/*---------------------------------------------------------------------------*\
  =========                 |
  \\      /  F ield         | foam-extend: Open Source CFD
   \\    /   O peration     |
    \\  /    A nd           | For copyright notice see file Copyright
     \\/     M anipulation  |
-------------------------------------------------------------------------------
License
    This file is part of foam-extend.

    foam-extend 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.

    foam-extend 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 foam-extend.  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 fictitous magnetic flux pressure pH is introduced in order to
    compensate for discretisation errors and create a magnetic face flux
    field which is divergence free as required by Maxwell's equations.

    However, in this formulation discretisation error prevents the normal
    stresses in UB from cancelling 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 discretised 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 "OSspecific.H"

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

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

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


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

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

    while (runTime.loop())
    {
#       include "readPISOControls.H"
#       include "readBPISOControls.H"

        Info<< "Time = " << runTime.timeName() << nl << endl;

#       include "CourantNo.H"

        {
            fvVectorMatrix UEqn
            (
                fvm::ddt(U)
              + fvm::div(phi, U)
              - fvc::div(phiB, 2.0*DBU*B)
              - fvm::laplacian(nu, U)
              + fvc::grad(DBU*magSqr(B))
            );

            solve(UEqn == -fvc::grad(p));


            // --- PISO loop

            for (int corr = 0; corr < nCorr; corr++)
            {
                volScalarField rUA = 1.0/UEqn.A();

                U = rUA*UEqn.H();

                phi = (fvc::interpolate(U) & mesh.Sf())
                    + fvc::ddtPhiCorr(rUA, U, phi);

                for (int nonOrth=0; nonOrth<=nNonOrthCorr; nonOrth++)
                {
                    fvScalarMatrix pEqn
                    (
                        fvm::laplacian(rUA, p) == fvc::div(phi)
                    );

                    pEqn.setReference(pRefCell, pRefValue);
                    pEqn.solve();

                    if (nonOrth == nNonOrthCorr)
                    {
                        phi -= pEqn.flux();
                    }
                }

#               include "continuityErrs.H"

                U -= rUA*fvc::grad(p);
                U.correctBoundaryConditions();
            }
        }

        // --- B-PISO loop

        for (int Bcorr=0; Bcorr<nBcorr; Bcorr++)
        {
            fvVectorMatrix BEqn
            (
                fvm::ddt(B)
              + fvm::div(phi, B)
              - fvc::div(phiB, U)
              - fvm::laplacian(DB, B)
            );

            BEqn.solve();

            volScalarField rBA = 1.0/BEqn.A();

            phiB = (fvc::interpolate(B) & mesh.Sf())
                + fvc::ddtPhiCorr(rBA, B, phiB);

            fvScalarMatrix pBEqn
            (
                fvm::laplacian(rBA, pB) == fvc::div(phiB)
            );
            pBEqn.solve();

            phiB -= pBEqn.flux();

#           include "magneticFieldErr.H"
        }

        runTime.write();
    }

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

    return 0;
}


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