LinearisedAdvection.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File LinearisedAdvection.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).
//
// License for the specific language governing rights and limitations under
// 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,
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// Software is furnished to do so, subject to the following conditions:
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// The above copyright notice and this permission notice shall be included
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//
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// 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
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// DEALINGS IN THE SOFTWARE.
//
// Description: Evaluation of the linearised advective term
//
///////////////////////////////////////////////////////////////////////////////

#include <IncNavierStokesSolver/AdvectionTerms/LinearisedAdvection.h>
#include <StdRegions/StdSegExp.h>

#include <MultiRegions/ContField3DHomogeneous1D.h>
#include <MultiRegions/ContField3DHomogeneous2D.h>
#include <MultiRegions/ContField1D.h>
#include <MultiRegions/ContField2D.h>
#include <MultiRegions/ContField3D.h>
#include <MultiRegions/DisContField1D.h>
#include <MultiRegions/DisContField2D.h>
#include <MultiRegions/DisContField3DHomogeneous1D.h>
#include <MultiRegions/DisContField3DHomogeneous2D.h>


namespace Nektar
{
string LinearisedAdvection::className
        = SolverUtils::GetAdvectionFactory().RegisterCreatorFunction(
                "Linearised",
                LinearisedAdvection::create);

/**
 * Constructor. Creates ...
 *
 * \param
 * \param
 */

LinearisedAdvection::LinearisedAdvection():
    Advection()
{
}


void LinearisedAdvection::v_InitObject(
        LibUtilities::SessionReaderSharedPtr        pSession,
        Array<OneD, MultiRegions::ExpListSharedPtr> pFields)
{
    Advection::v_InitObject(pSession, pFields);

    m_session            = pSession;
    m_boundaryConditions = MemoryManager<SpatialDomains::BoundaryConditions>
        ::AllocateSharedPtr(m_session, pFields[0]->GetGraph());
    m_spacedim           = pFields[0]->GetGraph()->GetSpaceDimension();
    m_expdim             = pFields[0]->GetGraph()->GetMeshDimension();
    m_CoeffState         = MultiRegions::eLocal;

    //Setting parameters for homogeneous problems
    m_HomoDirec          = 0;
    m_useFFT             = false;
    m_HomogeneousType    = eNotHomogeneous;
    m_SingleMode         = false;
    m_HalfMode           = false;
    m_MultipleModes      = false;
    m_homogen_dealiasing = false;

    if(m_session->DefinesSolverInfo("HOMOGENEOUS"))
    {
        std::string HomoStr = m_session->GetSolverInfo("HOMOGENEOUS");
        m_spacedim          = 3;

        if((HomoStr == "HOMOGENEOUS1D")||(HomoStr == "Homogeneous1D")||
           (HomoStr == "1D")||(HomoStr == "Homo1D"))
        {
            m_HomogeneousType = eHomogeneous1D;
            m_LhomZ           = m_session->GetParameter("LZ");
            m_HomoDirec       = 1;

            m_homogen_dealiasing = pSession->DefinesSolverInfo("DEALIASING");

            if(m_session->DefinesSolverInfo("ModeType"))
            {
                m_session->MatchSolverInfo("ModeType","SingleMode",m_SingleMode,false);
                m_session->MatchSolverInfo("ModeType","HalfMode",m_HalfMode,false);
                m_session->MatchSolverInfo("ModeType","MultipleModes",m_MultipleModes,false);
            }

            if(m_session->DefinesSolverInfo("ModeType"))
            {
                if(m_SingleMode)
                {
                    m_npointsZ=2;

                }
                else if(m_HalfMode)
                {
                    m_npointsZ=1;

                }
                else if(m_MultipleModes)
                {
                    m_npointsZ        = m_session->GetParameter("HomModesZ");
                }
                else
                {
                    ASSERTL0(false, "SolverInfo ModeType not valid");


                }
            }
            else
            {
                m_session->LoadParameter("HomModesZ",m_npointsZ);

            }

        }

        if((HomoStr == "HOMOGENEOUS2D")||(HomoStr == "Homogeneous2D")||
           (HomoStr == "2D")||(HomoStr == "Homo2D"))
        {
            m_HomogeneousType = eHomogeneous2D;
            m_session->LoadParameter("HomModesY", m_npointsY);
            m_session->LoadParameter("LY",        m_LhomY);
            m_session->LoadParameter("HomModesZ", m_npointsZ);
            m_session->LoadParameter("LZ",        m_LhomZ);
            m_HomoDirec       = 2;
        }

        if((HomoStr == "HOMOGENEOUS3D")||(HomoStr == "Homogeneous3D")||
           (HomoStr == "3D")||(HomoStr == "Homo3D"))
        {
            m_HomogeneousType = eHomogeneous3D;
            m_session->LoadParameter("HomModesX",m_npointsX);
            m_session->LoadParameter("LX",       m_LhomX   );
            m_session->LoadParameter("HomModesY",m_npointsY);
            m_session->LoadParameter("LY",       m_LhomY   );
            m_session->LoadParameter("HomModesZ",m_npointsZ);
            m_session->LoadParameter("LZ",       m_LhomZ   );
            m_HomoDirec       = 3;
        }

        if(m_session->DefinesSolverInfo("USEFFT"))
        {
            m_useFFT = true;
        }
    }
    else
    {
        m_npointsZ = 1; // set to default value so can use to identify 2d or 3D (homogeneous) expansions
    }

    if(m_session->DefinesSolverInfo("PROJECTION"))
    {
        std::string ProjectStr
        = m_session->GetSolverInfo("PROJECTION");

        if((ProjectStr == "Continuous")||(ProjectStr == "Galerkin")||
           (ProjectStr == "CONTINUOUS")||(ProjectStr == "GALERKIN"))
        {
            m_projectionType = MultiRegions::eGalerkin;
        }
        else if(ProjectStr == "DisContinuous")
        {
            m_projectionType = MultiRegions::eDiscontinuous;
        }
        else
        {
            ASSERTL0(false,"PROJECTION value not recognised");
        }
    }
    else
    {
        cerr << "Projection type not specified in SOLVERINFO,"
            "defaulting to continuous Galerkin" << endl;
        m_projectionType = MultiRegions::eGalerkin;
    }

    int nvar = m_session->GetVariables().size();
    m_baseflow = Array<OneD, Array<OneD, NekDouble> >(nvar);
    for (int i = 0; i < nvar; ++i)
    {
        m_baseflow[i] = Array<OneD, NekDouble>(pFields[i]->GetTotPoints(), 0.0);
    }

    ASSERTL0(m_session->DefinesFunction("BaseFlow"),
             "Base flow must be defined for linearised forms.");
    string file = m_session->GetFunctionFilename("BaseFlow", 0);


    //Periodic base flows
    if(m_session->DefinesParameter("N_slices"))
    {
        m_session->LoadParameter("N_slices",m_slices);
        if(m_slices>1)
        {
            DFT(file,pFields,m_slices);
        }
        else
        {
            ASSERTL0(false,"Number of slices must be a positive number greater than 1");
        }
    }
    //Steady base-flow
    else
    {
        m_slices=1;

        //BaseFlow from file
        if (m_session->GetFunctionType("BaseFlow", m_session->GetVariable(0))
            == LibUtilities::eFunctionTypeFile)
        {
            ImportFldBase(file,pFields,1);

        }
        //analytic base flow
        else
        {
            int nq = pFields[0]->GetNpoints();
            Array<OneD,NekDouble> x0(nq);
            Array<OneD,NekDouble> x1(nq);
            Array<OneD,NekDouble> x2(nq);

            // get the coordinates (assuming all fields have the same
            // discretisation)
            pFields[0]->GetCoords(x0,x1,x2);

            for(unsigned int i = 0 ; i < pFields.num_elements(); i++)
            {
                LibUtilities::EquationSharedPtr ifunc
                    = m_session->GetFunction("BaseFlow", i);

                ifunc->Evaluate(x0,x1,x2,m_baseflow[i]);
            }
        }
    }

    if(m_session->DefinesParameter("period"))
    {
        m_period=m_session->GetParameter("period");
    }
    else
    {
        m_period=(m_session->GetParameter("TimeStep")*m_slices)/(m_slices-1.);
    }

}

LinearisedAdvection::~LinearisedAdvection()
{
}


//Advection function

void LinearisedAdvection::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)
{
    int nqtot            = fields[0]->GetTotPoints();
    ASSERTL1(nConvectiveFields == inarray.num_elements(),"Number of convective fields and Inarray are not compatible");

    Array<OneD, NekDouble > Deriv = Array<OneD, NekDouble> (nqtot*nConvectiveFields);

    for(int n = 0; n < nConvectiveFields; ++n)
    {
        int ndim       = advVel.num_elements();
        int nPointsTot = fields[0]->GetNpoints();

        Array<OneD, NekDouble> grad0,grad1,grad2;

        //Evaluation of the gradiend of each component of the base flow
        //\nabla U
        Array<OneD, NekDouble> grad_base_u0,grad_base_u1,grad_base_u2;

        // \nabla V
        Array<OneD, NekDouble> grad_base_v0,grad_base_v1,grad_base_v2;

        // \nabla W
        Array<OneD, NekDouble> grad_base_w0,grad_base_w1,grad_base_w2;

        grad0 = Array<OneD, NekDouble> (nPointsTot);
        grad_base_u0 = Array<OneD, NekDouble> (nPointsTot);
        grad_base_v0 = Array<OneD, NekDouble> (nPointsTot);
        grad_base_w0 = Array<OneD, NekDouble> (nPointsTot);

        //Evaluation of the base flow for periodic cases
        //(it requires fld files)
        if(m_slices>1)
        {
            if (m_session->GetFunctionType("BaseFlow", 0)
                == LibUtilities::eFunctionTypeFile)
            {
                for(int i=0; i<ndim;++i)
                {
                    UpdateBase(m_slices,m_interp[i],m_baseflow[i],time,m_period);
                }
            }
            else
            {
                ASSERTL0(false, "Periodic Base flow requires filename_ files");
            }
        }


        //Evaluate the linearised advection term
        switch(ndim)
        {
            // 1D
        case 1:
            fields[0]->PhysDeriv(inarray[n],grad0);
            fields[0]->PhysDeriv(m_baseflow[0],grad_base_u0);
            //Evaluate  U du'/dx
            Vmath::Vmul(nPointsTot,grad0,1,m_baseflow[0],1,outarray[n],1);
            //Evaluate U du'/dx+ u' dU/dx
            Vmath::Vvtvp(nPointsTot,grad_base_u0,1,advVel[0],1,outarray[n],1,outarray[n],1);
            break;

            //2D
        case 2:
            grad1 = Array<OneD, NekDouble> (nPointsTot);
            grad_base_u1 = Array<OneD, NekDouble> (nPointsTot);
            grad_base_v1 = Array<OneD, NekDouble> (nPointsTot);
            fields[0]->PhysDeriv(inarray[n],grad0,grad1);

            //Derivates of the base flow
            fields[0]-> PhysDeriv(m_baseflow[0], grad_base_u0, grad_base_u1);
            fields[0]-> PhysDeriv(m_baseflow[1], grad_base_v0, grad_base_v1);

            //Since the components of the velocity are passed one by
            //one, it is necessary to distinguish which term is
            //consider
            switch (n)
            {
                //x-equation
            case 0:
                // Evaluate U du'/dx
                Vmath::Vmul (nPointsTot,grad0,1,m_baseflow[0],1,outarray[n],1);
                //Evaluate U du'/dx+ V du'/dy
                Vmath::Vvtvp(nPointsTot,grad1,1,m_baseflow[1],1,outarray[n],1,outarray[n],1);
                //Evaluate (U du'/dx+ V du'/dy)+u' dU/dx
                Vmath::Vvtvp(nPointsTot,grad_base_u0,1,advVel[0],1,outarray[n],1,outarray[n],1);
                //Evaluate (U du'/dx+ V du'/dy +u' dU/dx)+v' dU/dy
                Vmath::Vvtvp(nPointsTot,grad_base_u1,1,advVel[1],1,outarray[n],1,outarray[n],1);
                break;

                //y-equation
            case 1:
                // Evaluate U dv'/dx
                Vmath::Vmul (nPointsTot,grad0,1,m_baseflow[0],1,outarray[n],1);
                //Evaluate U dv'/dx+ V dv'/dy
                Vmath::Vvtvp(nPointsTot,grad1,1,m_baseflow[1],1,outarray[n],1,outarray[n],1);
                //Evaluate (U dv'/dx+ V dv'/dy)+u' dV/dx
                Vmath::Vvtvp(nPointsTot,grad_base_v0,1,advVel[0],1,outarray[n],1,outarray[n],1);
                //Evaluate (U dv'/dx+ V dv'/dy +u' dv/dx)+v' dV/dy
                Vmath::Vvtvp(nPointsTot,grad_base_v1,1,advVel[1],1,outarray[n],1,outarray[n],1);
                break;
            }
            break;

            //3D
        case 3:
        {
            grad1 = Array<OneD, NekDouble> (nPointsTot);
            grad2 = Array<OneD, NekDouble> (nPointsTot);
            grad_base_u1 = Array<OneD, NekDouble> (nPointsTot);
            grad_base_v1 = Array<OneD, NekDouble> (nPointsTot);
            grad_base_w1 = Array<OneD, NekDouble> (nPointsTot);

            grad_base_u2 = Array<OneD, NekDouble> (nPointsTot);
            grad_base_v2 = Array<OneD, NekDouble> (nPointsTot);
            grad_base_w2 = Array<OneD, NekDouble> (nPointsTot);

            // Differentiate base flow in physical space
            bool oldwavespace = fields[0]->GetWaveSpace();
            fields[0]->SetWaveSpace(false);
            fields[0]->PhysDeriv(m_baseflow[0],
                                 grad_base_u0, grad_base_u1, grad_base_u2);
            fields[0]->PhysDeriv(m_baseflow[1],
                                 grad_base_v0, grad_base_v1, grad_base_v2);
            fields[0]->PhysDeriv(m_baseflow[2],
                                 grad_base_w0, grad_base_w1, grad_base_w2);
            fields[0]->SetWaveSpace(oldwavespace);

            //HalfMode has W(x,y,t)=0
            if(m_HalfMode || m_SingleMode)
            {
                for(int i=0; i<grad_base_u2.num_elements();++i)
                {
                    grad_base_u2[i]=0;
                    grad_base_v2[i]=0;
                    grad_base_w2[i]=0;
                }
            }

            fields[0]->PhysDeriv(inarray[n], grad0, grad1, grad2);
            if (oldwavespace)
            {
                fields[0]->HomogeneousBwdTrans(grad0, grad0);
                fields[0]->HomogeneousBwdTrans(grad1, grad1);
                fields[0]->HomogeneousBwdTrans(grad2, grad2);
            }

            switch (n)
            {
                //x-equation
            case 0:
                if(m_homogen_dealiasing)
                {
                    //U du'/dx
                    fields[0]->DealiasedProd(m_baseflow[0],grad0,grad0,m_CoeffState);

                    //V du'/dy
                    fields[0]->DealiasedProd(m_baseflow[1],grad1,grad1,m_CoeffState);

                    //W du'/dx
                    fields[0]->DealiasedProd(m_baseflow[2],grad2,grad2,m_CoeffState);

                    // u' dU/dx
                    fields[0]->DealiasedProd(advVel[0],grad_base_u0,grad_base_u0,m_CoeffState);
                    // v' dU/dy
                    fields[0]->DealiasedProd(advVel[1],grad_base_u1,grad_base_u1,m_CoeffState);
                    // w' dU/dz
                    fields[0]->DealiasedProd(advVel[2],grad_base_u2,grad_base_u2,m_CoeffState);

                    Vmath::Vadd(nPointsTot,grad0,1,grad1,1,outarray[n],1);
                    Vmath::Vadd(nPointsTot,grad2,1,outarray[n],1,outarray[n],1);
                    Vmath::Vadd(nPointsTot,grad_base_u0,1,outarray[n],1,outarray[n],1);
                    Vmath::Vadd(nPointsTot,grad_base_u1,1,outarray[n],1,outarray[n],1);
                    Vmath::Vadd(nPointsTot,grad_base_u2,1,outarray[n],1,outarray[n],1);
                }
                else
                {
                    //Evaluate U du'/dx
                    Vmath::Vmul (nPointsTot, grad0,       1,  m_baseflow[0], 1,
                                             outarray[n], 1);
                    //Evaluate U du'/dx+ V du'/dy
                    Vmath::Vvtvp(nPointsTot, grad1,       1,  m_baseflow[1], 1,
                                             outarray[n], 1,  outarray[n],   1);
                    //Evaluate (U du'/dx+ V du'/dy)+u' dU/dx
                    Vmath::Vvtvp(nPointsTot,grad_base_u0,1,advVel[0],1,outarray[n],1,outarray[n],1);
                    //Evaluate (U du'/dx+ V du'/dy +u' dU/dx)+v' dU/dy
                    Vmath::Vvtvp(nPointsTot,grad_base_u1,1,advVel[1],1,outarray[n],1,outarray[n],1);
                    //Evaluate (U du'/dx+ V du'/dy +u' dU/dx +v' dU/dy) + W du'/dz
                    Vmath::Vvtvp(nPointsTot, grad2,       1,  m_baseflow[2], 1,
                                             outarray[n], 1,  outarray[n],   1);
                    //Evaluate (U du'/dx+ V du'/dy +u' dU/dx +v' dU/dy + W du'/dz)+ w' dU/dz
                    Vmath::Vvtvp(nPointsTot,grad_base_u2,1,advVel[2],1,outarray[n],1,outarray[n],1);
                }
                break;
                //y-equation
            case 1:
                if(m_homogen_dealiasing)
                {
                    //U dv'/dx
                    fields[0]->DealiasedProd(m_baseflow[0],grad0,grad0,m_CoeffState);
                    //V dv'/dy
                    fields[0]->DealiasedProd(m_baseflow[1],grad1,grad1,m_CoeffState);
                    //W dv'/dx
                    fields[0]->DealiasedProd(m_baseflow[2],grad2,grad2,m_CoeffState);
                    // u' dV/dx
                    fields[0]->DealiasedProd(advVel[0],grad_base_v0,grad_base_v0,m_CoeffState);
                    // v' dV/dy
                    fields[0]->DealiasedProd(advVel[1],grad_base_v1,grad_base_v1,m_CoeffState);
                    // w' dV/dz
                    fields[0]->DealiasedProd(advVel[2],grad_base_v2,grad_base_v2,m_CoeffState);

                    Vmath::Vadd(nPointsTot,grad0,1,grad1,1,outarray[n],1);
                    Vmath::Vadd(nPointsTot,grad2,1,outarray[n],1,outarray[n],1);
                    Vmath::Vadd(nPointsTot,grad_base_v0,1,outarray[n],1,outarray[n],1);
                    Vmath::Vadd(nPointsTot,grad_base_v1,1,outarray[n],1,outarray[n],1);
                    Vmath::Vadd(nPointsTot,grad_base_v2,1,outarray[n],1,outarray[n],1);
                }
                else
                {
                    //Evaluate U dv'/dx
                    Vmath::Vmul (nPointsTot, grad0,       1,  m_baseflow[0], 1,
                                             outarray[n], 1);
                    //Evaluate U dv'/dx+ V dv'/dy
                    Vmath::Vvtvp(nPointsTot, grad1,       1,  m_baseflow[1], 1,
                                             outarray[n], 1,  outarray[n],   1);
                    //Evaluate (U dv'/dx+ V dv'/dy)+u' dV/dx
                    Vmath::Vvtvp(nPointsTot,grad_base_v0,1,advVel[0],1,outarray[n],1,outarray[n],1);
                    //Evaluate (U du'/dx+ V du'/dy +u' dV/dx)+v' dV/dy
                    Vmath::Vvtvp(nPointsTot,grad_base_v1,1,advVel[1],1,outarray[n],1,outarray[n],1);
                    //Evaluate (U du'/dx+ V dv'/dy +u' dV/dx +v' dV/dy) + W du'/dz
                    Vmath::Vvtvp(nPointsTot, grad2,       1,  m_baseflow[2], 1,
                                             outarray[n], 1,  outarray[n],   1);
                    //Evaluate (U du'/dx+ V dv'/dy +u' dV/dx +v' dV/dy + W dv'/dz)+ w' dV/dz
                    Vmath::Vvtvp(nPointsTot,grad_base_v2,1,advVel[2],1,outarray[n],1,outarray[n],1);
                }
                break;

                //z-equation
            case 2:
                if(m_homogen_dealiasing)
                {
                    //U dw'/dx
                    fields[0]->DealiasedProd(m_baseflow[0],grad0,grad0,m_CoeffState);
                    //V dw'/dy
                    fields[0]->DealiasedProd(m_baseflow[1],grad1,grad1,m_CoeffState);
                    //W dw'/dx
                    fields[0]->DealiasedProd(m_baseflow[2],grad2,grad2,m_CoeffState);
                    // u' dW/dx
                    fields[0]->DealiasedProd(advVel[0],grad_base_w0,grad_base_w0,m_CoeffState);
                    // v' dW/dy
                    fields[0]->DealiasedProd(advVel[1],grad_base_w1,grad_base_w1,m_CoeffState);
                    // w' dW/dz
                    fields[0]->DealiasedProd(advVel[2],grad_base_w2,grad_base_w2,m_CoeffState);

                    Vmath::Vadd(nPointsTot,grad0,1,grad1,1,outarray[n],1);
                    Vmath::Vadd(nPointsTot,grad2,1,outarray[n],1,outarray[n],1);
                    Vmath::Vadd(nPointsTot,grad_base_w0,1,outarray[n],1,outarray[n],1);
                    Vmath::Vadd(nPointsTot,grad_base_w1,1,outarray[n],1,outarray[n],1);
                    Vmath::Vadd(nPointsTot,grad_base_w2,1,outarray[n],1,outarray[n],1);
                }
                else
                {
                    //Evaluate U dw'/dx
                    Vmath::Vmul (nPointsTot, grad0,        1, m_baseflow[0], 1,
                                             outarray[n],  1);
                    //Evaluate U dw'/dx+ V dw'/dx
                    Vmath::Vvtvp(nPointsTot, grad1,        1, m_baseflow[1], 1,
                                             outarray[n],  1, outarray[n],   1);
                    //Evaluate (U dw'/dx+ V dw'/dx)+u' dW/dx
                    Vmath::Vvtvp(nPointsTot,grad_base_w0,1,advVel[0],1,outarray[n],1,outarray[n],1);
                    //Evaluate (U dw'/dx+ V dw'/dx +w' dW/dx)+v' dW/dy
                    Vmath::Vvtvp(nPointsTot,grad_base_w1,1,advVel[1],1,outarray[n],1,outarray[n],1);
                    //Evaluate (U dw'/dx+ V dw'/dx +u' dW/dx +v' dW/dy) + W dw'/dz
                    Vmath::Vvtvp(nPointsTot, grad2,        1, m_baseflow[2], 1,
                                             outarray[n],  1, outarray[n],   1);
                    //Evaluate (U dw'/dx+ V dw'/dx +u' dW/dx +v' dW/dy + W dw'/dz)+ w' dW/dz
                    Vmath::Vvtvp(nPointsTot,grad_base_w2,1,advVel[2],1,outarray[n],1,outarray[n],1);
                }
                break;
            }

            if (oldwavespace)
            {
                fields[0]->HomogeneousFwdTrans(outarray[n],outarray[n]);
            }
            break;
        }
        default:
            ASSERTL0(false,"dimension unknown");
        }

        Vmath::Neg(nqtot,outarray[n],1);
    }
}

void LinearisedAdvection::v_SetBaseFlow(
    const Array<OneD, Array<OneD, NekDouble> >    &inarray)
{
    if (m_session->GetSolverInfo("EqType") == "UnsteadyNavierStokes")
    {
        // The SFD method is only applied to the velocity variables in
        // incompressible
        ASSERTL1(inarray.num_elements() == (m_baseflow.num_elements() - 1),
                 "Number of base flow variables does not match what is "
                 "expected.");
    }
    else
    {
        ASSERTL1(inarray.num_elements() == (m_baseflow.num_elements()),
             "Number of base flow variables does not match what is expected.");
    }

    int npts = inarray[0].num_elements();

    for (int i = 0; i < inarray.num_elements(); ++i)
    {
        ASSERTL1(npts == m_baseflow[i].num_elements(),
             "Size of base flow array does not match expected.");
        Vmath::Vcopy(npts, inarray[i], 1, m_baseflow[i], 1);
    }
}


/**
 * Import field from infile and load into \a m_fields. This routine will
 * also perform a \a BwdTrans to ensure data is in both the physical and
 * coefficient storage.
 * @param   infile          Filename to read.
 */
void LinearisedAdvection::ImportFldBase(std::string pInfile,
        Array<OneD, MultiRegions::ExpListSharedPtr>& pFields, int slice)
{
    std::vector<LibUtilities::FieldDefinitionsSharedPtr> FieldDef;
    std::vector<std::vector<NekDouble> > FieldData;

    int nqtot = m_baseflow[0].num_elements();
    int nvar = m_session->GetVariables().size();
    int s;
    Array<OneD, NekDouble> tmp_coeff(pFields[0]->GetNcoeffs(), 0.0);

    //Get Homogeneous
    LibUtilities::FieldIOSharedPtr fld =
    MemoryManager<LibUtilities::FieldIO>::AllocateSharedPtr(
                                                    m_session->GetComm());
    fld->Import(pInfile, FieldDef, FieldData);


    if(m_session->DefinesSolverInfo("HOMOGENEOUS"))
    {
        std::string HomoStr = m_session->GetSolverInfo("HOMOGENEOUS");
    }

    // copy FieldData into m_fields
    for(int j = 0; j < nvar; ++j)
    {
        for(int i = 0; i < FieldDef.size(); ++i)
        {
            if((m_session->DefinesSolverInfo("HOMOGENEOUS") &&
               (m_session->GetSolverInfo("HOMOGENEOUS")=="HOMOGENEOUS1D" ||
                m_session->GetSolverInfo("HOMOGENEOUS")=="1D" ||
                m_session->GetSolverInfo("HOMOGENEOUS")=="Homo1D")) &&
                 m_MultipleModes==false)
            {
                // w-component must be ignored and set to zero.
                if (j != nvar - 2)
                {
                    // p component (it is 4th variable of the 3D and corresponds 3nd variable of 2D)
                    s = (j == nvar - 1) ? 2 : j;

                    //extraction of the 2D
                    pFields[j]->ExtractDataToCoeffs(
                                        FieldDef[i],
                                        FieldData[i],
                                        FieldDef[i]->m_fields[s],
                                        tmp_coeff);

                }

                //Put zero on higher modes
                int ncplane = (pFields[0]->GetNcoeffs()) / m_npointsZ;

                if (m_npointsZ > 2)
                {
                    Vmath::Zero(ncplane*(m_npointsZ-2),
                                &tmp_coeff[2*ncplane], 1);
                }
            }
            // 2D cases and Homogeneous1D Base Flows
            else
            {
                bool flag = FieldDef[i]->m_fields[j] ==
                                                m_session->GetVariable(j);

                ASSERTL0(flag, (std::string("Order of ") + pInfile
                                + std::string(" data and that defined in "
                                              "m_boundaryconditions differs")).c_str());

                pFields[j]->ExtractDataToCoeffs(FieldDef[i], FieldData[i],
                                               FieldDef[i]->m_fields[j],
                                               tmp_coeff);
            }
        }

        if(m_SingleMode || m_HalfMode)
        {
            //pFields[j]->SetWaveSpace(true);

            pFields[j]->GetPlane(0)->BwdTrans(tmp_coeff, m_baseflow[j]);

            if(m_SingleMode)
            {
                //copy the bwd into the second plane for single Mode Analysis
                int ncplane=(pFields[0]->GetNpoints())/m_npointsZ;
                Vmath::Vcopy(ncplane,&m_baseflow[j][0],1,&m_baseflow[j][ncplane],1);
            }
        }
        else
        {
            bool oldwavespace = pFields[j]->GetWaveSpace();
            pFields[j]->SetWaveSpace(false);
            pFields[j]->BwdTrans(tmp_coeff, m_baseflow[j]);
            pFields[j]->SetWaveSpace(oldwavespace);
        }
    }

    if(m_session->DefinesParameter("N_slices"))
    {
        int nConvectiveFields = pFields.num_elements()-1;

        for(int i=0; i<nConvectiveFields;++i)
        {

            Vmath::Vcopy(nqtot, &m_baseflow[i][0], 1, &m_interp[i][slice*nqtot], 1);
        }

    }
}


void LinearisedAdvection::UpdateBase( const NekDouble m_slices,
                                      const Array<OneD, const NekDouble> &inarray,
                                      Array<OneD, NekDouble> &outarray,
                                      const NekDouble m_time,
                                      const NekDouble m_period)
{
    int npoints=m_baseflow[0].num_elements();

    NekDouble BetaT=2*M_PI*fmod (m_time, m_period) / m_period;
    NekDouble phase;
    Array<OneD, NekDouble> auxiliary(npoints);

    Vmath::Vcopy(npoints,&inarray[0],1,&outarray[0],1);
    Vmath::Svtvp(npoints, cos(0.5*m_slices*BetaT),&inarray[npoints],1,&outarray[0],1,&outarray[0],1);

    for (int i = 2; i < m_slices; i += 2)
    {
        phase = (i>>1) * BetaT;

        Vmath::Svtvp(npoints, cos(phase),&inarray[i*npoints],1,&outarray[0],1,&outarray[0],1);
        Vmath::Svtvp(npoints, sin(phase), &inarray[(i+1)*npoints], 1, &outarray[0], 1,&outarray[0],1);
    }

}

DNekBlkMatSharedPtr LinearisedAdvection::GetFloquetBlockMatrix(FloquetMatType mattype, bool UseContCoeffs) const
{
    DNekMatSharedPtr    loc_mat;
    DNekBlkMatSharedPtr BlkMatrix;
    int n_exp = 0;

    n_exp = m_baseflow[0].num_elements(); // will operatore on m_phys

    Array<OneD,unsigned int> nrows(n_exp);
    Array<OneD,unsigned int> ncols(n_exp);

    nrows = Array<OneD, unsigned int>(n_exp,m_slices);
    ncols = Array<OneD, unsigned int>(n_exp,m_slices);

    MatrixStorage blkmatStorage = eDIAGONAL;
    BlkMatrix = MemoryManager<DNekBlkMat>
        ::AllocateSharedPtr(nrows,ncols,blkmatStorage);


    const LibUtilities::PointsKey Pkey(m_slices,LibUtilities::eFourierEvenlySpaced);
    const LibUtilities::BasisKey  BK(LibUtilities::eFourier,m_slices,Pkey);
    StdRegions::StdSegExp StdSeg(BK);

    StdRegions::StdMatrixKey matkey(StdRegions::eFwdTrans,
                                    StdSeg.DetShapeType(),
                                    StdSeg);

    loc_mat = StdSeg.GetStdMatrix(matkey);

    // set up array of block matrices.
    for(int i = 0; i < n_exp; ++i)
    {
        BlkMatrix->SetBlock(i,i,loc_mat);
    }

    return BlkMatrix;
}

//Discrete Fourier Transform for Floquet analysis
void LinearisedAdvection::DFT(const string file,
        Array<OneD, MultiRegions::ExpListSharedPtr>& pFields,
        const NekDouble m_slices)
{
    int npoints=m_baseflow[0].num_elements();

    //Convected fields
    int ConvectedFields=m_baseflow.num_elements()-1;

    m_interp= Array<OneD, Array<OneD, NekDouble> > (ConvectedFields);
    for(int i=0; i<ConvectedFields;++i)
    {
        m_interp[i]=Array<OneD,NekDouble>(npoints*m_slices);
    }

    // Import the slides into auxiliary vector
    // The base flow should be stored in the form "filename_%d.ext"
    // A subdirectory can also be included, such as "dir/filename_%d.ext"
    size_t found = file.find("%d");
    ASSERTL0(found != string::npos && file.find("%d", found+1) == string::npos,
             "Since N_slices is specified, the filename provided for function "
             "'BaseFlow' must include exactly one instance of the format "
             "specifier '%d', to index the time-slices.");
    char* buffer = new char[file.length() + 8];
    for (int i = 0; i < m_slices; ++i)
    {
        sprintf(buffer, file.c_str(), i);
        ImportFldBase(buffer,pFields,i);
    }
    delete[] buffer;


    // Discrete Fourier Transform of the fields
    for(int k=0; k< ConvectedFields;++k)
    {
#ifdef NEKTAR_USING_FFTW

        //Discrete Fourier Transform using FFTW
        Array<OneD, NekDouble> fft_in(npoints*m_slices);
        Array<OneD, NekDouble> fft_out(npoints*m_slices);

        Array<OneD, NekDouble> m_tmpIN(m_slices);
        Array<OneD, NekDouble> m_tmpOUT(m_slices);

        //Shuffle the data
        for(int j= 0; j < m_slices; ++j)
        {
            Vmath::Vcopy(npoints,&m_interp[k][j*npoints],1,&(fft_in[j]),m_slices);
        }

        m_FFT = LibUtilities::GetNektarFFTFactory().CreateInstance("NekFFTW", m_slices);

        //FFT Transform
        for(int i=0; i<npoints; i++)
        {
            m_FFT->FFTFwdTrans(m_tmpIN =fft_in + i*m_slices, m_tmpOUT =fft_out + i*m_slices);

        }

        //Reshuffle data
        for(int s = 0; s < m_slices; ++s)
        {
            Vmath::Vcopy(npoints,&fft_out[s],m_slices,&m_interp[k][s*npoints],1);

        }

        Vmath::Zero(fft_in.num_elements(),&fft_in[0],1);
        Vmath::Zero(fft_out.num_elements(),&fft_out[0],1);
#else
        //Discrete Fourier Transform using MVM
        DNekBlkMatSharedPtr blkmat;
        blkmat = GetFloquetBlockMatrix(eForwardsPhys);

        int nrows = blkmat->GetRows();
        int ncols = blkmat->GetColumns();

        Array<OneD, NekDouble> sortedinarray(ncols);
        Array<OneD, NekDouble> sortedoutarray(nrows);

        //Shuffle the data
        for(int j= 0; j < m_slices; ++j)
        {
            Vmath::Vcopy(npoints,&m_interp[k][j*npoints],1,&(sortedinarray[j]),m_slices);
        }

        // Create NekVectors from the given data arrays
        NekVector<NekDouble> in (ncols,sortedinarray,eWrapper);
        NekVector<NekDouble> out(nrows,sortedoutarray,eWrapper);

        // Perform matrix-vector multiply.
        out = (*blkmat)*in;

        //Reshuffle data
        for(int s = 0; s < m_slices; ++s)
        {
            Vmath::Vcopy(npoints,&sortedoutarray[s],m_slices,&m_interp[k][s*npoints],1);
        }

        for(int r=0; r<sortedinarray.num_elements();++r)
        {
            sortedinarray[0]=0;
            sortedoutarray[0]=0;
        }

#endif

        //scaling of the Fourier coefficients
        NekDouble j=-1;
        for (int i = 2; i < m_slices; i += 2)
        {
            Vmath::Smul(2*npoints,j,&m_interp[k][i*npoints],1,&m_interp[k][i*npoints],1);
            j=-j;

        }

    }

}

} //end of namespace