APE.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File APE.cpp
//
// For more information, please see: http://www.nektar.info
//
// The MIT License
//
// Copyright (c) 2015 Kilian Lackhove
// 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,
// 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: APE1/APE4 (Acoustic Perturbation Equations)
//
///////////////////////////////////////////////////////////////////////////////

#include <iostream>

#include <MultiRegions/AssemblyMap/AssemblyMapDG.h>
#include <APESolver/EquationSystems/APE.h>

using namespace std;

namespace Nektar
{
string APE::className = GetEquationSystemFactory().RegisterCreatorFunction(
            "APE", APE::create,
            "APE1/APE4 (Acoustic Perturbation Equations)");


APE::APE(
        const LibUtilities::SessionReaderSharedPtr& pSession)
    : UnsteadySystem(pSession)
{
}


/**
 * @brief Initialization object for the APE class.
 */
void APE::v_InitObject()
{
    UnsteadySystem::v_InitObject();

    // TODO: We have a bug somewhere in the 1D boundary conditions. Therefore 1D
    // problems are currently disabled. This should get fixed in the future.
    ASSERTL0(m_spacedim > 1, "1D problems currently not supported by the APE class.");

    ASSERTL0(m_projectionType == MultiRegions::eDiscontinuous,
             "Only Projection=DisContinuous supported by the APE class.");

    // Load isentropic coefficient, Ratio of specific heats
    m_session->LoadParameter("Gamma", m_gamma, 1.4);

    // Define Baseflow fields
    m_basefield = Array<OneD, Array<OneD, NekDouble> >(m_spacedim + 2);
    m_basefield_names.push_back("p0");
    m_basefield_names.push_back("rho0");
    m_basefield_names.push_back("u0");
    m_basefield_names.push_back("v0");
    m_basefield_names.push_back("w0");

    // Resize the advection velocities vector to dimension of the problem
    m_basefield_names.resize(m_spacedim + 2);

    //  Initialize the sourceterm
    m_sourceTerms = Array<OneD, NekDouble>(GetTotPoints());

    // Do not forwards transform initial condition
    m_homoInitialFwd = false;

    // Define the normal velocity fields
    if (m_fields[0]->GetTrace())
    {
        m_traceBasefield = Array<OneD, Array<OneD, NekDouble> > (m_spacedim + 2);
        for (int i = 0; i < m_spacedim + 2; i++)
        {
            m_traceBasefield[i] = Array<OneD, NekDouble>(GetTraceNpoints());
        }
    }

    // Set up locations of velocity and base velocity vectors.
    m_vecLocs = Array<OneD, Array<OneD, NekDouble> >(1);
    m_vecLocs[0] = Array<OneD, NekDouble>(m_spacedim);
    for (int i = 0; i < m_spacedim; ++i)
    {
        // u', v', w'
        m_vecLocs[0][i] = 1 + i;
    }

    string riemName;
    m_session->LoadSolverInfo("UpwindType", riemName, "APEUpwind");
    m_riemannSolver = SolverUtils::GetRiemannSolverFactory().CreateInstance(
                          riemName);
    m_riemannSolver->SetVector("N",         &APE::GetNormals,   this);
    m_riemannSolver->SetVector("basefield", &APE::GetBasefield, this);
    m_riemannSolver->SetAuxVec("vecLocs",   &APE::GetVecLocs,   this);
    m_riemannSolver->SetParam("Gamma",     &APE::GetGamma,     this);

    // Set up advection operator
    string advName;
    m_session->LoadSolverInfo("AdvectionType", advName, "WeakDG");
    m_advection = SolverUtils::GetAdvectionFactory()
                  .CreateInstance(advName, advName);
    m_advection->SetFluxVector(&APE::GetFluxVector, this);
    m_advection->SetRiemannSolver(m_riemannSolver);
    m_advection->InitObject(m_session, m_fields);

    if (m_explicitAdvection)
    {
        m_ode.DefineOdeRhs(&APE::DoOdeRhs,        this);
        m_ode.DefineProjection(&APE::DoOdeProjection, this);
    }
    else
    {
        ASSERTL0(false, "Implicit APE not set up.");
    }
}


/**
 * @brief Destructor for APE class.
 */
APE::~APE()
{
    
}


/**
 * @brief Return the flux vector for the APE equations.
 *
 * @param physfield   Fields.
 * @param flux        Resulting flux. flux[eq][dir][pt]
 */
void APE::GetFluxVector(
        const Array<OneD, Array<OneD, NekDouble> > &physfield,
        Array<OneD, Array<OneD, Array<OneD, NekDouble> > > &flux)
{
    UpdateBasefield();

    int nq = physfield[0].num_elements();
    Array<OneD, NekDouble> tmp1(nq);
    Array<OneD, NekDouble> tmp2(nq);

    ASSERTL1(flux[0].num_elements() == m_spacedim,
                 "Dimension of flux array and velocity array do not match");

    // F_{adv,p',j} = \rho_0 u'_j + p' \bar{u}_j / c^2
    for (int j = 0; j < m_spacedim; ++j)
    {
        Vmath::Zero(nq, flux[0][j], 1);

        // construct rho_0 u'_j term
        Vmath::Vmul(nq, m_basefield[1], 1, physfield[j + 1], 1, flux[0][j], 1);

        // construct p' \bar{u}_j / c^2 term
        // c^2
        Vmath::Vdiv(nq, m_basefield[0], 1, m_basefield[1], 1, tmp1, 1);
        Vmath::Smul(nq, m_gamma, tmp1, 1, tmp1, 1);

        // p' \bar{u}_j / c^2 term
        Vmath::Vmul(nq, physfield[0], 1, m_basefield[j + 2], 1, tmp2, 1);
        Vmath::Vdiv(nq, tmp2, 1, tmp1, 1, tmp2, 1);

        // \rho_0 u'_j + p' \bar{u}_j / c^2
        Vmath::Vadd(nq, flux[0][j], 1, tmp2, 1, flux[0][j], 1);
    }

    for (int i = 1; i < flux.num_elements(); ++i)
    {
        ASSERTL1(flux[i].num_elements() == m_spacedim,
                 "Dimension of flux array and velocity array do not match");

        // F_{adv,u'_i,j} = (p'/ \bar{rho} + \bar{u}_k u'_k) \delta_{ij}
        for (int j = 0; j < m_spacedim; ++j)
        {
            Vmath::Zero(nq, flux[i][j], 1);

            if (i - 1 == j)
            {
                // contruct p'/ \bar{rho} term
                Vmath::Vdiv(nq, physfield[0], 1, m_basefield[1], 1, flux[i][j], 1);

                // construct \bar{u}_k u'_k term
                Vmath::Zero(nq, tmp1, 1);
                for (int k = 0; k < m_spacedim; ++k)
                {
                    Vmath::Vvtvp(nq, physfield[k + 1], 1, m_basefield[k + 2], 1, tmp1, 1, tmp1, 1);
                }

                // add terms
                Vmath::Vadd(nq, flux[i][j], 1, tmp1, 1, flux[i][j], 1);
            }
        }
    }
}


/**
 * @brief Compute the right-hand side.
 */
void APE::DoOdeRhs(const Array<OneD, const Array<OneD, NekDouble> >&inarray,
                         Array<OneD,       Array<OneD, NekDouble> >&outarray,
                   const NekDouble time)
{
    int nVariables = inarray.num_elements();
    int nq = GetTotPoints();
    Array<OneD, NekDouble> tmp1(nq);

    // WeakDG does not use advVel, so we only provide a dummy array
    Array<OneD, Array<OneD, NekDouble> > advVel(m_spacedim);
    m_advection->Advect(nVariables, m_fields, advVel, inarray, outarray, time);

    for (int i = 0; i < nVariables; ++i)
    {
        if (i ==  0)
        {
            // c^2 = gamma*p0/rho0
            Vmath::Vdiv(nq, m_basefield[0], 1, m_basefield[1], 1, tmp1, 1);
            Vmath::Smul(nq, m_gamma, tmp1, 1, tmp1, 1);
            Vmath::Vmul(nq, tmp1, 1, outarray[i], 1, outarray[i], 1);
        }

        Vmath::Neg(nq, outarray[i], 1);
    }

    AddSource(outarray);
}


/**
 * @brief Compute the projection and call the method for imposing the
 * boundary conditions in case of discontinuous projection.
 */
void APE::DoOdeProjection(const Array<OneD, const Array<OneD, NekDouble> >&inarray,
                                Array<OneD,       Array<OneD, NekDouble> >&outarray,
                          const NekDouble time)
{
    int nvariables = inarray.num_elements();
    int nq = m_fields[0]->GetNpoints();

    // deep copy
    for (int i = 0; i < nvariables; ++i)
    {
        Vmath::Vcopy(nq, inarray[i], 1, outarray[i], 1);
    }

    SetBoundaryConditions(outarray, time);
}


/**
 * @brief Apply the Boundary Conditions to the APE equations.
 */
void APE::SetBoundaryConditions(Array<OneD, Array<OneD, NekDouble> > &inarray,
                                NekDouble time)
{
    std::string varName;
    int nvariables = m_fields.num_elements();
    int cnt        = 0;
    int nTracePts  = GetTraceTotPoints();

    // Extract trace for boundaries. Needs to be done on all processors to avoid
    // deadlock.
    Array<OneD, Array<OneD, NekDouble> > Fwd(nvariables);
    for (int i = 0; i < nvariables; ++i)
    {
        Fwd[i] = Array<OneD, NekDouble>(nTracePts);
        m_fields[i]->ExtractTracePhys(inarray[i], Fwd[i]);
    }

    // loop over Boundary Regions
    for(int n = 0; n < m_fields[0]->GetBndConditions().num_elements(); ++n)
    {
        // Wall Boundary Condition
        if (boost::iequals(m_fields[0]->GetBndConditions()[n]->GetUserDefined(),"Wall"))
        {
            WallBC(n, cnt, Fwd, inarray);
        }

        // Time Dependent Boundary Condition (specified in meshfile)
        if (m_fields[0]->GetBndConditions()[n]->IsTimeDependent())
        {
            for (int i = 0; i < nvariables; ++i)
            {
                varName = m_session->GetVariable(i);
                m_fields[i]->EvaluateBoundaryConditions(time, varName);
            }
        }
        cnt +=m_fields[0]->GetBndCondExpansions()[n]->GetExpSize();
    }
}


/**
 * @brief Wall boundary conditions for the APE equations.
 */
void APE::WallBC(int bcRegion, int cnt,
                 Array<OneD, Array<OneD, NekDouble> > &Fwd,
                 Array<OneD, Array<OneD, NekDouble> > &physarray)
{
    int nVariables = physarray.num_elements();

    const Array<OneD, const int> &traceBndMap = m_fields[0]->GetTraceBndMap();

    // Adjust the physical values of the trace to take
    // user defined boundaries into account
    int id1, id2, nBCEdgePts;
    int eMax = m_fields[0]->GetBndCondExpansions()[bcRegion]->GetExpSize();

    for (int e = 0; e < eMax; ++e)
    {
        nBCEdgePts = m_fields[0]->GetBndCondExpansions()[bcRegion]->
                GetExp(e)->GetTotPoints();
        id1 = m_fields[0]->GetBndCondExpansions()[bcRegion]->GetPhys_Offset(e);
        id2 = m_fields[0]->GetTrace()->GetPhys_Offset(traceBndMap[cnt+e]);

        // For 2D/3D, define: v* = v - 2(v.n)n
        Array<OneD, NekDouble> tmp(nBCEdgePts, 0.0);

        // Calculate (v.n)
        for (int i = 0; i < m_spacedim; ++i)
        {
            Vmath::Vvtvp(nBCEdgePts,
                         &Fwd[1+i][id2], 1,
                         &m_traceNormals[i][id2], 1,
                         &tmp[0], 1,
                         &tmp[0], 1);
        }

        // Calculate 2.0(v.n)
        Vmath::Smul(nBCEdgePts, -2.0, &tmp[0], 1, &tmp[0], 1);

        // Calculate v* = v - 2.0(v.n)n
        for (int i = 0; i < m_spacedim; ++i)
        {
            Vmath::Vvtvp(nBCEdgePts,
                         &tmp[0], 1,
                         &m_traceNormals[i][id2], 1,
                         &Fwd[1+i][id2], 1,
                         &Fwd[1+i][id2], 1);
        }

        // Copy boundary adjusted values into the boundary expansion
        for (int i = 0; i < nVariables; ++i)
        {
            Vmath::Vcopy(nBCEdgePts,
                         &Fwd[i][id2], 1,
                         &(m_fields[i]->GetBndCondExpansions()[bcRegion]->UpdatePhys())[id1], 1);
        }
    }
}


/**
 * @brief sourceterm for p' equation obtained from GetSource
 */
void APE::AddSource(Array< OneD, Array< OneD, NekDouble > > &outarray)
{
    UpdateSourceTerms();
    Vmath::Vadd(GetTotPoints(), m_sourceTerms, 1, outarray[0], 1, outarray[0], 1);
}


void APE::v_ExtraFldOutput(
    std::vector<Array<OneD, NekDouble> > &fieldcoeffs,
    std::vector<std::string>             &variables)
{
    UpdateBasefield();

    const int nCoeffs = m_fields[0]->GetNcoeffs();

    for (int i = 0; i < m_spacedim + 2; i++)
    {
        variables.push_back(m_basefield_names[i]);

        Array<OneD, NekDouble> tmpFwd(nCoeffs);
        m_fields[0]->FwdTrans(m_basefield[i], tmpFwd);
        fieldcoeffs.push_back(tmpFwd);
    }
}


/**
 * @brief Get the normal vectors.
 */
const Array<OneD, const Array<OneD, NekDouble> > &APE::GetNormals()
{
    return m_traceNormals;
}


/**
 * @brief Get the locations of the components of the directed fields within the fields array.
 */
const Array<OneD, const Array<OneD, NekDouble> > &APE::GetVecLocs()
{
    return m_vecLocs;
}


/**
 * @brief Get the baseflow field.
 */
const Array<OneD, const Array<OneD, NekDouble> > &APE::GetBasefield()
{
    for (int i = 0; i < m_spacedim + 2; i++)
    {
        m_fields[0]->ExtractTracePhys(m_basefield[i], m_traceBasefield[i]);
    }
    return m_traceBasefield;
}


/**
 * @brief Get the heat capacity ratio.
 */
NekDouble APE::GetGamma()
{
    return m_gamma;
}


void APE::UpdateBasefield()
{
    static NekDouble last_update = -1.0;

    if (m_time > last_update)
    {
        last_update = m_time;
        EvaluateFunction(m_basefield_names, m_basefield, "Baseflow", m_time);
    }
}

void APE::UpdateSourceTerms()
{
    static NekDouble last_update = -1.0;

    if (m_time > last_update)
    {
        Array<OneD, NekDouble> sourceC(m_fields[0]->GetNcoeffs());

        EvaluateFunction("S", m_sourceTerms, "Source", m_time);

        m_fields[0]->IProductWRTBase(m_sourceTerms, sourceC);
        m_fields[0]->MultiplyByElmtInvMass(sourceC, sourceC);
        m_fields[0]->BwdTrans(sourceC, m_sourceTerms);

        last_update = m_time;
    }
}


} //end of namespace