EigenValuesAdvection.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File EigenValuesAdvection.cpp
//
// For more information, please see: http://www.nektar.info
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// 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
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// Description: 
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///////////////////////////////////////////////////////////////////////////////

#include <iostream>

#include <ADRSolver/EquationSystems/EigenValuesAdvection.h>

using namespace std;

namespace Nektar
{
    string EigenValuesAdvection::className = GetEquationSystemFactory().RegisterCreatorFunction("EigenValuesAdvection", EigenValuesAdvection::create, "Eigenvalues of the weak advection operator.");

    EigenValuesAdvection::EigenValuesAdvection(
            const LibUtilities::SessionReaderSharedPtr& pSession)
        : EquationSystem(pSession)
    {
    }

    void EigenValuesAdvection::v_InitObject()
    {
        EquationSystem::v_InitObject();

        // Define Velocity fields
        m_velocity = Array<OneD, Array<OneD, NekDouble> >(m_spacedim);
        std::vector<std::string> vel;
        vel.push_back("Vx");
        vel.push_back("Vy");
        vel.push_back("Vz");
        vel.resize(m_spacedim);

        EvaluateFunction(vel, m_velocity, "AdvectionVelocity");
    }
    
    void EigenValuesAdvection::v_DoInitialise()
    {
       
    }

    EigenValuesAdvection::~EigenValuesAdvection()
    {

    }

    void EigenValuesAdvection::v_DoSolve()
    {
        int nvariables = 1;
        int i,dofs = GetNcoeffs();
        //bool UseContCoeffs = false;
        
        Array<OneD, Array<OneD, NekDouble> > inarray(nvariables);
        Array<OneD, Array<OneD, NekDouble> > tmp(nvariables);
        Array<OneD, Array<OneD, NekDouble> > outarray(nvariables);
        Array<OneD, Array<OneD, NekDouble> > WeakAdv(nvariables);
        
        int npoints = GetNpoints();
        int ncoeffs = GetNcoeffs();
        
        switch (m_projectionType)
        {
                case MultiRegions::eDiscontinuous:
                    {
                        dofs = ncoeffs;
                        break;
                    }
                case MultiRegions::eGalerkin:
                case MultiRegions::eMixed_CG_Discontinuous:
                    {
                        //dofs = GetContNcoeffs();
                        //UseContCoeffs = true;
                        break;
                    }
        }
        
        cout << endl;
        cout << "Num Phys Points = " << npoints << endl; // phisical points
        cout << "Num Coeffs      = " << ncoeffs << endl; //
        cout << "Num Cont Coeffs = " << dofs << endl;
        
        inarray[0]  = Array<OneD, NekDouble>(npoints,0.0);
        outarray[0] = Array<OneD, NekDouble>(npoints,0.0);
        tmp[0] = Array<OneD, NekDouble>(npoints,0.0);
        
        WeakAdv[0]  = Array<OneD, NekDouble>(ncoeffs,0.0);
        Array<OneD, NekDouble> MATRIX(npoints*npoints,0.0);
        
        for (int j = 0; j < npoints; j++)
        {
        
        inarray[0][j] = 1.0;
       
        /// Feeding the weak Advection oprator with  a vector (inarray)
        /// Looping on inarray and changing the position of the only non-zero entry
        /// we simulate the multiplication by the identity matrix.
        /// The results stored in outarray is one of the columns of the weak advection oprators
        /// which are then stored in MATRIX for the futher eigenvalues calculation.

        switch (m_projectionType)
        {
        case MultiRegions::eDiscontinuous:
            {
                WeakDGAdvection(inarray, WeakAdv,true,true,1);
                
                m_fields[0]->MultiplyByElmtInvMass(WeakAdv[0],WeakAdv[0]);
        
                m_fields[0]->BwdTrans(WeakAdv[0],outarray[0]);
                
                Vmath::Neg(npoints,outarray[0],1);
                break;
            }
        case MultiRegions::eGalerkin:
        case MultiRegions::eMixed_CG_Discontinuous:
            {
                // Calculate -V\cdot Grad(u);
                for(i = 0; i < nvariables; ++i)
                {
                    //Projection
                    m_fields[i]->FwdTrans(inarray[i],WeakAdv[i]);
                    
                    m_fields[i]->BwdTrans_IterPerExp(WeakAdv[i],tmp[i]);
                    
                    //Advection operator
                    AdvectionNonConservativeForm(m_velocity,tmp[i],outarray[i]);
                    
                    Vmath::Neg(npoints,outarray[i],1);
                    
                    //m_fields[i]->MultiplyByInvMassMatrix(WeakAdv[i],WeakAdv[i]);
                    //Projection
                    m_fields[i]->FwdTrans(outarray[i],WeakAdv[i]);
                    
                    m_fields[i]->BwdTrans_IterPerExp(WeakAdv[i],outarray[i]);
                }
                break;
            }
        }
    
        /// The result is stored in outarray (is the j-th columns of the weak advection operator).
        /// We now store it in MATRIX(j)
        Vmath::Vcopy(npoints,&(outarray[0][0]),1,&(MATRIX[j]),npoints);
    
        /// Set the j-th entry of inarray back to zero
        inarray[0][j] = 0.0;
        }
                
        ////////////////////////////////////////////////////////////////////////////////
        /// Calulating the eigenvalues of the weak advection operator stored in (MATRIX)
        /// using Lapack routines
        
        char jobvl = 'N';
        char jobvr = 'N';
        int info = 0, lwork = 3*npoints;
        NekDouble dum;
        
        Array<OneD, NekDouble> EIG_R(npoints);
        Array<OneD, NekDouble> EIG_I(npoints);
        
        Array<OneD, NekDouble> work(lwork);
        
        Lapack::Dgeev(jobvl,jobvr,npoints,MATRIX.get(),npoints,EIG_R.get(),EIG_I.get(),&dum,1,&dum,1,&work[0],lwork,info);
        
        ////////////////////////////////////////////////////////
        //Print Matrix
        FILE *mFile;
        
        mFile = fopen ("WeakAdvMatrix.txt","w");
        for(int j = 0; j<npoints; j++)
        {
            for(int k = 0; k<npoints; k++)
            {
                fprintf(mFile,"%e ",MATRIX[j*npoints+k]);
            }
            fprintf(mFile,"\n");
        }
        fclose (mFile);
        
        ////////////////////////////////////////////////////////
        //Output of the EigenValues
        FILE *pFile;
        
        pFile = fopen ("Eigenvalues.txt","w");
        for(int j = 0; j<npoints; j++)
        {
            fprintf(pFile,"%e %e\n",EIG_R[j],EIG_I[j]);
        }
        fclose (pFile);
        
        cout << "\nEigenvalues : " << endl;
        for(int j = 0; j<npoints; j++)
        {
            cout << EIG_R[j] << "\t" << EIG_I[j] << endl;
        }
        cout << endl;
    }

    void EigenValuesAdvection::v_GetFluxVector(const int i, Array<OneD, Array<OneD, NekDouble> > &physfield,
                                            Array<OneD, Array<OneD, NekDouble> > &flux)
    {
        ASSERTL1(flux.num_elements() == m_velocity.num_elements(),"Dimension of flux array and velocity array do not match");
        
        for(int j = 0; j < flux.num_elements(); ++j)
        {
            Vmath::Vmul(GetNpoints(),physfield[i],1,
                        m_velocity[j],1,flux[j],1);
        }
    }
    
    void EigenValuesAdvection::v_NumericalFlux(Array<OneD, Array<OneD, NekDouble> > &physfield, Array<OneD, Array<OneD, NekDouble> > &numflux)
    {
        int i;
        
        int nTraceNumPoints = GetTraceNpoints();
        int nvel = m_spacedim; //m_velocity.num_elements();
        
        Array<OneD, NekDouble > Fwd(nTraceNumPoints);
        Array<OneD, NekDouble > Bwd(nTraceNumPoints);
        Array<OneD, NekDouble > Vn (nTraceNumPoints,0.0);       
        
        //Get Edge Velocity - Could be stored if time independent
        for(i = 0; i < nvel; ++i)
        {
            m_fields[0]->ExtractTracePhys(m_velocity[i], Fwd);
            Vmath::Vvtvp(nTraceNumPoints,m_traceNormals[i],1,Fwd,1,Vn,1,Vn,1);
        }
        
        for(i = 0; i < numflux.num_elements(); ++i)
        {
            m_fields[i]->GetFwdBwdTracePhys(physfield[i],Fwd,Bwd);
            m_fields[i]->GetTrace()->Upwind(Vn,Fwd,Bwd,numflux[i]);
            // calculate m_fields[i]*Vn
            Vmath::Vmul(nTraceNumPoints,numflux[i],1,Vn,1,numflux[i],1);
        }
    }
}