fv::OUForce: New random Ornstein-Uhlenbeck) process force fvModel

Description
    Calculates and applies the random OU (Ornstein-Uhlenbeck) process force to
    the momentum equation for direct numerical simulation of boxes of isotropic
    turbulence.

    The energy spectrum is calculated and written at write-times which is
    particularly useful to test and compare LES SGS models.

Note
    This random OU process force uses a FFT to generate the force field which
    is not currently parallelised.  Also the mesh the FFT is applied to must
    be isotropic and have a power of 2 cells in each direction.

Usage
    Example usage:
    \verbatim
    OUForce
    {
        type    OUForce;

        libs    ("librandomProcesses.so");

        sigma   0.090295;
        alpha   0.81532;
        kUpper  10;
        kLower  7;
    }
    \endverbatim

The tutorials/incompressibleFluid/boxTurb16 tutorial case is an updated version
of the original tutorials/legacy/incompressible/dnsFoam/boxTurb16 case,
demonstrating the use of the OUForce fvModel with the incompressibleFluid solver
module to replicate the behaviour of the legacy dnsFoam solver application.

applications/legacy/incompressible/dnsFoam/dnsFoam.C

@@ -32,7 +32,7 @@ Description
 #include "argList.H"
 #include "timeSelector.H"
 #include "Kmesh.H"
-#include "UOprocess.H"
+#include "OUprocess.H"
 #include "fft.H"
 #include "writeEk.H"
 #include "writeFile.H"
@@ -76,7 +76,8 @@ int main(int argc, char *argv[])
         (
             fft::reverseTransform
             (
-                K/(mag(K) + 1.0e-6) ^ forceGen.newField(), K.nn()
+                (K/(mag(K) + 1.0e-6))
+              ^ forceGen.newField(runTime.deltaTValue()), K.nn()
             )
         );
 

applications/legacy/incompressible/dnsFoam/readTurbulenceProperties.H

@@ -18,4 +18,4 @@
     );
 
     Kmesh K(mesh);
-    UOprocess forceGen(K, runTime.deltaTValue(), momentumTransport);
+    OUprocess forceGen(K, runTime.deltaTValue(), momentumTransport);

src/finiteVolume/cfdTools/general/fvConstraints/fvConstraints.C

@@ -301,7 +301,7 @@ bool Foam::fvConstraints::writeData(Ostream& os) const
 
 bool Foam::fvConstraints::read()
 {
-    if (IOdictionary::regIOobject::read())
+    if (regIOobject::read())
     {
         checkTimeIndex_ = mesh().time().timeIndex() + 1;
 

src/finiteVolume/cfdTools/general/fvModels/fvModels.C

@@ -332,7 +332,7 @@ bool Foam::fvModels::writeData(Ostream& os) const
 
 bool Foam::fvModels::read()
 {
-    if (IOdictionary::regIOobject::read())
+    if (regIOobject::read())
     {
         checkTimeIndex_ = mesh().time().timeIndex() + 1;
 

src/randomProcesses/Make/files

@@ -5,7 +5,9 @@ fft/fftRenumber.C
 fft/writeEk.C
 fft/kShellIntegration.C
 
-processes/UOprocess/UOprocess.C
+processes/OUprocess/OUprocess.C
+
+OUForce/OUForce.C
 
 turbulence/turbGen.C
 

src/randomProcesses/OUForce/OUForce.C

@@ -0,0 +1,150 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Copyright (C) 2023 OpenFOAM Foundation
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+License
+    This file is part of OpenFOAM.
+
+    OpenFOAM is free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+    for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
+
+\*---------------------------------------------------------------------------*/
+
+#include "OUForce.H"
+#include "fvMatrices.H"
+#include "fft.H"
+#include "writeEk.H"
+#include "addToRunTimeSelectionTable.H"
+
+// * * * * * * * * * * * * * Static Member Functions * * * * * * * * * * * * //
+
+namespace Foam
+{
+namespace fv
+{
+    defineTypeNameAndDebug(OUForce, 0);
+
+    addToRunTimeSelectionTable
+    (
+        fvModel,
+        OUForce,
+        dictionary
+    );
+}
+}
+
+
+// * * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * //
+
+void Foam::fv::OUForce::readCoeffs()
+{
+    UName_ = coeffs().lookupOrDefault<word>("U", "U");
+}
+
+
+// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
+
+Foam::fv::OUForce::OUForce
+(
+    const word& name,
+    const word& modelType,
+    const fvMesh& mesh,
+    const dictionary& dict
+)
+:
+    fvModel(name, modelType, mesh, dict),
+    UName_(word::null),
+    K_(mesh),
+    forceGen_(K_, mesh.time().deltaTValue(), dict)
+{
+    readCoeffs();
+}
+
+
+// * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
+
+Foam::wordList Foam::fv::OUForce::addSupFields() const
+{
+    return wordList(1, UName_);
+}
+
+
+void Foam::fv::OUForce::addSup
+(
+    fvMatrix<vector>& eqn,
+    const word& fieldName
+) const
+{
+    if (mesh().time().writeTime())
+    {
+        writeEk(eqn.psi(), K_);
+    }
+
+    eqn += volVectorField::Internal
+    (
+        IOobject
+        (
+            "OUForce",
+            mesh().time().name(),
+            mesh()
+        ),
+        mesh(),
+        dimAcceleration,
+        ReImSum
+        (
+            fft::reverseTransform
+            (
+                (K_/(mag(K_) + 1.0e-6))
+              ^ forceGen_.newField(mesh().time().deltaTValue()), K_.nn()
+            )
+        )
+    );
+}
+
+
+bool Foam::fv::OUForce::movePoints()
+{
+    return true;
+}
+
+
+void Foam::fv::OUForce::topoChange(const polyTopoChangeMap&)
+{}
+
+
+void Foam::fv::OUForce::mapMesh(const polyMeshMap& map)
+{}
+
+
+void Foam::fv::OUForce::distribute(const polyDistributionMap&)
+{}
+
+
+bool Foam::fv::OUForce::read(const dictionary& dict)
+{
+    if (fvModel::read(dict))
+    {
+        readCoeffs();
+        return true;
+    }
+    else
+    {
+        return false;
+    }
+}
+
+
+// ************************************************************************* //

src/randomProcesses/OUForce/OUForce.H

@@ -0,0 +1,178 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Copyright (C) 2023 OpenFOAM Foundation
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+License
+    This file is part of OpenFOAM.
+
+    OpenFOAM is free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+    for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
+
+Class
+    Foam::fv::OUForce
+
+Description
+    Calculates and applies the random OU (Ornstein-Uhlenbeck) process force to
+    the momentum equation for direct numerical simulation of boxes of isotropic
+    turbulence.
+
+    The energy spectrum is calculated and written at write-times which is
+    particularly useful to test and compare LES SGS models.
+
+Note
+    This random OU process force uses a FFT to generate the force field which
+    is not currently parallelised.  Also the mesh the FFT is applied to must
+    be isotropic and have a power of 2 cells in each direction.
+
+Usage
+    Example usage:
+    \verbatim
+    OUForce
+    {
+        type    OUForce;
+
+        libs    ("librandomProcesses.so");
+
+        sigma   0.090295;
+        alpha   0.81532;
+        kUpper  10;
+        kLower  7;
+    }
+    \endverbatim
+
+SourceFiles
+    OUForce.C
+
+\*---------------------------------------------------------------------------*/
+
+#ifndef OUForce_H
+#define OUForce_H
+
+#include "fvModel.H"
+#include "Kmesh.H"
+#include "OUprocess.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+namespace fv
+{
+
+/*---------------------------------------------------------------------------*\
+                        Class OUForce Declaration
+\*---------------------------------------------------------------------------*/
+
+class OUForce
+:
+    public fvModel
+{
+    // Private Data
+
+        //- Name of the velocity field
+        word UName_;
+
+        //- The wavenumber mesh used for the random OU process
+        Kmesh K_;
+
+        //- The random OU process force generator
+        OUprocess forceGen_;
+
+
+    // Private Member Functions
+
+        //- Non-virtual read
+        void readCoeffs();
+
+
+public:
+
+    //- Runtime type information
+    TypeName("OUForce");
+
+
+    // Constructors
+
+        //- Construct from explicit source name and mesh
+        OUForce
+        (
+            const word& name,
+            const word& modelType,
+            const fvMesh& mesh,
+            const dictionary& dict
+        );
+
+        //- Disallow default bitwise copy construction
+        OUForce(const OUForce&) = delete;
+
+
+    // Member Functions
+
+        // Checks
+
+            //- Return the list of fields for which the fvModel adds source term
+            //  to the transport equation
+            virtual wordList addSupFields() const;
+
+
+        // Evaluate
+
+            //- Add explicit contribution to incompressible momentum equation
+            virtual void addSup
+            (
+                fvMatrix<vector>& eqn,
+                const word& fieldName
+            ) const;
+
+
+        // Mesh changes
+
+            //- Update for mesh motion
+            virtual bool movePoints();
+
+            //- Update topology using the given map
+            virtual void topoChange(const polyTopoChangeMap&);
+
+            //- Update from another mesh using the given map
+            virtual void mapMesh(const polyMeshMap&);
+
+            //- Redistribute or update using the given distribution map
+            virtual void distribute(const polyDistributionMap&);
+
+
+        // IO
+
+            //- Read source dictionary
+            virtual bool read(const dictionary& dict);
+
+
+    // Member Operators
+
+        //- Disallow default bitwise assignment
+        void operator=(const OUForce&) = delete;
+};
+
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace fv
+} // End namespace Foam
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#endif
+
+// ************************************************************************* //

src/randomProcesses/processes/OUprocess/OUprocess.C

@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2023 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -23,11 +23,8 @@ License
 
 \*---------------------------------------------------------------------------*/
 
-#include "error.H"
-
-#include "UOprocess.H"
+#include "OUprocess.H"
 #include "Kmesh.H"
-#include "dictionary.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
@@ -36,54 +33,51 @@ namespace Foam
 
 // * * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * //
 
-complexVector UOprocess::WeinerProcess()
+complexVector OUprocess::WeinerProcess(const scalar deltaT) const
 {
-    return RootDeltaT*complexVector
+    return sqrt(deltaT)*complexVector
     (
-        complex(GaussGen.scalarNormal(), GaussGen.scalarNormal()),
-        complex(GaussGen.scalarNormal(), GaussGen.scalarNormal()),
-        complex(GaussGen.scalarNormal(), GaussGen.scalarNormal())
+        complex(GaussGen_.scalarNormal(), GaussGen_.scalarNormal()),
+        complex(GaussGen_.scalarNormal(), GaussGen_.scalarNormal()),
+        complex(GaussGen_.scalarNormal(), GaussGen_.scalarNormal())
     );
 }
 
 
 // * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
 
-// from components
-UOprocess::UOprocess
+OUprocess::OUprocess
 (
     const Kmesh& kmesh,
     const scalar deltaT,
-    const dictionary& UOdict
+    const dictionary& OUdict
 )
 :
-    GaussGen(label(0)),
-    Mesh(kmesh),
-    DeltaT(deltaT),
-    RootDeltaT(sqrt(DeltaT)),
-    UOfield(Mesh.size()),
+    GaussGen_(label(0)),
+    Kmesh_(kmesh),
+    OUfield_(Kmesh_.size()),
 
-    Alpha(UOdict.lookup<scalar>("UOalpha")),
-    Sigma(UOdict.lookup<scalar>("UOsigma")),
-    Kupper(UOdict.lookup<scalar>("UOKupper")),
-    Klower(UOdict.lookup<scalar>("UOKlower")),
-    Scale((Kupper - Klower)*pow(scalar(Mesh.size()), 1.0/vector::dim))
+    alpha_(OUdict.lookup<scalar>("alpha")),
+    sigma_(OUdict.lookup<scalar>("sigma")),
+    kUpper_(OUdict.lookup<scalar>("kUpper")),
+    kLower_(OUdict.lookup<scalar>("kLower")),
+    scale_((kUpper_ - kLower_)*pow(scalar(Kmesh_.size()), 1.0/vector::dim))
 {
-    const vectorField& K = Mesh;
+    const vectorField& K = Kmesh_;
 
-    scalar sqrKupper = sqr(Kupper);
-    scalar sqrKlower = sqr(Klower) + small;
+    scalar sqrkUpper_ = sqr(kUpper_);
+    scalar sqrkLower_ = sqr(kLower_) + small;
     scalar sqrK;
 
-    forAll(UOfield, i)
+    forAll(OUfield_, i)
     {
-        if ((sqrK = magSqr(K[i])) < sqrKupper && sqrK > sqrKlower)
+        if ((sqrK = magSqr(K[i])) < sqrkUpper_ && sqrK > sqrkLower_)
         {
-            UOfield[i] = Scale*Sigma*WeinerProcess();
+            OUfield_[i] = scale_*sigma_*WeinerProcess(deltaT);
         }
         else
         {
-            UOfield[i] = complexVector
+            OUfield_[i] = complexVector
             (
                 complex(0, 0),
                 complex(0, 0),
@@ -96,29 +90,27 @@ UOprocess::UOprocess
 
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
-const complexVectorField& UOprocess::newField()
+const complexVectorField& OUprocess::newField(const scalar deltaT) const
 {
-    const vectorField& K = Mesh;
+    const vectorField& K = Kmesh_;
 
     label count = 0;
-    scalar sqrKupper = sqr(Kupper);
-    scalar sqrKlower = sqr(Klower) + small;
+    scalar sqrkUpper_ = sqr(kUpper_);
+    scalar sqrkLower_ = sqr(kLower_) + small;
     scalar sqrK;
 
-    forAll(UOfield, i)
+    forAll(OUfield_, i)
     {
-        if ((sqrK = magSqr(K[i])) < sqrKupper && sqrK > sqrKlower)
+        if ((sqrK = magSqr(K[i])) < sqrkUpper_ && sqrK > sqrkLower_)
         {
             count++;
-            UOfield[i] =
-                (1.0 - Alpha*DeltaT)*UOfield[i]
-              + Scale*Sigma*WeinerProcess();
+            OUfield_[i] =
+                (1.0 - alpha_*deltaT)*OUfield_[i]
+              + scale_*sigma_*WeinerProcess(deltaT);
         }
     }
 
-    Info<< "    Number of forced K = " << count << nl;
-
-    return UOfield;
+    return OUfield_;
 }
 
 

src/randomProcesses/processes/OUprocess/OUprocess.H

@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2023 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -22,18 +22,18 @@ License
     along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
 
 Class
-    Foam::UOprocess
+    Foam::OUprocess
 
 Description
-    Random UO process.
+    Random Ornstein-Uhlenbeck process
 
 SourceFiles
-    UOprocess.C
+    OUprocess.C
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef UOprocess_H
-#define UOprocess_H
+#ifndef OUprocess_H
+#define OUprocess_H
 
 #include "complexFields.H"
 #include "scalar.H"
@@ -45,40 +45,40 @@ namespace Foam
 {
 
 class Kmesh;
-class dictionary;
 
 /*---------------------------------------------------------------------------*\
-                          Class UOprocess Declaration
+                          Class OUprocess Declaration
 \*---------------------------------------------------------------------------*/
 
-class UOprocess
+class OUprocess
 {
     // Private Data
 
-        Random GaussGen;
+        mutable Random GaussGen_;
 
-        const Kmesh& Mesh;
-        const scalar DeltaT, RootDeltaT;
-        complexVectorField UOfield;
+        const Kmesh& Kmesh_;
+        mutable complexVectorField OUfield_;
 
-        scalar Alpha;
-        scalar Sigma;
-        scalar Kupper;
-        scalar Klower;
-        scalar Scale;
+        // Ornstein-Uhlenbeck process coefficients
+        scalar alpha_;
+        scalar sigma_;
+        scalar kUpper_;
+        scalar kLower_;
+        scalar scale_;
 
 
     // Private Member Functions
 
-        complexVector WeinerProcess();
+        //- Return the Weiner process field
+        complexVector WeinerProcess(const scalar deltaT) const;
 
 
 public:
 
     // Constructors
 
-        //- Construct from wavenumber mesh and timestep
-        UOprocess
+        //- Construct from wavenumber mesh, timestep and coefficients dict
+        OUprocess
         (
             const Kmesh& kmesh,
             const scalar deltaT,
@@ -88,7 +88,8 @@ public:
 
     // Member Functions
 
-        const complexVectorField& newField();
+        //- Return the current random Ornstein-Uhlenbeck process field
+        const complexVectorField& newField(const scalar deltaT) const;
 };
 
 

tutorials/incompressibleFluid/boxTurb16/0/U.orig

@@ -0,0 +1,50 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  dev
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    format      ascii;
+    class       volVectorField;
+    location    "0";
+    object      U.orig;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+dimensions      [0 1 -1 0 0 0 0];
+
+internalField   uniform (0 0 0);
+
+boundaryField
+{
+    patch0_half0
+    {
+        type            cyclic;
+    }
+    patch0_half1
+    {
+        type            cyclic;
+    }
+    patch1_half0
+    {
+        type            cyclic;
+    }
+    patch1_half1
+    {
+        type            cyclic;
+    }
+    patch2_half0
+    {
+        type            cyclic;
+    }
+    patch2_half1
+    {
+        type            cyclic;
+    }
+}
+
+
+// ************************************************************************* //

tutorials/incompressibleFluid/boxTurb16/0/p

@@ -0,0 +1,50 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  dev
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    format      ascii;
+    class       volScalarField;
+    location    "1";
+    object      p;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+dimensions      [0 2 -2 0 0 0 0];
+
+internalField   uniform 0;
+
+boundaryField
+{
+    patch0_half0
+    {
+        type            cyclic;
+    }
+    patch1_half0
+    {
+        type            cyclic;
+    }
+    patch2_half0
+    {
+        type            cyclic;
+    }
+    patch2_half1
+    {
+        type            cyclic;
+    }
+    patch1_half1
+    {
+        type            cyclic;
+    }
+    patch0_half1
+    {
+        type            cyclic;
+    }
+}
+
+
+// ************************************************************************* //

tutorials/incompressibleFluid/boxTurb16/Allclean

@@ -0,0 +1,10 @@
+#!/bin/sh
+cd ${0%/*} || exit 1    # Run from this directory
+
+# Source tutorial clean functions
+. $WM_PROJECT_DIR/bin/tools/CleanFunctions
+
+cleanCase
+rm -rf 0/enstrophy
+
+#------------------------------------------------------------------------------

tutorials/incompressibleFluid/boxTurb16/Allrun

@@ -0,0 +1,15 @@
+#!/bin/sh
+cd ${0%/*} || exit 1    # Run from this directory
+
+# Source tutorial run functions
+. $WM_PROJECT_DIR/bin/tools/RunFunctions
+
+# Get application name
+application=$(getApplication)
+
+runApplication blockMesh
+runApplication boxTurb
+runApplication $application
+runApplication -s enstrophy foamPostProcess -func enstrophy
+
+#------------------------------------------------------------------------------

tutorials/incompressibleFluid/boxTurb16/constant/boxTurbDict

@@ -0,0 +1,22 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  dev
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    format      ascii;
+    class       dictionary;
+    location    "constant";
+    object      boxTurbDict;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+Ea              10;
+
+k0              5;
+
+
+// ************************************************************************* //

tutorials/incompressibleFluid/boxTurb16/constant/fvModels

@@ -0,0 +1,29 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  dev
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    format      ascii;
+    class       dictionary;
+    location    "constant";
+    object      fvModels;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+OUForce
+{
+    type    OUForce;
+
+    libs    ("librandomProcesses.so");
+
+    sigma   0.090295;
+    alpha   0.81532;
+    kUpper  10;
+    kLower  7;
+}
+
+// ************************************************************************* //

tutorials/incompressibleFluid/boxTurb16/constant/momentumTransport

@@ -0,0 +1,19 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  dev
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    format      ascii;
+    class       dictionary;
+    location    "constant";
+    object      momentumTransport;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+simulationType  laminar;
+
+// ************************************************************************* //

tutorials/incompressibleFluid/boxTurb16/constant/physicalProperties

@@ -0,0 +1,21 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  dev
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    format      ascii;
+    class       dictionary;
+    location    "constant";
+    object      physicalProperties;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+viscosityModel  constant;
+
+nu              0.025;
+
+// ************************************************************************* //

tutorials/incompressibleFluid/boxTurb16/system/blockMeshDict

@@ -0,0 +1,94 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  dev
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    format      ascii;
+    class       dictionary;
+    object      blockMeshDict;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+convertToMeters 1;
+
+vertices
+(
+    (0 0 0)
+    (1 0 0)
+    (1 1 0)
+    (0 1 0)
+    (0 0 1)
+    (1 0 1)
+    (1 1 1)
+    (0 1 1)
+);
+
+blocks
+(
+    hex (0 1 2 3 4 5 6 7) (16 16 16) simpleGrading (1 1 1)
+);
+
+boundary
+(
+    patch0_half0
+    {
+        type cyclic;
+        neighbourPatch patch0_half1;
+        faces
+        (
+            (0 3 2 1)
+        );
+    }
+    patch0_half1
+    {
+        type cyclic;
+        neighbourPatch patch0_half0;
+        faces
+        (
+            (4 5 6 7)
+        );
+    }
+    patch1_half0
+    {
+        type cyclic;
+        neighbourPatch patch1_half1;
+        faces
+        (
+            (0 4 7 3)
+        );
+    }
+    patch1_half1
+    {
+        type cyclic;
+        neighbourPatch patch1_half0;
+        faces
+        (
+            (2 6 5 1)
+        );
+    }
+    patch2_half0
+    {
+        type cyclic;
+        neighbourPatch patch2_half1;
+        faces
+        (
+            (3 7 6 2)
+        );
+    }
+    patch2_half1
+    {
+        type cyclic;
+        neighbourPatch patch2_half0;
+        faces
+        (
+            (1 5 4 0)
+        );
+    }
+);
+
+
+// ************************************************************************* //

tutorials/incompressibleFluid/boxTurb16/system/controlDict

@@ -0,0 +1,51 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  dev
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    format      ascii;
+    class       dictionary;
+    location    "system";
+    object      controlDict;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+application     foamRun;
+
+solver          incompressibleFluid;
+
+startFrom       startTime;
+
+startTime       0;
+
+stopAt          endTime;
+
+endTime         10;
+
+deltaT          0.025;
+
+writeControl    runTime;
+
+writeInterval   0.25;
+
+purgeWrite      0;
+
+writeFormat     ascii;
+
+writePrecision  6;
+
+writeCompression off;
+
+timeFormat      general;
+
+timePrecision   6;
+
+runTimeModifiable true;
+
+graphFormat     raw;
+
+// ************************************************************************* //

tutorials/incompressibleFluid/boxTurb16/system/fvSchemes

@@ -0,0 +1,49 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  dev
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    format      ascii;
+    class       dictionary;
+    location    "system";
+    object      fvSchemes;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+ddtSchemes
+{
+    default         Euler;
+}
+
+gradSchemes
+{
+    default         Gauss linear;
+}
+
+divSchemes
+{
+    default         none;
+    div(phi,U)      Gauss cubic;
+}
+
+laplacianSchemes
+{
+    default         Gauss linear corrected;
+}
+
+interpolationSchemes
+{
+    default         linear;
+}
+
+snGradSchemes
+{
+    default         corrected;
+}
+
+
+// ************************************************************************* //

tutorials/incompressibleFluid/boxTurb16/system/fvSolution

@@ -0,0 +1,45 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  dev
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    format      ascii;
+    class       dictionary;
+    location    "system";
+    object      fvSolution;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+solvers
+{
+    "p.*"
+    {
+        solver          PCG;
+        preconditioner  DIC;
+        tolerance       1e-06;
+        relTol          0;
+    }
+
+    "U.*"
+    {
+        solver          smoothSolver;
+        smoother        symGaussSeidel;
+        tolerance       1e-05;
+        relTol          0;
+    }
+}
+
+PIMPLE
+{
+    nCorrectors     2;
+    nNonOrthogonalCorrectors 0;
+    pRefCell        0;
+    pRefValue       0;
+}
+
+
+// ************************************************************************* //

tutorials/legacy/incompressible/dnsFoam/boxTurb16/constant/momentumTransport

@@ -14,13 +14,9 @@ FoamFile
 }
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
-UOsigma         0.090295;
-
-UOalpha         0.81532;
-
-UOKupper        10;
-
-UOKlower        7;
-
+sigma   0.090295;
+alpha   0.81532;
+kUpper  10;
+kLower  7;
 
 // ************************************************************************* //