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How to add an algebric expression for vector field.

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Old   September 8, 2022, 07:04
Smile How to add an algebric expression for vector field.
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prakash verma
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Hi everyone,

I'm developing a solver for ferrofluid flow, where I have to define the Magnetic field in X and Y directions in terms of x and y variables (in form of algebraic expressions).

I have already defined the H vector field, but I'm getting problems defining the H field in terms of x and y variables.

Can someone please tell me how to define a volume vector field in OpenFOAM when u know the algebraic expression for the x and y component of the vector field?


I'm modifying mhdFoam solver by adding a new momentum source term in UEqn and my solver looks like this.


/*---------------------------------------------------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Copyright (C) 2011-2021 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/>.

Application
mhdFoam

Description
Solver for magnetohydrodynamics (MHD): incompressible, laminar flow of a
conducting fluid under the influence of a magnetic field.

An applied magnetic field H acts as a driving force,
at present boundary conditions cannot be set via the
electric field E or current density J. The fluid viscosity nu,
conductivity sigma and permeability mu are read in as uniform
constants.

A fictitious magnetic flux pressure pB is introduced in order to
compensate for discretization errors and create a magnetic face flux
field which is divergence-free as required by Maxwell's equations.

However, in this formulation discretization error prevents the normal
stresses in UB from canceling with those from BU, but it is unknown
whether this is a serious error. A correction could be introduced
whereby the normal stresses in the discretized BU term are replaced
by those from the UB term, but this would violate the boundedness
constraint presently observed in the present numerics which
guarantees div(U) and div(H) are zero.

\*---------------------------------------------------------------------------*/

#include "fvCFD.H"
#include "pisoControl.H"
#include "pressureReference.H"

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

int main(int argc, char *argv[])
{
#include "postProcess.H"

#include "setRootCaseLists.H"
#include "createTime.H"
#include "createMesh.H"
#include "createControl.H"
#include "createFields.H"
#include "initContinuityErrs.H"

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

Info<< nl << "Starting time loop" << endl;

while (runTime.loop())
{
Info<< "Time = " << runTime.userTimeName() << nl << endl;

#include "CourantNo.H"
// #include "HEqn.H"

H == B/(mu*(1+Chi));



{
fvVectorMatrix UEqn
(
fvm::ddt(U)
+ fvm::div(phi, U)

- fvm::laplacian(nu, U)


-(mu/rho)*Chi*(H&fvc::grad(Chi))*H

);

if (piso.momentumPredictor())
{
solve(UEqn == -fvc::grad(p));
}


// --- PISO loop
while (piso.correct())
{
volScalarField rAU(1.0/UEqn.A());
surfaceScalarField rAUf("rAUf", fvc::interpolate(rAU));
volVectorField HbyA(constrainHbyA(rAU*UEqn.H(), U, p));
surfaceScalarField phiHbyA
(
"phiHbyA",
fvc::flux(HbyA)
+ rAUf*fvc::ddtCorr(U, phi)
);

// Update the pressure BCs to ensure flux consistency
constrainPressure(p, U, phiHbyA, rAUf);

while (piso.correctNonOrthogonal())
{
fvScalarMatrix pEqn
(
fvm::laplacian(rAUf, p) == fvc::div(phiHbyA)
);

pEqn.setReference
(
pressureReference.refCell(),
pressureReference.refValue()
);

pEqn.solve();

if (piso.finalNonOrthogonalIter())
{
phi = phiHbyA - pEqn.flux();
}
}

#include "continuityErrs.H"

U = HbyA - rAU*fvc::grad(p);
U.correctBoundaryConditions();

}


#include "TEqn.H"

Chi == Chi0/(1+betaT*(T-Tr));

}


// --- B-PISO loop
while (bpiso.correct())
{
fvVectorMatrix BEqn
(
fvm::ddt(B)
+ fvm::div(phi, B)
- fvc::div(phiB, U)
- fvm::laplacian(DB, B)
);

BEqn.solve();

volScalarField rAB(1.0/BEqn.A());
surfaceScalarField rABf("rABf", fvc::interpolate(rAB));

phiB = fvc::flux(B);

while (bpiso.correctNonOrthogonal())
{
fvScalarMatrix pBEqn
(
fvm::laplacian(rABf, pB) == fvc::div(phiB)
);

pBEqn.solve();

if (bpiso.finalNonOrthogonalIter())
{
phiB -= pBEqn.flux();
}
}

#include "magneticFieldErr.H"
}

runTime.write();
}

Info<< "End\n" << endl;

return 0;
}


// ************************************************** *********************** //
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