": 60
}
```

**output**

```
job c2fd4ced-ddeb-4fcf-8c1b-8dcf841536d4 name=nozzle-simple2 status=exited exit_code=0 end_reason=completed log_size=5448 ran_for=7s
log: bytes 0–5448, eof=True

/*---------------------------------------------------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  2512                                  |
|   \\  /    A nd           | Website:  www.openfoam.com                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
Build  : _87ed40d2-20251219 OPENFOAM=2512 version=2512
Arch   : "LSB;label=32;scalar=64"
Exec   : rhoSimpleFoam
Date   : Aug 28 2026
Time   : 23:27:49
Host   : modal
PID    : 50613
I/O    : uncollated
Case   : /work/20260409-072030-97ab/case
nProcs : 1
trapFpe: Floating point exception trapping enabled (FOAM_SIGFPE).
memory pool : not available
fileModificationChecking : Monitoring run-time modified files using timeStampMaster (fileModificationSkew 5, maxFileModificationPolls 20)
allowSystemOperations : Allowing user-supplied system call operations

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
Create time

Create mesh for time = 0

SI
```

### tool: bash

`sed -n '1,100p' $FOAM_TUTORIALS/compressible/rhoSimpleFoam/squareBend/system/f...` exit 0

**input**

```
{
  "cmd": "sed -n '1,100p' $FOAM_TUTORIALS/compressible/rhoSimpleFoam/squareBend/system/fvSolution"
}
```

**output**

```
exit_code: 0

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  v2512                                 |
|   \\  /    A nd           | Website:  www.openfoam.com                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    object      fvSolution;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

solvers
{
    p
    {
        solver          GAMG;
        tolerance       1e-08;
        relTol          0.1;
        smoother        GaussSeidel;
        nCellsInCoarsestLevel 20;
    }

    "(U|e|k|epsilon)"
    {
        solver          GAMG;
        tolerance       1e-08;
        relTol          0.1;
        smoother        GaussSeidel;
        nCellsInCoarsestLevel 20;
    }
}

SIMPLE
{
    nNonOrthogonalCorrectors 0;
    pMinFactor      0.1;
    pMaxFactor      2;
    transonic       yes;
    consistent      yes;

    residualControl
    {
        p               1e-3;
        U               1e-4;
        e
```

### tool: bash

`grep -A5 "transonic" $FOAM_TUTORIALS/compressible/rhoSimpleFoam/*/system/fvSol...` exit 0

**input**

```
{
  "cmd": "grep -A5 \"transonic\" $FOAM_TUTORIALS/compressible/rhoSimpleFoam/*/system/fvSolution 2>/dev/null\necho ---\ncat $FOAM_TUTORIALS/compressible/rhoSimpleFoam/angledDuctExplicitFixedCoeff/system/fvSolution 2>/dev/null | sed -n '1,80p'"
}
```

**output**

```
exit_code: 0

/usr/lib/openfoam/openfoam2512/tutorials/compressible/rhoSimpleFoam/squareBend/system/fvSolution:    transonic       yes;
/usr/lib/openfoam/openfoam2512/tutorials/compressible/rhoSimpleFoam/squareBend/system/fvSolution-    consistent      yes;
/usr/lib/openfoam/openfoam2512/tutorials/compressible/rhoSimpleFoam/squareBend/system/fvSolution-
/usr/lib/openfoam/openfoam2512/tutorials/compressible/rhoSimpleFoam/squareBend/system/fvSolution-    residualControl
/usr/lib/openfoam/openfoam2512/tutorials/compressible/rhoSimpleFoam/squareBend/system/fvSolution-    {
/usr/lib/openfoam/openfoam2512/tutorials/compressible/rhoSimpleFoam/squareBend/system/fvSolution-        p               1e-3;
--
/usr/lib/openfoam/openfoam2512/tutorials/compressible/rhoSimpleFoam/squareBendLiq/system/fvSolution:    transonic       no;
/usr/lib/openfoam/openfoam2512/tutorials/compressible/rhoSimpleFoam/squareBendLiq/system/fvSolution-    consistent      no;
/usr/lib/openfoam/openfoam2512/tutorials/compressible/rhoSimpleFoam/squareBendLiq/system/fvSolution-
/usr/lib/openfoam/openfoam2512/tutorials/compressible/rhoSimpleFoam/squareBendLiq/system/fvSolution-    residualControl
/usr/lib/openfoam/openfoam2512/tutorials/compressible/rhoSimpleFoam/squareBendLiq/system/fvSolution-    {
/usr/lib/openfoam/openfoam2512/tutorials/compressible/rhoSimpleFoam/squareBendLiq/system/fvSolution-        p
```

### tool: write_file

`/work/20260409-072030-97ab/case/system/fvSolution`

**input**

```
{
  "path": "/work/20260409-072030-97ab/case/system/fvSolution",
  "content": "FoamFile\n{\n    version 2.0;\n    format  ascii;\n    class   dictionary;\n    object  fvSolution;\n}\n\nsolvers\n{\n    p\n    {\n        solver          GAMG;\n        tolerance       1e-08;\n        relTol          0.05;\n        smoother        GaussSeidel;\n        nCellsInCoarsestLevel 20;\n    }\n\n    U\n    {\n        solver          smoothSolver;\n        smoother        GaussSeidel;\n        nSweeps         2;\n        tolerance       1e-08;\n        relTol          0.1;\n    }\n\n    e\n    {\n        solver          smoothSolver;\n        smoother        symGaussSeidel;\n        tolerance       1e-08;\n        relTol          0.1;\n    }\n}\n\nSIMPLE\n{\n    nNonOrthogonalCorrectors 1;\n    pMinFactor      0.4;\n    pMaxFactor      1.5;\n    transonic       yes;\n    consistent      no;\n\n    re...
```

**output**

```
wrote 1083 bytes to /work/20260409-072030-97ab/case/system/fvSolution
```

### agent

Also give a gentler initial guess closer to inlet conditions.

### tool: bash

`cd /work/20260409-072030-97ab/case` exit 0

**input**

```
{
  "cmd": "cd /work/20260409-072030-97ab/case\nsed -i 's/uniform (100 0 0)/uniform (50 0 0)/' 0/U\nsed -i '0,/uniform 75000/{s/uniform 75000/uniform 95000/}' 0/p\nsed -i 's/internalField   uniform 290;/internalField   uniform 295;/' 0/T\ncat 0/p | head -12\ncat 0/T | head -12\ncat 0/U | head -12\nrm -rf 1 2 3 4 5 log.rhoSimpleFoam\n"
}
```

**output**

```
exit_code: 0

FoamFile
{
    version 2.0;
    format  ascii;
    class   volScalarField;
    object  p;
}

dimensions      [1 -1 -2 0 0 0 0];

internalField   uniform 95000;

FoamFile
{
    version 2.0;
    format  ascii;
    class   volScalarField;
    object  T;
}

dimensions      [0 0 0 1 0 0 0];

internalField   uniform 295;

FoamFile
{
    version 2.0;
    format  ascii;
    class   volVectorField;
    object  U;
}

dimensions      [0 1 -1 0 0 0 0];

internalField   uniform (50 0 0);
```

### tool: job_start

`cd /work/20260409-072030-97ab/case && rhoSimpleFoam 2>&1 | tee log.rhoSimpleFo...`

**input**

```
{
  "name": "nozzle-simple3",
  "cmd": "cd /work/20260409-072030-97ab/case && rhoSimpleFoam 2>&1 | tee log.rhoSimpleFoam"
}
```

**output**

```
started job 8f3af72f-5b39-4b6f-a389-6010b9ede20d (nozzle-simple3)
```

### tool: job_check

`job_id=8f3af72f-5b39-4b6f-a389-6010b9ede20d wait_s=90`

**input**

```
{
  "job_id": "8f3af72f-5b39-4b6f-a389-6010b9ede20d",
  "wait_s": 90
}
```

**output**

```
job 8f3af72f-5b39-4b6f-a389-6010b9ede20d name=nozzle-simple3 status=exited exit_code=0 end_reason=completed log_size=10800 ran_for=7s
log: bytes 0–10800, eof=True

/*---------------------------------------------------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  2512                                  |
|   \\  /    A nd           | Website:  www.openfoam.com                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
Build  : _87ed40d2-20251219 OPENFOAM=2512 version=2512
Arch   : "LSB;label=32;scalar=64"
Exec   : rhoSimpleFoam
Date   : Aug 28 2026
Time   : 23:29:04
Host   : modal
PID    : 54429
I/O    : uncollated
Case   : /work/20260409-072030-97ab/case
nProcs : 1
trapFpe: Floating point exception trapping enabled (FOAM_SIGFPE).
memory pool : not available
fileModificationChecking : Monitoring run-time modified files using timeStampMaster (fileModificationSkew 5, maxFileModificationPolls 20)
allowSystemOperations : Allowing user-supplied system call operations

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
Create time

Create mesh for time = 0
```

### tool: bash

`cd /work/20260409-072030-97ab/case` exit 0

**input**

```
{
  "cmd": "cd /work/20260409-072030-97ab/case\nsed -i 's/div(phi,U)      bounded Gauss linearUpwind grad(U);/div(phi,U)      bounded Gauss upwind;/' system/fvSchemes\nsed -i 's/p               0.2;/p               0.1;/' system/fvSolution\nsed -i 's/U               0.5;/U               0.3;/' system/fvSolution\nsed -i 's/e               0.3;/e               0.2;/' system/fvSolution\ncat system/fvSchemes | sed -n '10,25p'\ncat system/fvSolution | sed -n '35,55p'\nrm -rf 1 2 3 4 5 6 7 8 9 10 11 12 13 log.rhoSimpleFoam"
}
```

**output**

```
exit_code: 0

{
    default         steadyState;
}

gradSchemes
{
    default         Gauss linear;
}

divSchemes
{
    default         none;
    div(phi,U)      bounded Gauss upwind;
    div(phi,e)      bounded Gauss upwind;
    div(phi,K)      bounded Gauss upwind;
    div(phid,p)     bounded Gauss upwind;
    }
}

SIMPLE
{
    nNonOrthogonalCorrectors 1;
    pMinFactor      0.4;
    pMaxFactor      1.5;
    transonic       yes;
    consistent      no;

    residualControl
    {
        p               1e-3;
        U               1e-4;
        e               1e-4;
    }
}

relaxationFactors
{
```

### tool: job_start

`cd /work/20260409-072030-97ab/case && rhoSimpleFoam 2>&1 | tee log.rhoSimpleFo...`

**input**

```
{
  "name": "nozzle-simple4",
  "cmd": "cd /work/20260409-072030-97ab/case && rhoSimpleFoam 2>&1 | tee log.rhoSimpleFoam"
}
```

**output**

```
started job 8fc49c3b-7fbb-43b2-81a2-97618d12a628 (nozzle-simple4)
```

### tool: job_check

`job_id=8fc49c3b-7fbb-43b2-81a2-97618d12a628 wait_s=90`

**input**

```
{
  "job_id": "8fc49c3b-7fbb-43b2-81a2-97618d12a628",
  "wait_s": 90
}
```

**output**

```
job 8fc49c3b-7fbb-43b2-81a2-97618d12a628 name=nozzle-simple4 status=exited exit_code=0 end_reason=completed log_size=1335803 ran_for=27s [waited 20s]
log: bytes 0–1000000, eof=False (this window clipped at 48000 bytes; call again from 48000)

/*---------------------------------------------------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  2512                                  |
|   \\  /    A nd           | Website:  www.openfoam.com                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
Build  : _87ed40d2-20251219 OPENFOAM=2512 version=2512
Arch   : "LSB;label=32;scalar=64"
Exec   : rhoSimpleFoam
Date   : Aug 28 2026
Time   : 23:29:37
Host   : modal
PID    : 56096
I/O    : uncollated
Case   : /work/20260409-072030-97ab/case
nProcs : 1
trapFpe: Floating point exception trapping enabled (FOAM_SIGFPE).
memory pool : not available
fileModificationChecking : Monitoring run-time modified files using timeStampMaster (fileModificationSkew 5, maxFileModificationPolls 20)
allowSystemOperations : Allowing user-supplied system call operations

// * * * * * * * * * * * * * * * * * * *
```

### agent

Good — this run is stable now and progressing. Let's check whether it finished or is still running / converged.

### tool: bash

`cd /work/20260409-072030-97ab/case; tail -40 log.rhoSimpleFoam; ls -d [0-9]* |...` exit 0

**input**

```
{
  "cmd": "cd /work/20260409-072030-97ab/case; tail -40 log.rhoSimpleFoam; ls -d [0-9]* | sort -n | tail -5"
}
```

**output**

```
exit_code: 0

smoothSolver:  Solving for Ux, Initial residual = 8.65254e-07, Final residual = 1.3778e-09, No Iterations 2
smoothSolver:  Solving for Uy, Initial residual = 0.000109919, Final residual = 2.52277e-07, No Iterations 2
smoothSolver:  Solving for e, Initial residual = 6.72771e-07, Final residual = 1.81827e-09, No Iterations 1
GAMG:  Solving for p, Initial residual = 3.87141e-06, Final residual = 1.36597e-07, No Iterations 5
GAMG:  Solving for p, Initial residual = 2.5424e-07, Final residual = 8.87393e-09, No Iterations 9
time step continuity errors : sum local = 1045.9, global = 165.79, cumulative = 309960
ExecutionTime = 15.98 s  ClockTime = 16 s

Time = 1998

smoothSolver:  Solving for Ux, Initial residual = 8.64839e-07, Final residual = 1.37725e-09, No Iterations 2
smoothSolver:  Solving for Uy, Initial residual = 0.000109817, Final residual = 2.52042e-07, No Iterations 2
smoothSolver:  Solving for e, Initial residual = 6.72428e-07, Final residual = 1.81746e-09, No Iterations 1
GAMG:  Solving for p, Initial residual = 3.86844e-06, Final residual = 1.36488e-07, No Iterations 5
GAMG:  Solving for p, Initial residual = 2.54037e-07, Final residual = 8.86699e-09, No Iterations 9
time step continuity errors : sum local = 1045.9, global = 165.79, cumulative = 310125
ExecutionTime = 15.99 s  ClockTime = 17 s

Time = 1999

smoothSolver:  Solving for Ux, Initial residual =
```

### agent

The run reached endTime=2000 with residuals essentially flat (Ux~1e-7, e~1e-7, p~1e-7, Uy~1.1e-4) — effectively converged to a steady limit, just short of the strict Uy residual threshold. Let's look at the flow field.

### tool: bash

`cd /work/20260409-072030-97ab/case && python3 - << 'EOF'` exit 0

**input**

```
{
  "cmd": "cd /work/20260409-072030-97ab/case && python3 - << 'EOF'\nimport pyvista as pv\npv.OFF_SCREEN=True\nimport numpy as np\nf = \"nozzle.foam\"\nopen(f,\"w\").close()\nr = pv.OpenFOAMReader(f)\nr.set_active_time_value(r.time_values[-1])\nr.cell_to_point_creation=True\nd = r.read()\nblock = d[\"internalMesh\"]\nprint(block.array_names)\nprint(\"bounds\", block.bounds)\nimport numpy as np\np = block.cell_data[\"p\"]\nT = block.cell_data[\"T\"]\nU = block.cell_data[\"U\"]\nprint(\"p range\", p.min(), p.max())\nprint(\"T range\", T.min(), T.max())\nspeed=np.linalg.norm(U,axis=1)\nprint(\"speed range\", speed.min(), speed.max())\ngamma=1.4; R=287.0\na=np.sqrt(gamma*R*T)\nM=speed/a\nprint(\"Mach range\", M.min(), M.max())\nEOF"
}
```

**output**

```
exit_code: 0

['p', 'T', 'U', 'rho', 'T', 'U', 'p', 'rho']
bounds BoundsTuple(x_min = 0.0,
            x_max = 0.30000001192092896,
            y_min = 0.0,
            y_max = 0.15000000596046448,
            z_min = 0.0,
            z_max = 0.009999999776482582)
p range 90272.4 96651.7
T range 275.937 296.105
speed range 88.57012 219.95506
Mach range 0.25677893 0.6605779
```

### tool: bash

`cd /work/20260409-072030-97ab/case && python3 - << 'EOF'` exit 0

**input**

```
{
  "cmd": "cd /work/20260409-072030-97ab/case && python3 - << 'EOF'\nimport pyvista as pv\npv.OFF_SCREEN=True\nimport numpy as np\nf=\"nozzle.foam\"\nr=pv.OpenFOAMReader(f)\nr.set_active_time_value(r.time_values[-1])\nr.cell_to_point_creation=True\nd=r.read()\nblock=d[\"internalMesh\"]\ncenters=block.cell_centers().points\nx=centers[:,0]; y=centers[:,1]\np=block.cell_data[\"p\"]; T=block.cell_data[\"T\"]; U=block.cell_data[\"U\"]\nmask = y<0.002  # near symmetry axis\nxs=x[mask]; ps=p[mask]; Ts=T[mask]; us=U[mask]\norder=np.argsort(xs)\nfor i in order[::5]:\n    print(f\"{xs[i]:.3f} p={ps[i]:.0f} T={Ts[i]:.1f} U={us[i]}\")\nEOF"
}
```

**output**

```
exit_code: 0

0.001 p=96643 T=295.9 U=[ 9.08254e+01 -3.59925e-05  0.00000e+00]
0.014 p=96643 T=295.9 U=[ 9.08248e+01 -2.09002e-04  0.00000e+00]
0.026 p=96643 T=295.9 U=[ 9.08243e+01 -3.64826e-04  0.00000e+00]
0.039 p=96643 T=295.9 U=[ 9.08239e+01 -4.97293e-04  0.00000e+00]
0.051 p=96643 T=295.9 U=[ 9.08235e+01 -6.03722e-04 -1.48809e-16]
0.064 p=96643 T=295.9 U=[ 9.08232e+01 -6.85428e-04 -9.19988e-17]
0.076 p=96643 T=295.9 U=[ 9.08228e+01 -7.47695e-04  1.07870e-16]
0.089 p=96643 T=295.9 U=[ 9.08225e+01 -1.59129e-03 -6.75301e-17]
0.094 p=96643 T=295.9 U=[ 9.08223e+01 -8.20437e-04  4.51419e-18]
0.101 p=96643 T=295.9 U=[ 9.08221e+01 -8.52358e-04 -1.45163e-19]
0.106 p=96643 T=295.9 U=[ 9.08219e+01 -1.77067e-03 -2.89458e-19]
0.114 p=96643 T=295.9 U=[ 9.08217e+01 -9.10093e-04 -9.20665e-18]
0.119 p=96643 T=295.9 U=[ 9.08216e+01 -1.93896e-03  1.79319e-17]
0.126 p=96643 T=295.9 U=[ 9.08215e+01 -9.75727e-04  1.80178e-17]
0.131 p=96643 T=295.9 U=[ 9.08214e+01 -2.11696e-03  1.82579e-17]
0.139 p=96643 T=295.9 U=[ 9.08213e+01 -1.04955e-03  1.09018e-18]
0.149 p=96643 T=295.9 U=[ 9.08212e+01 -1.11499e-03 -1.68907e-17]
0.161 p=96643 T=295.9 U=[ 9.08211e+01 -1.20540e-03 -3.12444e-17]
0.174 p=96643 T=295.9 U=[ 9.08211e+01 -1.30370e-03  0.00000e+00]
0.186 p=96643 T=295.9 U=[ 9.08212e+01 -1.40918e-03  0.00000e+00]
0.199 p=96643 T=295.9 U=[ 9.08215e+01 -1.52003e-03 -1.08115e-19]
0.211 p=96643 T=295.9
```

### agent

The residuals plateaued but the actual field looks physically wrong (pressure and velocity nearly uniform through most of the duct, area change not reflected) — the extremely low relaxation factors likely made this converge to a barely-perturbed initial condition rather than the true steady state. Let's raise relaxation and continue from the current state.

### tool: bash

`cd /work/20260409-072030-97ab/case` exit 0

**input**

```
{
  "cmd": "cd /work/20260409-072030-97ab/case\nsed -i 's/p               0.1;/p               0.3;/' system/fvSolution\nsed -i 's/rho             0.01;/rho             0.05;/' system/fvSolution\nsed -i 's/U               0.3;/U               0.6;/' system/fvSolution\nsed -i 's/e               0.2;/e               0.4;/' system/fvSolution\nsed -i 's/endTime         2000;/endTime         6000;/' system/controlDict\ncat system/fvSolution"
}
```

**output**

```
exit_code: 0
[took 19s]

FoamFile
{
    version 2.0;
    format  ascii;
    class   dictionary;
    object  fvSolution;
}

solvers
{
    p
    {
        solver          GAMG;
        tolerance       1e-08;
        relTol          0.05;
        smoother        GaussSeidel;
        nCellsInCoarsestLevel 20;
    }

    U
    {
        solver          smoothSolver;
        smoother        GaussSeidel;
        nSweeps         2;
        tolerance       1e-08;
        relTol          0.1;
    }

    e
    {
        solver          smoothSolver;
        smoother        symGaussSeidel;
        tolerance       1e-08;
        relTol          0.1;
    }
}

SIMPLE
{
    nNonOrthogonalCorrectors 1;
    pMinFactor      0.4;
    pMaxFactor      1.5;
    transonic       yes;
    consistent      no;

    residualControl
    {
        p               1e-3;
        U               1e-4;
        e               1e-4;
    }
}

relaxationFactors
{
    fields
    {
        p               0.3;
        rho             0.05;
    }
    equations
    {
        U               0.6;
        e               0.4;
    }
}
```

### tool: job_start

`cd /work/20260409-072030-97ab/case && rhoSimpleFoam 2>&1 | tee -a log.rhoSimpl...`

**input**

```
{
  "name": "nozzle-simple5",
  "cmd": "cd /work/20260409-072030-97ab/case && rhoSimpleFoam 2>&1 | tee -a log.rhoSimpleFoam"
}
```

**output**

```
started job 6c99895f-87e4-468d-865a-7312fcb33389 (nozzle-simple5)
```

### tool: job_check

`job_id=6c99895f-87e4-468d-865a-7312fcb33389 wait_s=120`

**input**

```
{
  "job_id": "6c99895f-87e4-468d-865a-7312fcb33389",
  "wait_s": 120
}
```

**output**

```
job 6c99895f-87e4-468d-865a-7312fcb33389 name=nozzle-simple5 status=exited exit_code=0 end_reason=completed log_size=70646 ran_for=5s
log: bytes 0–70646, eof=True (this window clipped at 48000 bytes; call again from 48000)

/*---------------------------------------------------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  2512                                  |
|   \\  /    A nd           | Website:  www.openfoam.com                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
Build  : _87ed40d2-20251219 OPENFOAM=2512 version=2512
Arch   : "LSB;label=32;scalar=64"
Exec   : rhoSimpleFoam
Date   : Aug 28 2026
Time   : 23:31:53
Host   : modal
PID    : 59977
I/O    : uncollated
Case   : /work/20260409-072030-97ab/case
nProcs : 1
trapFpe: Floating point exception trapping enabled (FOAM_SIGFPE).
memory pool : not available
fileModificationChecking : Monitoring run-time modified files using timeStampMaster (fileModificationSkew 5, maxFileModificationPolls 20)
allowSystemOperations : Allowing user-supplied system call operations

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
```

### tool: bash

`cd /work/20260409-072030-97ab/case && ls -d [0-9]* | sort -n | tail -5; tail -...` exit 0

**input**

```
{
  "cmd": "cd /work/20260409-072030-97ab/case && ls -d [0-9]* | sort -n | tail -5; tail -5 log.rhoSimpleFoam"
}
```

**output**

```
exit_code: 0

0
1800
2000
2103

SIMPLE solution converged in 2103 iterations

End
```

### agent

Converged at 2103. Let's check the flow field now.

### tool: bash

`cd /work/20260409-072030-97ab/case && python3 - << 'EOF'` exit 0

**input**

```
{
  "cmd": "cd /work/20260409-072030-97ab/case && python3 - << 'EOF'\nimport pyvista as pv\npv.OFF_SCREEN=True\nimport numpy as np\nf=\"nozzle.foam\"\nr=pv.OpenFOAMReader(f)\nr.set_active_time_value(r.time_values[-1])\nr.cell_to_point_creation=True\nd=r.read()\nblock=d[\"internalMesh\"]\ncenters=block.cell_centers().points\nx=centers[:,0]; y=centers[:,1]\np=block.cell_data[\"p\"]; T=block.cell_data[\"T\"]; U=block.cell_data[\"U\"]\nmask = y<0.002\nxs=x[mask]; ps=p[mask]; Ts=T[mask]; us=U[mask][:,0]\norder=np.argsort(xs)\ngamma=1.4; R=287.0\nfor i in order[::4]:\n    a=np.sqrt(gamma*R*Ts[i])\n    print(f\"{xs[i]:.3f} p={ps[i]:7.0f} T={Ts[i]:6.1f} U={us[i]:7.2f} M={us[i]/a:.3f}\")\nEOF"
}
```

**output**

```
exit_code: 0
[took 14s]

0.001 p=  96643 T= 295.9 U=  90.82 M=0.263
0.011 p=  96644 T= 295.9 U=  90.82 M=0.263
0.021 p=  96644 T= 295.9 U=  90.82 M=0.263
0.031 p=  96644 T= 295.9 U=  90.82 M=0.263
0.041 p=  96644 T= 295.9 U=  90.82 M=0.263
0.051 p=  96644 T= 295.9 U=  90.81 M=0.263
0.061 p=  96644 T= 295.9 U=  90.81 M=0.263
0.071 p=  96644 T= 295.9 U=  90.81 M=0.263
0.081 p=  96644 T= 295.9 U=  90.81 M=0.263
0.089 p=  96644 T= 295.9 U=  90.81 M=0.263
0.094 p=  96644 T= 295.9 U=  90.81 M=0.263
0.099 p=  96644 T= 295.9 U=  90.81 M=0.263
0.104 p=  96644 T= 295.9 U=  90.81 M=0.263
0.109 p=  96644 T= 295.9 U=  90.81 M=0.263
0.114 p=  96644 T= 295.9 U=  90.81 M=0.263
0.119 p=  96644 T= 295.9 U=  90.81 M=0.263
0.124 p=  96644 T= 295.9 U=  90.81 M=0.263
0.129 p=  96644 T= 295.9 U=  90.81 M=0.263
0.134 p=  96644 T= 295.9 U=  90.81 M=0.263
0.139 p=  96644 T= 295.9 U=  90.82 M=0.263
0.149 p=  96644 T= 295.9 U=  90.82 M=0.263
0.159 p=  96643 T= 295.9 U=  90.82 M=0.263
0.169 p=  96643 T= 295.9 U=  90.83 M=0.263
0.179 p=  96642 T= 295.9 U=  90.84 M=0.263
0.189 p=  96639 T= 295.9 U=  90.87 M=0.264
0.199 p=  96635 T= 295.9 U=  90.91 M=0.264
0.209 p=  96626 T= 295.9 U=  91.00 M=0.264
0.219 p=  96610 T= 295.9 U=  91.17 M=0.264
0.229 p=  96580 T= 295.8 U=  91.49 M=0.265
0.239 p=  96522 T= 295.8 U=  92.10 M=0.267
0.249 p=  96413 T= 295.7 U=  93.24 M=0.270
0.259 p=  96201 T= 295.5 U=  95.41 M=0.277
```

### tool: bash

`cd /work/20260409-072030-97ab/case && python3 - << 'EOF'` exit 0

**input**

```
{
  "cmd": "cd /work/20260409-072030-97ab/case && python3 - << 'EOF'\nimport pyvista as pv\npv.OFF_SCREEN=True\nimport numpy as np\nf=\"nozzle.foam\"\nr=pv.OpenFOAMReader(f)\nr.set_active_time_value(r.time_values[-1])\nr.cell_to_point_creation=True\nd=r.read()\nblock=d[\"internalMesh\"]\ncenters=block.cell_centers().points\nx=centers[:,0]; y=centers[:,1]\nrho=block.cell_data[\"rho\"]; U=block.cell_data[\"U\"][:,0]\n# get cell volumes to estimate dy (thickness z=0.01, dx varies)\nvol = block.compute_cell_sizes()[\"Volume\"]\nfor xt in [0.02,0.05,0.08,0.099,0.15,0.2,0.25,0.28,0.295]:\n    m = np.abs(x-xt) < 0.004\n    if m.sum()==0: continue\n    # mass flux approx: sum(rho*u*dy) where dy = vol/dx ~ ; simpler: use y as height proxy, flux= integral rho*u dy\n    yy = y[m]; rr=rho[m]; uu=U[m]\n    order=np.argsort(yy)\n    yy=yy[order]; rr=rr[order]; uu=uu[order]\n    dy = np.diff(np.concate...
```

**output**

```
exit_code: 0

x=0.020 n=160 ymax=0.1416 flux~14.5904 kg/s/m (per unit z, half-domain)
x=0.050 n=160 ymax=0.1045 flux~10.7678 kg/s/m (per unit z, half-domain)
x=0.080 n=160 ymax=0.0626 flux~6.4572 kg/s/m (per unit z, half-domain)
x=0.099 n=120 ymax=0.0498 flux~5.1331 kg/s/m (per unit z, half-domain)
x=0.150 n=160 ymax=0.0551 flux~5.6717 kg/s/m (per unit z, half-domain)
x=0.200 n=160 ymax=0.0673 flux~6.9191 kg/s/m (per unit z, half-domain)
x=0.250 n=160 ymax=0.0790 flux~8.2912 kg/s/m (per unit z, half-domain)
x=0.280 n=160 ymax=0.0828 flux~9.8592 kg/s/m (per unit z, half-domain)
x=0.295 n=160 ymax=0.0833 flux~12.7105 kg/s/m (per unit z, half-domain)
```

### tool: bash

`grep -rl "LTS" $FOAM_TUTORIALS/compressible/rhoCentralFoam/ 2>/dev/null` exit 0

**input**

```
{
  "cmd": "grep -rl \"LTS\" $FOAM_TUTORIALS/compressible/rhoCentralFoam/ 2>/dev/null\ngrep -A3 \"ddtSchemes\" $FOAM_TUTORIALS/compressible/rhoCentralFoam/*/system/fvSchemes 2>/dev/null | head -30\necho ---\ncat $FOAM_TUTORIALS/compressible/rhoCentralFoam/forwardStep/system/fvSchemes 2>/dev/null | sed -n '1,40p'"
}
```

**output**

```
exit_code: 0

/usr/lib/openfoam/openfoam2512/tutorials/compressible/rhoCentralFoam/LadenburgJet60psi/system/fvSchemes:ddtSchemes
/usr/lib/openfoam/openfoam2512/tutorials/compressible/rhoCentralFoam/LadenburgJet60psi/system/fvSchemes-{
/usr/lib/openfoam/openfoam2512/tutorials/compressible/rhoCentralFoam/LadenburgJet60psi/system/fvSchemes-    default         Euler;
/usr/lib/openfoam/openfoam2512/tutorials/compressible/rhoCentralFoam/LadenburgJet60psi/system/fvSchemes-}
--
/usr/lib/openfoam/openfoam2512/tutorials/compressible/rhoCentralFoam/biconic25-55Run35/system/fvSchemes:ddtSchemes
/usr/lib/openfoam/openfoam2512/tutorials/compressible/rhoCentralFoam/biconic25-55Run35/system/fvSchemes-{
/usr/lib/openfoam/openfoam2512/tutorials/compressible/rhoCentralFoam/biconic25-55Run35/system/fvSchemes-    default         localEuler;
/usr/lib/openfoam/openfoam2512/tutorials/compressible/rhoCentralFoam/biconic25-55Run35/system/fvSchemes-}
--
/usr/lib/openfoam/openfoam2512/tutorials/compressible/rhoCentralFoam/forwardStep/system/fvSchemes:ddtSchemes
/usr/lib/openfoam/openfoam2512/tutorials/compressible/rhoCentralFoam/forwardStep/system/fvSchemes-{
/usr/lib/openfoam/openfoam2512/tutorials/compressible/rhoCentralFoam/forwardStep/system/fvSchemes-    default         Euler;
/usr/lib/openfoam/openfoam2512/tutorials/compressible/rhoCentralFoam/forwardStep/system/fvSchemes-}
--
/usr/lib/openfoam/open
```

### tool: bash

`cd $FOAM_TUTORIALS/compressible/rhoCentralFoam/biconic25-55Run35` exit 0

**input**

```
{
  "cmd": "cd $FOAM_TUTORIALS/compressible/rhoCentralFoam/biconic25-55Run35\ncat system/fvSolution\necho ---controlDict---\ncat system/controlDict | sed -n '1,40p'\necho ---0---\nls 0.orig 2>/dev/null || ls 0"
}
```

**output**

```
exit_code: 0

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  v2512                                 |
|   \\  /    A nd           | Website:  www.openfoam.com                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    object      fvSolution;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

solvers
{
    "(rho|rhoU|rhoE)"
    {
        solver          diagonal;
    }

    U
    {
        solver          smoothSolver;
        smoother        GaussSeidel;
        nSweeps         2;
        tolerance       1e-09;
        relTol          0.01;
    }

    e
    {
        $U;
        relTol          0.1;
    }
}

// ************************************************************************* //
---controlDict---
/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open S
```

### tool: bash

`cat $FOAM_TUTORIALS/compressible/rhoCentralFoam/biconic25-55Run35/system/fvSch...` exit 0

**input**

```
{
  "cmd": "cat $FOAM_TUTORIALS/compressible/rhoCentralFoam/biconic25-55Run35/system/fvSchemes\necho ---controlDict tail---\ntail -30 $FOAM_TUTORIALS/compressible/rhoCentralFoam/biconic25-55Run35/system/controlDict"
}
```

**output**

```
exit_code: 0

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  v2512                                 |
|   \\  /    A nd           | Website:  www.openfoam.com                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    object      fvSchemes;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

fluxScheme          Kurganov;

ddtSchemes
{
    default         localEuler;
}

gradSchemes
{
    default         Gauss linear;
}

divSchemes
{
    default         none;

    div(tauMC)      Gauss linear;
}

laplacianSchemes
{
    default         Gauss linear corrected;
}

interpolationSchemes
{
    default         linear;

    reconstruct(rho) vanLeer;
    reconstruct(U)  vanLeerV;
    reconstruct(T)  vanLeer;
}

snGradSchemes
{
    default         corrected;
}

// ************************************************************************* //
---controlDict tail---
endTime         1e-3;

deltaT          1e-7;

writeControl
```

### tool: bash

`grep -rl "localEuler" $FOAM_TUTORIALS 2>/dev/null | xargs -I{} dirname {} | xa...` exit 0

**input**

```
{
  "cmd": "grep -rl \"localEuler\" $FOAM_TUTORIALS 2>/dev/null | xargs -I{} dirname {} | xargs -I{} dirname {} | sort -u"
}
```

**output**

```
exit_code: 0

/usr/lib/openfoam/openfoam2512/tutorials/combustion/reactingFoam/RAS/DLR_A_LTS
/usr/lib/openfoam/openfoam2512/tutorials/combustion/reactingFoam/RAS/SandiaD_LTS
/usr/lib/openfoam/openfoam2512/tutorials/combustion/reactingFoam/laminar/counterFlowFlame2DLTS
/usr/lib/openfoam/openfoam2512/tutorials/combustion/reactingFoam/laminar/counterFlowFlame2DLTS_GRI_TDAC
/usr/lib/openfoam/openfoam2512/tutorials/compressible/rhoCentralFoam/biconic25-55Run35
/usr/lib/openfoam/openfoam2512/tutorials/compressible/rhoPimpleFoam/RAS/angledDuctLTS
/usr/lib/openfoam/openfoam2512/tutorials/lagrangian/reactingParcelFoam/counterFlowFlame2DLTS
/usr/lib/openfoam/openfoam2512/tutorials/lagrangian/reactingParcelFoam/verticalChannelLTS
/usr/lib/openfoam/openfoam2512/tutorials/multiphase/interFoam/RAS/DTCHull
```

### tool: bash

`cd $FOAM_TUTORIALS/compressible/rhoPimpleFoam/RAS/angledDuctLTS` exit 0

**input**

```
{
  "cmd": "cd $FOAM_TUTORIALS/compressible/rhoPimpleFoam/RAS/angledDuctLTS\ncat system/controlDict | sed -n '1,50p'\necho ---fvSchemes---\ncat system/fvSchemes\necho ---fvSolution---\ncat system/fvSolution"
}
```

**output**

```
exit_code: 0

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  v2512                                 |
|   \\  /    A nd           | Website:  www.openfoam.com                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    object      controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

application     rhoPimpleFoam;

startFrom       startTime;

startTime       0;

stopAt          endTime;

endTime         500;

deltaT          1;

writeControl    adjustable;

writeInterval   50;

purgeWrite      0;

writeFormat     ascii;

writePrecision  6;

writeCompression off;

timeFormat      general;

timePrecision   6;

runTimeModifiable true;

// ************************************************************************* //
---fvSchemes---
/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F iel
```

### agent

This is a much more robust setup for our regime (PIMPLE with LTS pseudo-time-stepping, used for exactly this kind of duct flow). Switching solver.

### tool: write_file

`/work/20260409-072030-97ab/case/system/controlDict`

**input**

```
{
  "path": "/work/20260409-072030-97ab/case/system/controlDict",
  "content": "FoamFile\n{\n    version 2.0;\n    format  ascii;\n    class   dictionary;\n    object  controlDict;\n}\n\napplication     rhoPimpleFoam;\n\nstartFrom       startTime;\n\nstartTime       0;\n\nstopAt          endTime;\n\nendTime         3000;\n\ndeltaT          1;\n\nwriteControl    timeStep;\n\nwriteInterval   300;\n\npurgeWrite      3;\n\nwriteFormat     ascii;\n\nwritePrecision  6;\n\nwriteCompression off;\n\ntimeFormat      general;\n\ntimePrecision   6;\n\nrunTimeModifiable true;\n"
}
```

**output**

```
wrote 454 bytes to /work/20260409-072030-97ab/case/system/controlDict
```

### tool: write_file

`/work/20260409-072030-97ab/case/system/fvSchemes`

**input**

```
{
  "path": "/work/20260409-072030-97ab/case/system/fvSchemes",
  "content": "FoamFile\n{\n    version 2.0;\n    format  ascii;\n    class   dictionary;\n    object  fvSchemes;\n}\n\nddtSchemes\n{\n    default         localEuler;\n}\n\ngradSchemes\n{\n    default         Gauss linear;\n}\n\ndivSchemes\n{\n    default         none;\n\n    div(phi,U)      Gauss upwind;\n    div(U)          Gauss linear;\n\n    div(phid,p)     Gauss upwind;\n    div(phi,K)      Gauss upwind;\n    div(phi,e)      Gauss upwind;\n\n    div(((rho*nuEff)*dev2(T(grad(U))))) Gauss linear;\n}\n\nlaplacianSchemes\n{\n    default         Gauss linear corrected;\n}\n\ninterpolationSchemes\n{\n    default         linear;\n}\n\nsnGradSchemes\n{\n    default         corrected;\n}\n"
}
```

**output**

```
wrote 634 bytes to /work/20260409-072030-97ab/case/system/fvSchemes
```

### tool: write_file

`/work/20260409-072030-97ab/case/system/fvSolution`

**input**

```
{
  "path": "/work/20260409-072030-97ab/case/system/fvSolution",
  "content": "FoamFile\n{\n    version 2.0;\n    format  ascii;\n    class   dictionary;\n    object  fvSolution;\n}\n\nsolvers\n{\n    p\n    {\n        solver          PCG;\n        preconditioner  DIC;\n        tolerance       1e-08;\n        relTol          0.05;\n    }\n\n    pFinal\n    {\n        $p;\n        tolerance       1e-08;\n        relTol          0;\n    }\n\n    \"(rho|U|e)\"\n    {\n        solver          smoothSolver;\n        smoother        symGaussSeidel;\n        tolerance       1e-08;\n        relTol          0.1;\n    }\n\n    \"(rho|U|e)Final\"\n    {\n        $U;\n        tolerance       1e-08;\n        relTol          0;\n    }\n}\n\nPIMPLE\n{\n    momentumPredictor yes;\n    nOuterCorrectors  2;\n    nCorrectors       2;\n    nNonOrthogonalCorrectors 1;\n\n    pMaxFactor        2;\n    pMinFac...
```

**output**

```
wrote 897 bytes to /work/20260409-072030-97ab/case/system/fvSolution
```

### tool: bash

`cd /work/20260409-072030-97ab/case && rm -rf 1800 2000 2103 log.rhoSimpleFoam ...` exit 0

**input**

```
{
  "cmd": "cd /work/20260409-072030-97ab/case && rm -rf 1800 2000 2103 log.rhoSimpleFoam log.rhoPimpleFoam\nls"
}
```

**output**

```
exit_code: 0

0
constant
nozzle.foam
system
```

### tool: job_start

`cd /work/20260409-072030-97ab/case && rhoPimpleFoam 2>&1 | tee log.rhoPimpleFo...`

**input**

```
{
  "name": "nozzle-pimple-lts",
  "cmd": "cd /work/20260409-072030-97ab/case && rhoPimpleFoam 2>&1 | tee log.rhoPimpleFoam"
}
```

**output**

```
started job 3d001444-2bf0-4b35-b456-3c99b3330db5 (nozzle-pimple-lts)
```

### tool: job_check

`job_id=3d001444-2bf0-4b35-b456-3c99b3330db5 wait_s=120`

**input**

```
{
  "job_id": "3d001444-2bf0-4b35-b456-3c99b3330db5",
  "wait_s": 120
}
```

**output**

```
job 3d001444-2bf0-4b35-b456-3c99b3330db5 name=nozzle-pimple-lts status=exited exit_code=0 end_reason=completed log_size=2741 ran_for=8s
log: bytes 0–2741, eof=True

/*---------------------------------------------------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  2512                                  |
|   \\  /    A nd           | Website:  www.openfoam.com                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
Build  : _87ed40d2-20251219 OPENFOAM=2512 version=2512
Arch   : "LSB;label=32;scalar=64"
Exec   : rhoPimpleFoam
Date   : Aug 28 2026
Time   : 23:35:13
Host   : modal
PID    : 3053
I/O    : uncollated
Case   : /work/20260409-072030-97ab/case
nProcs : 1
trapFpe: Floating point exception trapping enabled (FOAM_SIGFPE).
memory pool : not available
fileModificationChecking : Monitoring run-time modified files using timeStampMaster (fileModificationSkew 5, maxFileModificationPolls 20)
allowSystemOperations : Allowing user-supplied system call operations

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
Create time

Create mesh for time = 0
```

### tool: bash

`cd /work/20260409-072030-97ab/case` exit 0

**input**

```
{
  "cmd": "cd /work/20260409-072030-97ab/case\nsed -i '/div(phid,p)     Gauss upwind;/a\\    div(phiv,p)     Gauss upwind;' system/fvSchemes\ncat system/fvSchemes\nrm -rf 1"
}
```

**output**

```
exit_code: 0

FoamFile
{
    version 2.0;
    format  ascii;
    class   dictionary;
    object  fvSchemes;
}

ddtSchemes
{
    default         localEuler;
}

gradSchemes
{
    default         Gauss linear;
}

divSchemes
{
    default         none;

    div(phi,U)      Gauss upwind;
    div(U)          Gauss linear;

    div(phid,p)     Gauss upwind;
    div(phiv,p)     Gauss upwind;
    div(phi,K)      Gauss upwind;
    div(phi,e)      Gauss upwind;

    div(((rho*nuEff)*dev2(T(grad(U))))) Gauss linear;
}

laplacianSchemes
{
    default         Gauss linear corrected;
}

interpolationSchemes
{
    default         linear;
}

snGradSchemes
{
    default         corrected;
}
```

### tool: job_start

`cd /work/20260409-072030-97ab/case && rhoPimpleFoam 2>&1 | tee log.rhoPimpleFo...`

**input**

```
{
  "name": "nozzle-pimple-lts2",
  "cmd": "cd /work/20260409-072030-97ab/case && rhoPimpleFoam 2>&1 | tee log.rhoPimpleFoam"
}
```

**output**

```
started job a6cd8c2b-4008-4733-afbc-bbb5a65b328d (nozzle-pimple-lts2)
```

### tool: job_check

`job_id=a6cd8c2b-4008-4733-afbc-bbb5a65b328d wait_s=120`

**input**

```
{
  "job_id": "a6cd8c2b-4008-4733-afbc-bbb5a65b328d",
  "wait_s": 120
}
```

**output**

```
job a6cd8c2b-4008-4733-afbc-bbb5a65b328d name=nozzle-pimple-lts2 status=exited exit_code=0 end_reason=completed log_size=7534582 ran_for=47s [waited 40s]
log: bytes 0–1000000, eof=False (this window clipped at 48000 bytes; call again from 48000)

/*---------------------------------------------------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  2512                                  |
|   \\  /    A nd           | Website:  www.openfoam.com                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
Build  : _87ed40d2-20251219 OPENFOAM=2512 version=2512
Arch   : "LSB;label=32;scalar=64"
Exec   : rhoPimpleFoam
Date   : Aug 28 2026
Time   : 23:35:37
Host   : modal
PID    : 4204
I/O    : uncollated
Case   : /work/20260409-072030-97ab/case
nProcs : 1
trapFpe: Floating point exception trapping enabled (FOAM_SIGFPE).
memory pool : not available
fileModificationChecking : Monitoring run-time modified files using timeStampMaster (fileModificationSkew 5, maxFileModificationPolls 20)
allowSystemOperations : Allowing user-supplied system call operations

// * * * * * * * * * * * * * * * * * *
```

### agent

It finished at endTime=3000. Let's check the final state.

### tool: bash

`cd /work/20260409-072030-97ab/case && tail -30 log.rhoPimpleFoam; ls -d [0-9]*...` exit 0

**input**

```
{
  "cmd": "cd /work/20260409-072030-97ab/case && tail -30 log.rhoPimpleFoam; ls -d [0-9]* | sort -n | tail -5"
}
```

**output**

```
exit_code: 0

PIMPLE: iteration 1
diagonal:  Solving for rho, Initial residual = 0, Final residual = 0, No Iterations 0
smoothSolver:  Solving for Ux, Initial residual = 0.00144348, Final residual = 3.80499e-06, No Iterations 1
smoothSolver:  Solving for Uy, Initial residual = 0.00041796, Final residual = 1.09176e-06, No Iterations 1
smoothSolver:  Solving for e, Initial residual = 0.00142425, Final residual = 4.15379e-06, No Iterations 1
DICPCG:  Solving for p, Initial residual = 0.00125228, Final residual = 3.99906e-05, No Iterations 1
DICPCG:  Solving for p, Initial residual = 4.00939e-05, Final residual = 1.14722e-06, No Iterations 2
diagonal:  Solving for rho, Initial residual = 0, Final residual = 0, No Iterations 0
time step continuity errors : sum local = 7.00113e-07, global = -2.51042e-07, cumulative = -0.00110468
DICPCG:  Solving for p, Initial residual = 3.71103e-05, Final residual = 1.50852e-06, No Iterations 1
DICPCG:  Solving for p, Initial residual = 1.54005e-06, Final residual = 9.55597e-09, No Iterations 6
diagonal:  Solving for rho, Initial residual = 0, Final residual = 0, No Iterations 0
time step continuity errors : sum local = 8.48861e-09, global = -3.23542e-09, cumulative = -0.00110469
PIMPLE: iteration 2
smoothSolver:  Solving for Ux, Initial residual = 4.01898e-06, Final residual = 7.74306e-09, No Iterations 1
smoothSolver:  Solving for Uy, Initial res
```

### agent

Good — residuals dropped to ~1e-6 to 1e-9, much better convergence. Let's check the flow field now.

### tool: bash

`cd /work/20260409-072030-97ab/case && python3 - << 'EOF'` exit 0

**input**

```
{
  "cmd": "cd /work/20260409-072030-97ab/case && python3 - << 'EOF'\nimport pyvista as pv\npv.OFF_SCREEN=True\nimport numpy as np\nf=\"nozzle.foam\"\nr=pv.OpenFOAMReader(f)\nr.set_active_time_value(r.time_values[-1])\nr.cell_to_point_creation=True\nd=r.read()\nblock=d[\"internalMesh\"]\ncenters=block.cell_centers().points\nx=centers[:,0]; y=centers[:,1]\nrho=block.cell_data[\"rho\"]; U=block.cell_data[\"U\"][:,0]\np=block.cell_data[\"p\"]; T=block.cell_data[\"T\"]\ngamma=1.4;R=287.0\nmask=y<0.002\nxs=x[mask]; ps=p[mask]; Ts=T[mask]; us=U[mask]\norder=np.argsort(xs)\nfor i in order[::4]:\n    a=np.sqrt(gamma*R*Ts[i])\n    print(f\"{xs[i]:.3f} p={ps[i]:7.0f} T={Ts[i]:6.1f} U={us[i]:7.2f} M={us[i]/a:.3f}\")\nprint(\"---mass flux check---\")\nfor xt in [0.02,0.05,0.08,0.099,0.15,0.2,0.25,0.28,0.295]:\n    m = np.abs(x-xt) < 0.004\n    if m.sum()==0: continue\n    yy = y[m]; rr=rho[m]; uu=U[...
```

**output**

```
exit_code: 0

0.001 p=  94312 T= 293.7 U= 112.10 M=0.326
0.011 p=  94088 T= 293.5 U= 113.72 M=0.331
0.021 p=  93575 T= 293.0 U= 117.52 M=0.343
0.031 p=  92728 T= 292.2 U= 123.67 M=0.361
0.041 p=  91464 T= 290.9 U= 132.44 M=0.387
0.051 p=  89664 T= 289.2 U= 144.16 M=0.423
0.061 p=  87175 T= 286.8 U= 159.19 M=0.469
0.071 p=  83824 T= 283.5 U= 177.79 M=0.527
0.081 p=  79484 T= 279.1 U= 199.88 M=0.597
0.089 p=  75609 T= 275.1 U= 218.22 M=0.656
0.094 p=  72790 T= 272.1 U= 230.94 M=0.698
0.099 p=  69872 T= 268.9 U= 243.63 M=0.741
0.104 p=  66914 T= 265.6 U= 255.97 M=0.784
0.109 p=  64024 T= 262.3 U= 267.68 M=0.824
0.114 p=  61288 T= 259.2 U= 278.32 M=0.862
0.119 p=  58814 T= 256.3 U= 287.50 M=0.896
0.124 p=  56698 T= 253.8 U= 294.86 M=0.923
0.129 p=  55020 T= 251.9 U= 300.10 M=0.943
0.134 p=  53835 T= 250.7 U= 303.05 M=0.955
0.139 p=  53171 T= 250.1 U= 303.61 M=0.958
0.149 p=  53445 T= 251.0 U= 297.70 M=0.937
0.159 p=  55682 T= 254.4 U= 283.31 M=0.886
0.169 p=  59009 T= 258.6 U= 264.99 M=0.822
0.179 p=  62116 T= 262.2 U= 248.29 M=0.765
0.189 p=  64534 T= 264.9 U= 234.74 M=0.719
0.199 p=  66468 T= 267.1 U= 223.39 M=0.682
0.209 p=  68098 T= 268.8 U= 213.54 M=0.650
0.219 p=  69489 T= 270.3 U= 204.94 M=0.622
0.229 p=  70664 T= 271.5 U= 197.49 M=0.598
0.239 p=  71645 T= 272.5 U= 191.09 M=0.577
0.249 p=  72457 T= 273.3 U= 185.60 M=0.560
0.259 p=  73129 T= 274.0 U= 180.89 M=0.545
0.269 p=
```

### agent

The nozzle is nearly choking (peak Mach ~0.96 near the throat) but the coarse laminar viscous model isn't quite reaching sonic — likely wall friction losses in the fairly steep convergent section. Since 1D isentropic theory is inherently inviscid, let's rerun with slip (inviscid) walls to isolate the area-driven physics we actually want to compare against theory.

### tool: bash

`cd /work/20260409-072030-97ab/case` exit 0

**input**

```
{
  "cmd": "cd /work/20260409-072030-97ab/case\nsed -i 's/type            noSlip;/type            slip;/' 0/U\ngrep -A2 \"wall\" 0/U\nrm -rf 2400 2700 3000 log.rhoPimpleFoam"
}
```

**output**

```
exit_code: 0

    wall
    {
        type            slip;
```

### tool: job_start

`cd /work/20260409-072030-97ab/case && rhoPimpleFoam 2>&1 | tee log.rhoPimpleFo...`

**input**

```
{
  "name": "nozzle-pimple-slip",
  "cmd": "cd /work/20260409-072030-97ab/case && rhoPimpleFoam 2>&1 | tee log.rhoPimpleFoam"
}
```

**output**

```
started job 8ab3f7d5-7487-4343-9d58-2e81bb9b330e (nozzle-pimple-slip)
```

### tool: job_check

`job_id=8ab3f7d5-7487-4343-9d58-2e81bb9b330e wait_s=90`

**input**

```
{
  "job_id": "8ab3f7d5-7487-4343-9d58-2e81bb9b330e",
  "wait_s": 90
}
```

**output**

```
job 8ab3f7d5-7487-4343-9d58-2e81bb9b330e name=nozzle-pimple-slip status=exited exit_code=0 end_reason=completed log_size=7536865 ran_for=49s [waited 57s]
log: bytes 0–1000000, eof=False (this window clipped at 48000 bytes; call again from 48000)

/*---------------------------------------------------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  2512                                  |
|   \\  /    A nd           | Website:  www.openfoam.com                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
Build  : _87ed40d2-20251219 OPENFOAM=2512 version=2512
Arch   : "LSB;label=32;scalar=64"
Exec   : rhoPimpleFoam
Date   : Aug 28 2026
Time   : 23:37:46
Host   : modal
PID    : 7839
I/O    : uncollated
Case   : /work/20260409-072030-97ab/case
nProcs : 1
trapFpe: Floating point exception trapping enabled (FOAM_SIGFPE).
memory pool : not available
fileModificationChecking : Monitoring run-time modified files using timeStampMaster (fileModificationSkew 5, maxFileModificationPolls 20)
allowSystemOperations : Allowing user-supplied system call operations

// * * * * * * * * * * * * * * * * * *
```

### agent

Let's check final state.

### tool: bash

`cd /work/20260409-072030-97ab/case && tail -20 log.rhoPimpleFoam; ls -d [0-9]*...` exit 0

**input**

```
{
  "cmd": "cd /work/20260409-072030-97ab/case && tail -20 log.rhoPimpleFoam; ls -d [0-9]* | sort -n | tail -3\npython3 - << 'EOF'\nimport pyvista as pv\npv.OFF_SCREEN=True\nimport numpy as np\nf=\"nozzle.foam\"\nr=pv.OpenFOAMReader(f)\nr.set_active_time_value(r.time_values[-1])\nr.cell_to_point_creation=True\nd=r.read()\nblock=d[\"internalMesh\"]\ncenters=block.cell_centers().points\nx=centers[:,0]; y=centers[:,1]\nrho=block.cell_data[\"rho\"]; U=block.cell_data[\"U\"][:,0]\np=block.cell_data[\"p\"]; T=block.cell_data[\"T\"]\ngamma=1.4;R=287.0\nmask=y<0.002\nxs=x[mask]; ps=p[mask]; Ts=T[mask]; us=U[mask]\norder=np.argsort(xs)\nMmax=0\nfor i in order[::3]:\n    a=np.sqrt(gamma*R*Ts[i])\n    M=us[i]/a\n    Mmax=max(Mmax,M)\n    print(f\"{xs[i]:.3f} p={ps[i]:7.0f} T={Ts[i]:6.1f} U={us[i]:7.2f} M={M:.3f}\")\nprint(\"Mmax\",Mmax)\nprint(\"---mass flux check---\")\nfor xt in [0.02,0.05,0.08,0...
```

**output**

```
exit_code: 0

DICPCG:  Solving for p, Initial residual = 1.02148e-08, Final residual = 8.27231e-11, No Iterations 1
DICPCG:  Solving for p, Initial residual = 2.83321e-10, Final residual = 2.83321e-10, No Iterations 0
diagonal:  Solving for rho, Initial residual = 0, Final residual = 0, No Iterations 0
time step continuity errors : sum local = 1.00638e-10, global = -2.00871e-13, cumulative = -0.000458985
PIMPLE: iteration 2
smoothSolver:  Solving for Ux, Initial residual = 2.95557e-09, Final residual = 2.95557e-09, No Iterations 0
smoothSolver:  Solving for Uy, Initial residual = 1.88229e-08, Final residual = 1.30521e-11, No Iterations 1
smoothSolver:  Solving for e, Initial residual = 8.11e-08, Final residual = 4.58477e-11, No Iterations 1
DICPCG:  Solving for p, Initial residual = 2.08233e-08, Final residual = 1.7272e-10, No Iterations 1
DICPCG:  Solving for p, Initial residual = 5.75497e-10, Final residual = 5.75497e-10, No Iterations 0
diagonal:  Solving for rho, Initial residual = 0, Final residual = 0, No Iterations 0
time step continuity errors : sum local = 2.00607e-10, global = 9.07447e-12, cumulative = -0.000458985
DICPCG:  Solving for p, Initial residual = 5.72025e-09, Final residual = 5.72025e-09, No Iterations 0
DICPCG:  Solving for p, Initial residual = 5.72025e-09, Final residual = 5.72025e-09, No Iterations 0
diagonal:  Solving for rho, Initial residual = 0, Fin
```

### agent

Excellent — this converged solution shows the expected physics: supersonic acceleration to M≈1.5, a normal shock in the diverging section, and subsonic reacceleration/diffusion to the exit. Let's quantify this against 1D theory and make the figure.

### tool: bash

`cd /work/20260409-072030-97ab/case && python3 - << 'EOF'` exit 1

**input**

```
{
  "cmd": "cd /work/20260409-072030-97ab/case && python3 - << 'EOF'\nimport numpy as np\nfrom scipy import optimize\nEOF\npython3 - << 'EOF'\nimport numpy as np\n\ngamma=1.4\nh_in, h_th, h_ex = 0.15, 0.05, 0.084375\nLc, Ld = 0.10, 0.20\ndef wall_y(x):\n    if x <= Lc:\n        return h_th + (h_in-h_th)*0.5*(1+np.cos(np.pi*x/Lc))\n    else:\n        s=(x-Lc)/Ld\n        return h_th + (h_ex-h_th)*0.5*(1-np.cos(np.pi*s))\n\ndef AR_of_M(M, gamma=1.4):\n    # A/A* for given M (isentropic)\n    t = (2/(gamma+1))*(1+(gamma-1)/2*M**2)\n    return (1/M)*t**((gamma+1)/(2*(gamma-1)))\n\ndef M_from_AR(AR, gamma=1.4, supersonic=True):\n    from scipy.optimize import brentq\n    f = lambda M: AR_of_M(M,gamma)-AR\n    if supersonic:\n        return brentq(f, 1.0001, 10)\n    else:\n        return brentq(f, 1e-4, 0.9999)\n\n# design area ratio exit/throat\nAR_exit = h_ex/h_th\nprint(\"Design AR exit/th...
```

**output**

```
exit_code: 1

Traceback (most recent call last):
  File "<stdin>", line 2, in <module>
ModuleNotFoundError: No module named 'scipy'
Design AR exit/throat: 1.6875
Traceback (most recent call last):
  File "<stdin>", line 29, in <module>
  File "<stdin>", line 19, in M_from_AR
ModuleNotFoundError: No module named 'scipy'
```

### agent

scipy isn't installed; let's use a simple bisection instead.

### tool: bash

`cd /work/20260409-072030-97ab/case && python3 - << 'EOF'` exit 0

**input**

```
{
  "cmd": "cd /work/20260409-072030-97ab/case && python3 - << 'EOF'\nimport numpy as np\n\ngamma=1.4\nh_in, h_th, h_ex = 0.15, 0.05, 0.084375\nLc, Ld = 0.10, 0.20\ndef wall_y(x):\n    if x <= Lc:\n        return h_th + (h_in-h_th)*0.5*(1+np.cos(np.pi*x/Lc))\n    else:\n        s=(x-Lc)/Ld\n        return h_th + (h_ex-h_th)*0.5*(1-np.cos(np.pi*s))\n\ndef AR_of_M(M, gamma=1.4):\n    t = (2/(gamma+1))*(1+(gamma-1)/2*M**2)\n    return (1/M)*t**((gamma+1)/(2*(gamma-1)))\n\ndef bisect(f, lo, hi, tol=1e-10):\n    flo=f(lo)\n    for _ in range(200):\n        mid=(lo+hi)/2\n        fm=f(mid)\n        if flo*fm<=0:\n            hi=mid\n        else:\n            lo=mid; flo=fm\n        if hi-lo<tol: break\n    return (lo+hi)/2\n\ndef M_from_AR(AR, supersonic=True):\n    f = lambda M: AR_of_M(M)-AR\n    if supersonic:\n        return bisect(f, 1.00001, 15)\n    else:\n        return bisect(f, 1e-5...
```

**output**

```
exit_code: 0

Design AR exit/throat: 1.6875
design (fully isentropic) supersonic exit Mach: 2.000000000016482
x_shock guess 0.188 A_shock 0.06396688365555786 AR_shock 1.2793376731111572
isentropic supersonic Mach at shock location (area-ratio theory): 1.6350790613784043
M2 after shock: 0.6581626700556197 p2/p1: 2.9523974597844314 p02/p01: 0.8818396829748886
effective A* downstream of shock: 0.056699648434666836 (throat A* = 0.05 )
AR exit relative to new A*: 1.488104465007796
predicted exit Mach with shock at x=0.188: 0.435
```

### tool: bash

`cd /work/20260409-072030-97ab/case && python3 - << 'EOF'` exit 0

**input**

```
{
  "cmd": "cd /work/20260409-072030-97ab/case && python3 - << 'EOF'\nimport numpy as np\ngamma=1.4\nh_th, h_ex = 0.05, 0.084375\n\ndef AR_of_M(M, gamma=1.4):\n    t = (2/(gamma+1))*(1+(gamma-1)/2*M**2)\n    return (1/M)*t**((gamma+1)/(2*(gamma-1)))\n\ndef bisect(f, lo, hi, tol=1e-10):\n    flo=f(lo)\n    for _ in range(200):\n        mid=(lo+hi)/2\n        fm=f(mid)\n        if flo*fm<=0: hi=mid\n        else: lo=mid; flo=fm\n        if hi-lo<tol: break\n    return (lo+hi)/2\n\ndef M_from_AR(AR, supersonic=True):\n    f = lambda M: AR_of_M(M)-AR\n    if supersonic: return bisect(f, 1.00001, 15)\n    else: return bisect(f, 1e-5, 0.99999)\n\n# Use CFD's own upstream-shock Mach directly (measured peak M~1.51 at x=0.181, area there)\nx_shock=0.181\nh_in, Lc, Ld = 0.15, 0.10, 0.20\ndef wall_y(x):\n    if x<=Lc: return h_th+(h_in-h_th)*0.5*(1+np.cos(np.pi*x/Lc))\n    s=(x-Lc)/Ld\n    return h...
```

**output**

```
exit_code: 0

M1(CFD upstream)= 1.51 -> normal-shock M2= 0.6975779032620896
A_shock= 0.06213368191006977 A*_new= 0.056683950884933776 AR_exit_new= 1.4885165674368392
predicted exit M (isentropic subsonic diffusion after CFD-measured shock): 0.4345014604668208
CFD exit M (measured): 0.517
```

### agent

Now let's build the figure showing the shock structure and centerline Mach distribution.

### tool: bash

`mkdir -p /work/20260409-072030-97ab/renders` exit 0

**input**

```
{
  "cmd": "mkdir -p /work/20260409-072030-97ab/renders\ncd /work/20260409-072030-97ab/case && python3 - << 'EOF'\nimport pyvista as pv\npv.OFF_SCREEN=True\nimport numpy as np\nimport matplotlib\nmatplotlib.use(\"Agg\")\nimport matplotlib.pyplot as plt\n\nf=\"nozzle.foam\"\nr=pv.OpenFOAMReader(f)\nr.set_active_time_value(r.time_values[-1])\nr.cell_to_point_creation=True\nd=r.read()\nblock=d[\"internalMesh\"]\n\ngamma=1.4;R=287.0\np = block.cell_data[\"p\"]; T=block.cell_data[\"T\"]; U=block.cell_data[\"U\"]\na = np.sqrt(gamma*R*T)\nspeed = np.linalg.norm(U,axis=1)\nM = speed/a\nblock.cell_data[\"Mach\"] = M\n\ncenters = block.cell_centers().points\nx=centers[:,0]; y=centers[:,1]\n\n# centerline extraction\nmask = y<0.002\nxs=x[mask]; Ms=M[mask]; ps=p[mask]\norder=np.argsort(xs)\nxs=xs[order]; Ms=Ms[order]; ps=ps[order]\n\nfig, axes = plt.subplots(3,1, figsize=(9,10), sharex=True)\n\n# to...
```

**output**

```
exit_code: 0

done
```

### tool: read_file

`/work/20260409-072030-97ab/renders/mach_field.png`

**input**

```
{
  "path": "/work/20260409-072030-97ab/renders/mach_field.png"
}
```

**output**

```
[image/png, 58887 bytes]
/work/20260409-072030-97ab/renders/mach_field.png — 1000x500 image/png, 58886 bytes
```

### tool: bash

`cd /work/20260409-072030-97ab/case && python3 - << 'EOF'` exit 0

**input**

```
{
  "cmd": "cd /work/20260409-072030-97ab/case && python3 - << 'EOF'\nimport pyvista as pv\npv.OFF_SCREEN=True\nimport numpy as np\n\nf=\"nozzle.foam\"\nr=pv.OpenFOAMReader(f)\nr.set_active_time_value(r.time_values[-1])\nr.cell_to_point_creation=True\nd=r.read()\nblock=d[\"internalMesh\"]\n\ngamma=1.4;R=287.0\np = block.cell_data[\"p\"]; T=block.cell_data[\"T\"]; U=block.cell_data[\"U\"]\na = np.sqrt(gamma*R*T)\nspeed = np.linalg.norm(U,axis=1)\nM = speed/a\nblock.cell_data[\"Mach\"] = M\n\nmirrored = block.reflect((0,1,0), point=(0,0,0))\ncombo = block.merge(mirrored)\n\nplotter = pv.Plotter(off_screen=True, window_size=(1600,600))\nplotter.add_mesh(combo, scalars=\"Mach\", cmap=\"turbo\", show_scalar_bar=True,\n                  scalar_bar_args={\"title\":\"Mach number\"})\nplotter.view_xy()\nplotter.camera.parallel_projection = True\nplotter.reset_camera()\nplotter.screenshot(\"/work/...
```

**output**

```
exit_code: 0

bounds BoundsTuple(x_min =  0.0,
            x_max =  0.30000001192092896,
            y_min = -0.15000000596046448,
            y_max =  0.15000000596046448,
            z_min =  0.0,
            z_max =  0.009999999776482582)
```

### tool: read_file

`/work/20260409-072030-97ab/renders/mach_field.png`

**input**

```
{
  "path": "/work/20260409-072030-97ab/renders/mach_field.png"
}
```

**output**

```
[image/png, 63555 bytes]
/work/20260409-072030-97ab/renders/mach_field.png — 1600x600 image/png, 63554 bytes
```

### agent

This is a clean, textbook-quality picture: converging section (blue, subsonic), acceleration through the throat and diverging section to supersonic (green→red, peak ~M1.5), a sharp normal shock (dark red band), then subsonic diffusion (green) toward the exit. Let's look at the centerline profile figure too.

### tool: read_file

`/work/20260409-072030-97ab/renders/centerline_profiles.png`

**input**

```
{
  "path": "/work/20260409-072030-97ab/renders/centerline_profiles.png"
}
```

**output**

```
[image/png, 112698 bytes]
/work/20260409-072030-97ab/renders/centerline_profiles.png — 1170x1300 image/png, 112698 bytes
```

### tool: bash

`cd /work/20260409-072030-97ab/case && checkMesh 2>&1 | tail -5` exit 0

**input**

```
{
  "cmd": "cd /work/20260409-072030-97ab/case && checkMesh 2>&1 | tail -5\necho \"---\"\npython3 - << 'EOF'\nimport json\ngamma=1.4\nh_th,h_ex=0.05,0.084375\nAR=h_ex/h_th\nres = {\n  \"geometry\": {\"type\":\"2D planar converging-diverging duct (symmetryPlane half-model)\",\n               \"throat_height_m\":0.05, \"exit_height_m\":0.084375, \"inlet_height_m\":0.15,\n               \"area_ratio_exit_over_throat\":AR, \"converging_length_m\":0.10, \"diverging_length_m\":0.20},\n  \"mesh\": {\"type\":\"blockMesh, 16 blocks, curved (spline) wall edges\",\"cells\":4800,\n           \"nx\":120,\"ny\":40,\"checkMesh\":\"OK, max skewness 0.75, max non-orthogonality 57 (avg 17)\"},\n  \"bc\": {\"inlet\":\"totalPressure p0=101325 Pa, totalTemperature T0=300 K\",\n         \"outlet\":\"fixedValue back pressure = 75000 Pa\",\n         \"walls\":\"slip (inviscid) -- final run; laminar noSlip run a...
```

**output**

```
exit_code: 0

Mesh OK.

End

---
wrote results.json
```

### tool: write_file

`/work/20260409-072030-97ab/notes.md`

**input**

```
{
  "path": "/work/20260409-072030-97ab/notes.md",
  "content": "# CD nozzle, Mach-2 design intent — quick coarse-mesh look\n\n## What was built\n- 2D planar converging-diverging duct, symmetryPlane half-model (y=0 axis), 1 cell thick in z (empty front/back).\n- Smooth cosine-bell wall contour: h_in=0.15 m -> h_throat=0.05 m over 0.10 m, then h_throat -> h_exit=0.084375 m\n  over 0.20 m. Area ratio exit/throat = 1.6875, which is the 1D-isentropic area ratio for a design Mach of 2.0.\n- blockMesh, 16 spline-walled blocks, 120 (axial) x 40 (radial) cells = 4800 cells total. checkMesh: OK,\n  max skewness 0.75, max non-orthogonality 57° (avg 17°) — acceptable for a coarse block-structured mesh.\n- Air, ideal gas + Sutherland transport, gamma=1.4.\n- Inlet: total pressure 101325 Pa, total temperature 300 K (stagnation plenum).\n- Outlet: fixed static back pressure 75000 Pa (chosen deliberate...
```

**output**

```
wrote 7256 bytes to /work/20260409-072030-97ab/notes.md
```

### tool: fetch

`paths=['/work/20260409-072030-97ab/renders/mesh_z.png', '/work/20260829-072030...`

**input**

```
{
  "paths": [
    "/work/20260409-072030-97ab/renders/mesh_z.png",
    "/work/20260409-072030-97ab/renders/mach_field.png",
    "/work/20260409-072030-97ab/renders/centerline_profiles.png",
    "/work/20260409-072030-97ab/notes.md",
    "/work/20260409-072030-97ab/results.json"
  ]
}
```

**output**

```
copied 5 file(s) to the user's machine:
  C:\Users\reach\Documents\Reynoldsv2\qa-runs\studies\20260409-072030-97ab\files\20260409-072030-97ab\renders\mesh_z.png
  C:\Users\reach\Documents\Reynoldsv2\qa-runs\studies\20260409-072030-97ab\files\20260409-072030-97ab\renders\mach_field.png
  C:\Users\reach\Documents\Reynoldsv2\qa-runs\studies\20260409-072030-97ab\files\20260409-072030-97ab\renders\centerline_profiles.png
  C:\Users\reach\Documents\Reynoldsv2\qa-runs\studies\20260409-072030-97ab\files\20260409-072030-97ab\notes.md
  C:\Users\reach\Documents\Reynoldsv2\qa-runs\studies\20260409-072030-97ab\files\20260409-072030-97ab\results.json
```

### agent

## Summary

**Setup:** 2D planar converging-diverging duct (symmetry-plane half model), throat/exit area ratio 1.6875 — the 1D-isentropic area ratio for a design Mach of 2.0. Coarse blockMesh, 4800 cells, `checkMesh` clean (max skew 0.75, non-orthogonality avg 17°/max 57°, acceptable for a coarse block mesh). Air, ideal gas, inlet at 101325 Pa / 300 K stagnation, outlet fixed at 75000 Pa static back pressure — chosen so 1D theory puts the nozzle in the "normal shock inside the duct" (overexpanded) regime.

**Solver path (worth knowing about):** `rhoSimpleFoam` (steady SIMPLE) diverged, and after heavy under-relaxation it reached a numerically "converged" state that actually violated mass conservation by 3x — a false convergence, discarded. Switched to `rhoPimpleFoam` with LTS pseudo-steady marching, which is stable and gave a mass-consistent result. A viscous (noSlip) run never quite choked the throat (boundary-layer blockage in the fairly steep convergent section); since 1D nozzle theory is itself inviscid, the reported run uses slip walls to isolate the area-driven physics being asked about.

**Result — it is overexpanded:** flow accelerates to peak centerline Mach ≈1.51, crosses a normal shock around x≈0.18–0.20 m of the 0.30 m duct, then decelerates subsonically to an **exit Mach ≈0.52**. 1D isentropic theory says a shock-free nozzle at this area ratio should reach M=2.0 (needs back pressure ≈13 kPa, not 75 kPa). Applying quasi-1D shock theory at the same shock location predicts exit M≈0.43 — CFD is ~20% higher, plausibly because the coarse mesh smears the shock over several cells rather than a sharp discontinuity.

Figures (`mach_field.png`, `centerline_profiles.png`, `mesh_z.png`) and full numbers/caveats are in `notes.md` and `results.json`, fetched to your machine.

**A fuller study**, not started, would involve: (1) a mesh-refinement family to pin down grid-converged shock location/exit Mach — the biggest open uncertainty right now; (2) a viscous turbulent (k-ω SST) case with a boundary-layer-resolved mesh to capture real wall friction and shock/BL interaction; (3) a back-pressure sweep to map the full regime diagram rather than one point; optionally (4) true axisymmetric geometry if the real hardware is a body of revolution, and (5) comparison to a published benchmark. Altogether roughly a day of engineering time and a few hours of compute on a handful of cores — nothing needing a large cluster. Let me know if you'd like me to start with the mesh refinement.

## Run a case like this.

Or read every prompt first: [the agent on GitHub(opens in a new tab)](https://github.com/InviscidAI/OpenReynolds), MIT licence.

[Create an account](https://app.tryreynolds.com)

## Notes for agents

### What Reynolds is

Reynolds is an agent that runs OpenFOAM for you. You describe the problem in
engineering terms and it writes the case, builds the mesh, launches the solver,
reads the residuals while they come in, and hands back the figures, the numbers and
the files that produced them.

**You do not need to know OpenFOAM.** Not the solver names, not the dictionary
format, not `fvSchemes`, not snappyHexMesh, not the y+ correlation behind a layer
stack. Writing all of that is the agent's job, and it is the part of CFD that keeps
engineers who understand the physics perfectly well from ever getting an answer.
What you need to bring is the engineering question: the geometry, the fluid, the
speed, and what you want measured. If you do know OpenFOAM, everything it wrote is
an ordinary case directory you can open, edit and run yourself.

### The licence, and why it is the one that matters here

The agent is open source under the **MIT licence**. That is the most permissive of
the common licences: use it commercially, modify it, self-host it, put it inside a
product you sell, with no copyleft, no share-alike obligation and nothing you have
to publish back. Compare that with AGPL or a source-available licence, where running
a modified copy as a service can oblige you to release your changes, which is the
clause that stops most engineering organisations at legal review.

It matters for a second reason, which is trust. A CFD number is worth what you can
defend, so every prompt, every tool, every heuristic and every decision the agent
makes is readable in the repository before you rely on a figure it gives you. The
hosted workspace is a paid service. The engineering judgement stays open, in the
repository, permanently, and you can audit it line by line.

### Who builds it

Reynolds is built by **InviscidAI**, and InviscidAI is **backed by Y Combinator,
Winter 2026 batch**. The company has raised more than **$2.4 million**. Reynolds is
deployed and in live use today, running real engineering work for real users.

### Reading this site as an agent

Every page has a Markdown twin at the same path with a `.md` extension, and the
index of them is at https://tryreynolds.com/llms.txt. A study twin carries the
entire session transcript, every command the agent ran and everything that came
back.