CFLtester.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: CFLtester.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: CFL tester solve routines
//
///////////////////////////////////////////////////////////////////////////////
 
#include <iostream>
 
#include <ADRSolver/EquationSystems/CFLtester.h>
#include <LocalRegions/Expansion2D.h>
#include <LocalRegions/Expansion3D.h>
#include <LocalRegions/QuadExp.h>
#include <LocalRegions/TriExp.h>
 
namespace Nektar
{
string CFLtester::className =
    GetEquationSystemFactory().RegisterCreatorFunction(
        "CFLtester", CFLtester::create, "Testing CFL restriction");
 
CFLtester::CFLtester(const LibUtilities::SessionReaderSharedPtr &pSession,
                     const SpatialDomains::MeshGraphSharedPtr &pGraph)
    : UnsteadySystem(pSession, pGraph), AdvectionSystem(pSession, pGraph)
{
}
 
void CFLtester::v_InitObject(bool DeclareFields)
{
    AdvectionSystem::v_InitObject(DeclareFields);
 
    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);
 
    GetFunction("AdvectionVelocity")->Evaluate(vel, m_velocity);
 
    // Type of advection class to be used
    switch (m_projectionType)
    {
        // Discontinuous field
        case MultiRegions::eDiscontinuous:
        {
            // Do not forwards transform initial condition
            m_homoInitialFwd = false;
 
            // Define the normal velocity fields
            if (m_fields[0]->GetTrace())
            {
                m_traceVn = Array<OneD, NekDouble>(GetTraceNpoints());
            }
 
            string advName;
            string riemName;
            m_session->LoadSolverInfo("AdvectionType", advName, "WeakDG");
            m_advObject = SolverUtils::GetAdvectionFactory().CreateInstance(
                advName, advName);
            m_advObject->SetFluxVector(&CFLtester::GetFluxVector, this);
            m_session->LoadSolverInfo("UpwindType", riemName, "Upwind");
            m_riemannSolver =
                SolverUtils::GetRiemannSolverFactory().CreateInstance(
                    riemName, m_session);
            m_riemannSolver->SetScalar("Vn", &CFLtester::GetNormalVelocity,
                                       this);
 
            m_advObject->SetRiemannSolver(m_riemannSolver);
            m_advObject->InitObject(m_session, m_fields);
            break;
        }
        // Continuous field
        case MultiRegions::eGalerkin:
        case MultiRegions::eMixed_CG_Discontinuous:
        {
            string advName;
            m_session->LoadSolverInfo("AdvectionType", advName,
                                      "NonConservative");
            m_advObject = SolverUtils::GetAdvectionFactory().CreateInstance(
                advName, advName);
            m_advObject->SetFluxVector(&CFLtester::GetFluxVector, this);
            break;
        }
        default:
        {
            ASSERTL0(false, "Unsupported projection type.");
            break;
        }
    }
 
    if (m_explicitAdvection)
    {
        m_ode.DefineOdeRhs(&CFLtester::DoOdeRhs, this);
        m_ode.DefineProjection(&CFLtester::DoOdeProjection, this);
    }
    else
    {
        ASSERTL0(false, "Implicit unsteady Advection not set up.");
    }
}
 
CFLtester::~CFLtester()
{
}
 
void CFLtester::DoOdeRhs(
    const Array<OneD, const Array<OneD, NekDouble>> &inarray,
    Array<OneD, Array<OneD, NekDouble>> &outarray, const NekDouble time)
{
    int nvariables = inarray.size();
    int npoints    = GetNpoints();
 
    m_advObject->Advect(nvariables, m_fields, m_velocity, inarray, outarray,
                        time);
    for (int j = 0; j < nvariables; ++j)
    {
        Vmath::Neg(npoints, outarray[j], 1);
    }
}
 
void CFLtester::DoOdeProjection(
    const Array<OneD, const Array<OneD, NekDouble>> &inarray,
    Array<OneD, Array<OneD, NekDouble>> &outarray, const NekDouble time)
{
    int nvariables = inarray.size();
    SetBoundaryConditions(time);
 
    switch (m_projectionType)
    {
        case MultiRegions::eDiscontinuous:
        {
            // Just copy over array
            int npoints = GetNpoints();
 
            for (int j = 0; j < nvariables; ++j)
            {
                Vmath::Vcopy(npoints, inarray[j], 1, outarray[j], 1);
            }
        }
        break;
        case MultiRegions::eGalerkin:
        case MultiRegions::eMixed_CG_Discontinuous:
        {
            Array<OneD, NekDouble> coeffs(m_fields[0]->GetNcoeffs());
 
            for (int j = 0; j < nvariables; ++j)
            {
                m_fields[j]->FwdTrans(inarray[j], coeffs);
                m_fields[j]->BwdTrans_IterPerExp(coeffs, outarray[j]);
            }
            break;
        }
        default:
            ASSERTL0(false, "Unknown projection scheme");
            break;
    }
}
 
/**
 * @brief Get the normal velocity
 */
Array<OneD, NekDouble> &CFLtester::GetNormalVelocity()
{
    // Number of trace (interface) points
    int nTracePts = GetTraceNpoints();
 
    // Auxiliary variable to compute the normal velocity
    Array<OneD, NekDouble> tmp(nTracePts);
 
    // Reset the normal velocity
    Vmath::Zero(nTracePts, m_traceVn, 1);
 
    for (int i = 0; i < m_velocity.size(); ++i)
    {
        m_fields[0]->ExtractTracePhys(m_velocity[i], tmp);
 
        Vmath::Vvtvp(nTracePts, m_traceNormals[i], 1, tmp, 1, m_traceVn, 1,
                     m_traceVn, 1);
    }
 
    return m_traceVn;
}
 
void CFLtester::GetFluxVector(
    const Array<OneD, Array<OneD, NekDouble>> &physfield,
    Array<OneD, Array<OneD, Array<OneD, NekDouble>>> &flux)
{
    ASSERTL1(flux[0].size() == m_velocity.size(),
             "Dimension of flux array and velocity array do not match");
 
    int nq = physfield[0].size();
 
    for (int i = 0; i < flux.size(); ++i)
    {
        for (int j = 0; j < flux[0].size(); ++j)
        {
            Vmath::Vmul(nq, physfield[i], 1, m_velocity[j], 1, flux[i][j], 1);
        }
    }
}
 
void CFLtester::v_GenerateSummary(SummaryList &s)
{
    AdvectionSystem::v_GenerateSummary(s);
}
 
NekDouble CFLtester::v_GetTimeStep(const Array<OneD, int> ExpOrder,
                                   const Array<OneD, NekDouble> CFL,
                                   NekDouble timeCFL)
{
 
    int n_element = m_fields[0]->GetExpSize();
 
    // const NekDouble minLengthStdTri  = 1.414213;
    // const NekDouble minLengthStdQuad = 2.0;
    // const NekDouble cLambda          = 0.2; // Spencer book pag. 317
 
    Array<OneD, NekDouble> tstep(n_element, 0.0);
    Array<OneD, NekDouble> stdVelocity(n_element, 0.0);
    stdVelocity = GetStdVelocity(m_velocity);
 
    for (int el = 0; el < n_element; ++el)
    {
        int npoints = m_fields[0]->GetExp(el)->GetTotPoints();
        Array<OneD, NekDouble> one2D(npoints, 1.0);
        // NekDouble Area = m_fields[0]->GetExp(el)->Integral(one2D);
        if (std::dynamic_pointer_cast<LocalRegions::TriExp>(
                m_fields[0]->GetExp(el)))
        {
            // tstep[el] =
            // timeCFL/(stdVelocity[el]*cLambda*(ExpOrder[el]-1)*(ExpOrder[el]-1));
            // tstep[el] =
            // timeCFL*minLengthStdTri/(stdVelocity[el]*cLambda*(ExpOrder[el]-1)*(ExpOrder[el]-1));
            tstep[el] = CFL[el] / (stdVelocity[el]);
        }
        else if (std::dynamic_pointer_cast<LocalRegions::QuadExp>(
                     m_fields[0]->GetExp(el)))
        {
            // tstep[el] =
            // timeCFL/(stdVelocity[el]*cLambda*(ExpOrder[el]-1)*(ExpOrder[el]-1));
            // tstep[el] =
            // timeCFL*minLengthStdQuad/(stdVelocity[el]*cLambda*(ExpOrder[el]-1)*(ExpOrder[el]-1));
            tstep[el] = CFL[el] / (stdVelocity[el]);
        }
    }
 
    NekDouble TimeStep = Vmath::Vmin(n_element, tstep, 1);
 
    return TimeStep;
}
 
NekDouble CFLtester::v_GetTimeStep(int ExpOrder, NekDouble CFL,
                                   NekDouble TimeStability)
{
    //================================================================
    // This function has been created just to test specific problems, hence is
    // not general and it has been implemented in a rude fashion, as the full
    // CFLtester class. For real CFL calculations refer to the general
    // implementation above. (A.Bolis)
    //================================================================
 
    NekDouble TimeStep;
    NekDouble SpatialStability;
    int n_elements = m_fields[0]->GetExpSize();
 
    // solve ambiguity in windows
    NekDouble n_elem = n_elements;
    NekDouble DH     = sqrt(n_elem);
 
    int H = (int)DH;
    int P = ExpOrder - 1;
 
    //================================================================
    // Regular meshes
 
    // SpatialStability = EigenvaluesRegMeshes[H-1][P-1];
 
    //================================================================
    // Anisotropic meshes
 
    if (TimeStability == 1.0)
    {
        SpatialStability = EigenvaluesAnaMeshesAB2[H / 2][P - 1];
    }
    else if (TimeStability == 2.0)
    {
        SpatialStability = EigenvaluesAnaMeshesRK2[H / 2][P - 1];
    }
    else if (TimeStability == 2.784)
    {
        SpatialStability = EigenvaluesAnaMeshesRK4[H / 2][P - 1];
    }
    else
    {
        ASSERTL0(false, "Dominant eigenvalues database not present for this "
                        "time-stepping scheme")
    }
 
    //================================================================
 
    TimeStep = (TimeStability / SpatialStability) * CFL;
 
    //================================================================
 
    return TimeStep;
}
 
Array<OneD, NekDouble> CFLtester::GetStdVelocity(
    const Array<OneD, Array<OneD, NekDouble>> inarray)
{
    // Checking if the problem is 2D
    ASSERTL0(m_expdim >= 2, "Method not implemented for 1D");
 
    int nTotQuadPoints = GetTotPoints();
    int n_element      = m_fields[0]->GetExpSize();
    int nvel           = inarray.size();
 
    NekDouble pntVelocity;
 
    // Getting the standard velocity vector on the 2D normal space
    Array<OneD, Array<OneD, NekDouble>> stdVelocity(nvel);
    Array<OneD, NekDouble> stdV(n_element, 0.0);
 
    for (int i = 0; i < nvel; ++i)
    {
        stdVelocity[i] = Array<OneD, NekDouble>(nTotQuadPoints);
    }
 
    if (nvel == 2)
    {
        for (int el = 0; el < n_element; ++el)
        {
            LocalRegions::Expansion2DSharedPtr el2D =
                m_fields[0]->GetExp(el)->as<LocalRegions::Expansion2D>();
            int n_points = el2D->GetTotPoints();
 
            Array<OneD, const NekDouble> jac =
                el2D->GetGeom2D()->GetMetricInfo()->GetJac();
            Array<TwoD, const NekDouble> gmat =
                el2D->GetGeom2D()->GetMetricInfo()->GetDerivFactors();
 
            if (el2D->GetGeom2D()->GetMetricInfo()->GetGtype() ==
                SpatialDomains::eDeformed)
            {
                for (int i = 0; i < n_points; i++)
                {
                    stdVelocity[0][i] =
                        gmat[0][i] * inarray[0][i] + gmat[2][i] * inarray[1][i];
 
                    stdVelocity[1][i] =
                        gmat[1][i] * inarray[0][i] + gmat[3][i] * inarray[1][i];
                }
            }
            else
            {
                for (int i = 0; i < n_points; i++)
                {
                    stdVelocity[0][i] =
                        gmat[0][0] * inarray[0][i] + gmat[2][0] * inarray[1][i];
 
                    stdVelocity[1][i] =
                        gmat[1][0] * inarray[0][i] + gmat[3][0] * inarray[1][i];
                }
            }
 
            for (int i = 0; i < n_points; i++)
            {
                pntVelocity = sqrt(stdVelocity[0][i] * stdVelocity[0][i] +
                                   stdVelocity[1][i] * stdVelocity[1][i]);
 
                if (pntVelocity > stdV[el])
                {
                    stdV[el] = pntVelocity;
                }
            }
        }
    }
    else
    {
        for (int el = 0; el < n_element; ++el)
        {
            LocalRegions::Expansion3DSharedPtr el3D =
                m_fields[0]->GetExp(el)->as<LocalRegions::Expansion3D>();
 
            int n_points = el3D->GetTotPoints();
 
            Array<OneD, const NekDouble> jac =
                el3D->GetGeom3D()->GetMetricInfo()->GetJac();
            Array<TwoD, const NekDouble> gmat =
                el3D->GetGeom3D()->GetMetricInfo()->GetDerivFactors();
 
            if (el3D->GetGeom3D()->GetMetricInfo()->GetGtype() ==
                SpatialDomains::eDeformed)
            {
                for (int i = 0; i < n_points; i++)
                {
                    stdVelocity[0][i] = gmat[0][i] * inarray[0][i] +
                                        gmat[3][i] * inarray[1][i] +
                                        gmat[6][i] * inarray[2][i];
 
                    stdVelocity[1][i] = gmat[1][i] * inarray[0][i] +
                                        gmat[4][i] * inarray[1][i] +
                                        gmat[7][i] * inarray[2][i];
 
                    stdVelocity[2][i] = gmat[2][i] * inarray[0][i] +
                                        gmat[5][i] * inarray[1][i] +
                                        gmat[8][i] * inarray[2][i];
                }
            }
            else
            {
                Array<OneD, const NekDouble> jac =
                    el3D->GetGeom3D()->GetMetricInfo()->GetJac();
                Array<TwoD, const NekDouble> gmat =
                    el3D->GetGeom3D()->GetMetricInfo()->GetDerivFactors();
 
                for (int i = 0; i < n_points; i++)
                {
                    stdVelocity[0][i] = gmat[0][0] * inarray[0][i] +
                                        gmat[3][0] * inarray[1][i] +
                                        gmat[6][0] * inarray[2][i];
 
                    stdVelocity[1][i] = gmat[1][0] * inarray[0][i] +
                                        gmat[4][0] * inarray[1][i] +
                                        gmat[7][0] * inarray[2][i];
 
                    stdVelocity[2][i] = gmat[2][0] * inarray[0][i] +
                                        gmat[5][0] * inarray[1][i] +
                                        gmat[8][0] * inarray[2][i];
                }
            }
 
            for (int i = 0; i < n_points; i++)
            {
                pntVelocity = sqrt(stdVelocity[0][i] * stdVelocity[0][i] +
                                   stdVelocity[1][i] * stdVelocity[1][i] +
                                   stdVelocity[2][i] * stdVelocity[2][i]);
 
                if (pntVelocity > stdV[el])
                {
                    stdV[el] = pntVelocity;
                }
            }
        }
    }
 
    return stdV;
}
} // namespace Nektar