SkewSymmetricAdvection.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File SkewSymmetricAdvection.cpp
//
// For more information, please see: http://www.nektar.info
//
// The MIT License
//
// Copyright (c) 2006 Division of Applied Mathematics, Brown University (USA),
// Department of Aeronautics, Imperial College London (UK), and Scientific
// Computing and Imaging Institute, University of Utah (USA).
//
// Permission is hereby granted, free of charge, to any person obtaining a
// copy of this software and associated documentation files (the "Software"),
// to deal in the Software without restriction, including without limitation
// the rights to use, copy, modify, merge, publish, distribute, sublicense,
// and/or sell copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included
// in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
// THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
// DEALINGS IN THE SOFTWARE.
//
// Description: Evaluation of the Navier Stokes advective term
//
///////////////////////////////////////////////////////////////////////////////
 
#include <IncNavierStokesSolver/AdvectionTerms/SkewSymmetricAdvection.h>
 
using namespace std;
 
namespace Nektar
{
string SkewSymmetricAdvection::className =
    SolverUtils::GetAdvectionFactory().RegisterCreatorFunction(
        "SkewSymmetric", SkewSymmetricAdvection::create, "Skew Symmetric");
 
/**
 *
 */
SkewSymmetricAdvection::SkewSymmetricAdvection() : Advection()
 
{
}
 
/**
 *
 */
SkewSymmetricAdvection::~SkewSymmetricAdvection()
{
}
 
/**
 *
 */
void SkewSymmetricAdvection::v_InitObject(
    LibUtilities::SessionReaderSharedPtr pSession,
    Array<OneD, MultiRegions::ExpListSharedPtr> pFields)
{
    Advection::v_InitObject(pSession, pFields);
 
    m_homogen_dealiasing = pSession->DefinesSolverInfo("dealiasing");
    pSession->MatchSolverInfo("ModeType", "SingleMode", m_SingleMode, false);
    pSession->MatchSolverInfo("ModeType", "HalfMode", m_HalfMode, false);
}
 
/**
 *
 */
void SkewSymmetricAdvection::v_Advect(
    const int nConvectiveFields,
    const Array<OneD, MultiRegions::ExpListSharedPtr> &fields,
    const Array<OneD, Array<OneD, NekDouble>> &advVel,
    const Array<OneD, Array<OneD, NekDouble>> &inarray,
    Array<OneD, Array<OneD, NekDouble>> &outarray, const NekDouble &time,
    const Array<OneD, Array<OneD, NekDouble>> &pFwd,
    const Array<OneD, Array<OneD, NekDouble>> &pBwd)
{
    // use dimension of Velocity vector to dictate dimension of operation
    int ndim  = advVel.size();
    int nqtot = fields[0]->GetTotPoints();
    ASSERTL1(nConvectiveFields == inarray.size(),
             "Number of convective fields and Inarray are not compatible");
 
    Array<OneD, Array<OneD, NekDouble>> velocity(ndim);
    for (int i = 0; i < ndim; ++i)
    {
        if (fields[i]->GetWaveSpace() && !m_SingleMode && !m_HalfMode)
        {
            velocity[i] = Array<OneD, NekDouble>(nqtot, 0.0);
            fields[i]->HomogeneousBwdTrans(advVel[i], velocity[i]);
        }
        else
        {
            velocity[i] = advVel[i];
        }
    }
 
    for (int n = 0; n < nConvectiveFields; ++n)
    {
        // ToDo: here we should add a check that V has right dimension
 
        int nPointsTot = fields[0]->GetNpoints();
        Array<OneD, NekDouble> gradV0, gradV1, gradV2, tmp, Up;
 
        gradV0 = Array<OneD, NekDouble>(nPointsTot);
        tmp    = Array<OneD, NekDouble>(nPointsTot);
 
        // Evaluate V\cdot Grad(u)
        switch (ndim)
        {
            case 1:
                fields[0]->PhysDeriv(inarray[n], gradV0);
                Vmath::Vmul(nPointsTot, gradV0, 1, velocity[0], 1, outarray[n],
                            1);
                Vmath::Vmul(nPointsTot, inarray[n], 1, velocity[0], 1, gradV0,
                            1);
                fields[0]->PhysDeriv(gradV0, tmp);
                Vmath::Vadd(nPointsTot, tmp, 1, outarray[n], 1, outarray[n], 1);
                Vmath::Smul(nPointsTot, 0.5, outarray[n], 1, outarray[n], 1);
                break;
            case 2:
                gradV1 = Array<OneD, NekDouble>(nPointsTot);
                fields[0]->PhysDeriv(inarray[n], gradV0, gradV1);
                Vmath::Vmul(nPointsTot, gradV0, 1, velocity[0], 1, outarray[n],
                            1);
                Vmath::Vvtvp(nPointsTot, gradV1, 1, velocity[1], 1, outarray[n],
                             1, outarray[n], 1);
                Vmath::Vmul(nPointsTot, inarray[n], 1, velocity[0], 1, gradV0,
                            1);
                Vmath::Vmul(nPointsTot, inarray[n], 1, velocity[1], 1, gradV1,
                            1);
                fields[0]->PhysDeriv(MultiRegions::DirCartesianMap[0], gradV0,
                                     tmp);
                Vmath::Vadd(nPointsTot, tmp, 1, outarray[n], 1, outarray[n], 1);
                fields[0]->PhysDeriv(MultiRegions::DirCartesianMap[1], gradV1,
                                     tmp);
                Vmath::Vadd(nPointsTot, tmp, 1, outarray[n], 1, outarray[n], 1);
                Vmath::Smul(nPointsTot, 0.5, outarray[n], 1, outarray[n], 1);
                break;
            case 3:
                gradV1 = Array<OneD, NekDouble>(nPointsTot);
                gradV2 = Array<OneD, NekDouble>(nPointsTot);
 
                fields[0]->PhysDeriv(inarray[n], gradV0, gradV1, gradV2);
 
                // outarray[n] = 1/2(u*du/dx + v*du/dy + w*du/dz + duu/dx +
                // duv/dy + duw/dz)
 
                if (m_homogen_dealiasing == true &&
                    fields[0]->GetWaveSpace() == false)
                {
                    fields[0]->DealiasedProd(velocity[0], gradV0, gradV0);
                    fields[0]->DealiasedProd(velocity[1], gradV1, gradV1);
                    fields[0]->DealiasedProd(velocity[2], gradV2, gradV2);
                    Vmath::Vadd(nPointsTot, gradV0, 1, gradV1, 1, outarray[n],
                                1);
                    Vmath::Vadd(nPointsTot, gradV2, 1, outarray[n], 1,
                                outarray[n], 1);
                    fields[0]->DealiasedProd(inarray[n], velocity[0], gradV0);
                    fields[0]->DealiasedProd(inarray[n], velocity[1], gradV1);
                    fields[0]->DealiasedProd(inarray[n], velocity[2], gradV2);
                    fields[0]->PhysDeriv(MultiRegions::DirCartesianMap[0],
                                         gradV0, tmp);
                    Vmath::Vadd(nPointsTot, tmp, 1, outarray[n], 1, outarray[n],
                                1);
                    fields[0]->PhysDeriv(MultiRegions::DirCartesianMap[1],
                                         gradV1, tmp);
                    Vmath::Vadd(nPointsTot, tmp, 1, outarray[n], 1, outarray[n],
                                1);
                    fields[0]->PhysDeriv(MultiRegions::DirCartesianMap[2],
                                         gradV2, tmp);
                    Vmath::Vadd(nPointsTot, tmp, 1, outarray[n], 1, outarray[n],
                                1);
                    Vmath::Smul(nPointsTot, 0.5, outarray[n], 1, outarray[n],
                                1);
                }
                else if (fields[0]->GetWaveSpace() == true &&
                         m_homogen_dealiasing == false)
                {
                    Up = Array<OneD, NekDouble>(nPointsTot);
                    // vector reused to avoid even more memory requirements
                    // names may be misleading
                    fields[0]->HomogeneousBwdTrans(gradV0, tmp);
                    Vmath::Vmul(nPointsTot, tmp, 1, velocity[0], 1, outarray[n],
                                1); // + u*du/dx
                    fields[0]->HomogeneousBwdTrans(gradV1, tmp);
                    Vmath::Vvtvp(nPointsTot, tmp, 1, velocity[1], 1,
                                 outarray[n], 1, outarray[n], 1); // + v*du/dy
                    fields[0]->HomogeneousBwdTrans(gradV2, tmp);
                    Vmath::Vvtvp(nPointsTot, tmp, 1, velocity[2], 1,
                                 outarray[n], 1, outarray[n], 1); // + w*du/dz
 
                    fields[0]->HomogeneousBwdTrans(inarray[n], Up);
                    Vmath::Vmul(nPointsTot, Up, 1, velocity[0], 1, gradV0, 1);
                    Vmath::Vmul(nPointsTot, Up, 1, velocity[1], 1, gradV1, 1);
                    Vmath::Vmul(nPointsTot, Up, 1, velocity[2], 1, gradV2, 1);
 
                    fields[0]->SetWaveSpace(false);
                    fields[0]->PhysDeriv(MultiRegions::DirCartesianMap[0],
                                         gradV0, tmp); // duu/dx
                    Vmath::Vadd(nPointsTot, tmp, 1, outarray[n], 1, outarray[n],
                                1);
                    fields[0]->PhysDeriv(MultiRegions::DirCartesianMap[1],
                                         gradV1, tmp); // duv/dy
                    Vmath::Vadd(nPointsTot, tmp, 1, outarray[n], 1, outarray[n],
                                1);
                    fields[0]->PhysDeriv(MultiRegions::DirCartesianMap[2],
                                         gradV2, tmp); // duw/dz
                    Vmath::Vadd(nPointsTot, tmp, 1, outarray[n], 1, outarray[n],
                                1);
                    fields[0]->SetWaveSpace(true);
 
                    Vmath::Smul(nPointsTot, 0.5, outarray[n], 1, tmp, 1);
                    fields[0]->HomogeneousFwdTrans(tmp, outarray[n]);
                }
                else if (fields[0]->GetWaveSpace() == false &&
                         m_homogen_dealiasing == false)
                {
                    Vmath::Vmul(nPointsTot, gradV0, 1, velocity[0], 1,
                                outarray[n], 1);
                    Vmath::Vvtvp(nPointsTot, gradV1, 1, velocity[1], 1,
                                 outarray[n], 1, outarray[n], 1);
                    Vmath::Vvtvp(nPointsTot, gradV2, 1, velocity[2], 1,
                                 outarray[n], 1, outarray[n], 1);
                    Vmath::Vmul(nPointsTot, inarray[n], 1, velocity[0], 1,
                                gradV0, 1);
                    Vmath::Vmul(nPointsTot, inarray[n], 1, velocity[1], 1,
                                gradV1, 1);
                    Vmath::Vmul(nPointsTot, inarray[n], 1, velocity[2], 1,
                                gradV2, 1);
                    fields[0]->PhysDeriv(MultiRegions::DirCartesianMap[0],
                                         gradV0, tmp);
                    Vmath::Vadd(nPointsTot, tmp, 1, outarray[n], 1, outarray[n],
                                1);
                    fields[0]->PhysDeriv(MultiRegions::DirCartesianMap[1],
                                         gradV1, tmp);
                    Vmath::Vadd(nPointsTot, tmp, 1, outarray[n], 1, outarray[n],
                                1);
                    fields[0]->PhysDeriv(MultiRegions::DirCartesianMap[2],
                                         gradV2, tmp);
                    Vmath::Vadd(nPointsTot, tmp, 1, outarray[n], 1, outarray[n],
                                1);
                    Vmath::Smul(nPointsTot, 0.5, outarray[n], 1, outarray[n],
                                1);
                }
                else
                {
                    ASSERTL0(false,
                             "Dealiasing is not allowed in combination "
                             "with the Skew-Symmetric advection form for "
                             "efficiency reasons.");
                }
                break;
            default:
                ASSERTL0(false, "dimension unknown");
        }
 
        Vmath::Neg(nqtot, outarray[n], 1);
    }
}
 
} // namespace Nektar