UnsteadyDiffusion.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: UnsteadyDiffusion.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
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// DEALINGS IN THE SOFTWARE.
//
// Description: Unsteady diffusion solve routines
//
///////////////////////////////////////////////////////////////////////////////
 
#include <ADRSolver/EquationSystems/UnsteadyDiffusion.h>
 
namespace Nektar
{
 
std::string UnsteadyDiffusion::className =
    GetEquationSystemFactory().RegisterCreatorFunction(
        "UnsteadyDiffusion", UnsteadyDiffusion::create);
 
UnsteadyDiffusion::UnsteadyDiffusion(
    const LibUtilities::SessionReaderSharedPtr &pSession,
    const SpatialDomains::MeshGraphSharedPtr &pGraph)
    : UnsteadySystem(pSession, pGraph)
{
}
 
/**
 * @brief Initialisation object for the unsteady diffusion problem.
 */
void UnsteadyDiffusion::v_InitObject(bool DeclareFields)
{
    UnsteadySystem::v_InitObject(DeclareFields);
 
    // Load diffusion parameter
    m_session->LoadParameter("epsilon", m_epsilon, 1.0);
 
    m_session->MatchSolverInfo("SpectralVanishingViscosity", "True",
                               m_useSpecVanVisc, false);
 
    if (m_useSpecVanVisc)
    {
        m_session->LoadParameter("SVVCutoffRatio", m_sVVCutoffRatio, 0.75);
        m_session->LoadParameter("SVVDiffCoeff", m_sVVDiffCoeff, 0.1);
    }
 
    int npoints = m_fields[0]->GetNpoints();
 
    if (m_session->DefinesParameter("d00"))
    {
        m_d00 = m_session->GetParameter("d00");
        m_varcoeff[StdRegions::eVarCoeffD00] =
            Array<OneD, NekDouble>(npoints, m_session->GetParameter("d00"));
    }
    if (m_session->DefinesParameter("d11"))
    {
        m_d11 = m_session->GetParameter("d11");
        m_varcoeff[StdRegions::eVarCoeffD11] =
            Array<OneD, NekDouble>(npoints, m_session->GetParameter("d11"));
    }
    if (m_session->DefinesParameter("d22"))
    {
        m_d22 = m_session->GetParameter("d22");
        m_varcoeff[StdRegions::eVarCoeffD22] =
            Array<OneD, NekDouble>(npoints, m_session->GetParameter("d22"));
    }
 
    switch (m_projectionType)
    {
        case MultiRegions::eDiscontinuous:
        {
            std::string diffName;
 
            // Do not forwards transform initial condition
            m_homoInitialFwd = false;
 
            m_session->LoadSolverInfo("DiffusionType", diffName, "LDG");
            m_diffusion = SolverUtils::GetDiffusionFactory().CreateInstance(
                diffName, diffName);
            m_diffusion->SetFluxVector(&UnsteadyDiffusion::GetFluxVector, this);
            m_diffusion->InitObject(m_session, m_fields);
            break;
        }
        case MultiRegions::eGalerkin:
        {
            // In case of Galerkin explicit diffusion gives an error
            if (m_explicitDiffusion)
            {
                ASSERTL0(false, "Explicit Galerkin diffusion not set up.");
            }
            // In case of Galerkin implicit diffusion: do nothing
            break;
        }
        default:
        {
            ASSERTL0(false, "Unknown projection scheme");
            break;
        }
    }
 
    m_ode.DefineOdeRhs(&UnsteadyDiffusion::DoOdeRhs, this);
    m_ode.DefineProjection(&UnsteadyDiffusion::DoOdeProjection, this);
    m_ode.DefineImplicitSolve(&UnsteadyDiffusion::DoImplicitSolve, this);
}
 
/* @brief Compute the right-hand side for the unsteady diffusion problem.
 *
 * @param inarray    Given fields.
 * @param outarray   Calculated solution.
 * @param time       Time.
 */
void UnsteadyDiffusion::DoOdeRhs(
    const Array<OneD, const Array<OneD, NekDouble>> &inarray,
    Array<OneD, Array<OneD, NekDouble>> &outarray,
    [[maybe_unused]] const NekDouble time)
{
    // Number of fields (variables of the problem)
    int nVariables = inarray.size();
 
    // RHS computation using the new diffusion base class
    m_diffusion->Diffuse(nVariables, m_fields, inarray, outarray);
}
 
/**
 * @brief Compute the projection for the unsteady diffusion problem.
 *
 * @param inarray    Given fields.
 * @param outarray   Calculated solution.
 * @param time       Time.
 */
void UnsteadyDiffusion::DoOdeProjection(
    const Array<OneD, const Array<OneD, NekDouble>> &inarray,
    Array<OneD, Array<OneD, NekDouble>> &outarray, const NekDouble time)
{
    int i;
    int nvariables = inarray.size();
    SetBoundaryConditions(time);
 
    switch (m_projectionType)
    {
        case MultiRegions::eDiscontinuous:
        {
            // Just copy over array
            if (inarray != outarray)
            {
                int npoints = GetNpoints();
 
                for (i = 0; i < nvariables; ++i)
                {
                    Vmath::Vcopy(npoints, inarray[i], 1, outarray[i], 1);
                }
            }
            break;
        }
        case MultiRegions::eGalerkin:
        {
            Array<OneD, NekDouble> coeffs(m_fields[0]->GetNcoeffs());
 
            for (i = 0; i < nvariables; ++i)
            {
                m_fields[i]->FwdTrans(inarray[i], coeffs);
                m_fields[i]->BwdTrans(coeffs, outarray[i]);
            }
            break;
        }
        default:
        {
            ASSERTL0(false, "Unknown projection scheme");
            break;
        }
    }
}
 
/**
 * @brief Implicit solution of the unsteady diffusion problem.
 */
void UnsteadyDiffusion::DoImplicitSolve(
    const Array<OneD, const Array<OneD, NekDouble>> &inarray,
    Array<OneD, Array<OneD, NekDouble>> &outarray,
    [[maybe_unused]] const NekDouble time, const NekDouble lambda)
{
    StdRegions::ConstFactorMap factors;
 
    int nvariables                     = inarray.size();
    int npoints                        = m_fields[0]->GetNpoints();
    factors[StdRegions::eFactorLambda] = 1.0 / lambda / m_epsilon;
    factors[StdRegions::eFactorTau]    = 1.0;
 
    if (m_useSpecVanVisc)
    {
        factors[StdRegions::eFactorSVVCutoffRatio] = m_sVVCutoffRatio;
        factors[StdRegions::eFactorSVVDiffCoeff]   = m_sVVDiffCoeff / m_epsilon;
    }
 
    // We solve ( \nabla^2 - HHlambda ) Y[i] = rhs [i]
    // inarray = input: \hat{rhs} -> output: \hat{Y}
    // outarray = output: nabla^2 \hat{Y}
    // where \hat = modal coeffs
    for (int i = 0; i < nvariables; ++i)
    {
        // Multiply 1.0/timestep/lambda
        Vmath::Smul(npoints, -factors[StdRegions::eFactorLambda], inarray[i], 1,
                    outarray[i], 1);
 
        // Solve a system of equations with Helmholtz solver
        m_fields[i]->HelmSolve(outarray[i], m_fields[i]->UpdateCoeffs(),
                               factors, m_varcoeff);
 
        m_fields[i]->BwdTrans(m_fields[i]->GetCoeffs(), outarray[i]);
 
        m_fields[i]->SetPhysState(false);
    }
}
 
/**
 * @brief Return the flux vector for the unsteady diffusion problem.
 */
void UnsteadyDiffusion::GetFluxVector(
    [[maybe_unused]] const Array<OneD, Array<OneD, NekDouble>> &inarray,
    const Array<OneD, Array<OneD, Array<OneD, NekDouble>>> &qfield,
    Array<OneD, Array<OneD, Array<OneD, NekDouble>>> &viscousTensor)
{
    unsigned int nDim              = qfield.size();
    unsigned int nConvectiveFields = qfield[0].size();
    unsigned int nPts              = qfield[0][0].size();
 
    NekDouble d[3] = {m_d00, m_d11, m_d22};
 
    for (unsigned int j = 0; j < nDim; ++j)
    {
        for (unsigned int i = 0; i < nConvectiveFields; ++i)
        {
            Vmath::Smul(nPts, m_epsilon * d[j], qfield[j][i], 1,
                        viscousTensor[j][i], 1);
        }
    }
}
 
void UnsteadyDiffusion::v_GenerateSummary(SummaryList &s)
{
    UnsteadySystem::v_GenerateSummary(s);
    if (m_useSpecVanVisc)
    {
        std::stringstream ss;
        ss << "SVV (cut off = " << m_sVVCutoffRatio
           << ", coeff = " << m_sVVDiffCoeff << ")";
        AddSummaryItem(s, "Smoothing", ss.str());
    }
}
 
} // namespace Nektar