NavierStokesCFE.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File NavierStokesCFE.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: Navier Stokes equations in conservative variables
//
///////////////////////////////////////////////////////////////////////////////

#include <CompressibleFlowSolver/EquationSystems/NavierStokesCFE.h>

using namespace std;

namespace Nektar
{
    string NavierStokesCFE::className =
        SolverUtils::GetEquationSystemFactory().RegisterCreatorFunction(
            "NavierStokesCFE", NavierStokesCFE::create,
            "NavierStokes equations in conservative variables.");

    NavierStokesCFE::NavierStokesCFE(
        const LibUtilities::SessionReaderSharedPtr& pSession,
        const SpatialDomains::MeshGraphSharedPtr& pGraph)
        : UnsteadySystem(pSession, pGraph),
          CompressibleFlowSystem(pSession, pGraph)
    {
    }

    NavierStokesCFE::~NavierStokesCFE()
    {

    }

    /**
     * @brief Initialization object for CompressibleFlowSystem class.
     */
    void NavierStokesCFE::v_InitObject()
    {
        CompressibleFlowSystem::v_InitObject();

        // Get gas constant from session file and compute Cp
        NekDouble gasConstant;
        m_session->LoadParameter ("GasConstant",   gasConstant,   287.058);
        m_Cp      = m_gamma / (m_gamma - 1.0) * gasConstant;

        // Viscosity
        int nPts = m_fields[0]->GetNpoints();
        m_session->LoadSolverInfo("ViscosityType", m_ViscosityType, "Constant");
        m_session->LoadParameter ("mu",            m_muRef,           1.78e-05);
        m_mu = Array<OneD, NekDouble>(nPts, m_muRef);

        // Thermal conductivity or Prandtl
        if( m_session->DefinesParameter("thermalConductivity"))
        {
            ASSERTL0( !m_session->DefinesParameter("Pr"),
                 "Cannot define both Pr and thermalConductivity.");

            m_session->LoadParameter ("thermalConductivity",
                                        m_thermalConductivityRef);
            m_Prandtl = m_Cp * m_muRef / m_thermalConductivityRef;
        }
        else
        {
            m_session->LoadParameter ("Pr", m_Prandtl, 0.72);
            m_thermalConductivityRef = m_Cp * m_muRef / m_Prandtl;
        }
        m_thermalConductivity =
                Array<OneD, NekDouble>(nPts, m_thermalConductivityRef);

        string diffName;
        m_session->LoadSolverInfo("DiffusionType", diffName, "LDGNS");

        m_diffusion = SolverUtils::GetDiffusionFactory()
                                    .CreateInstance(diffName, diffName);

        if (m_specHP_dealiasing)
        {
            m_diffusion->SetFluxVectorNS(
                &NavierStokesCFE::v_GetViscousFluxVectorDeAlias,
                this);
        }
        else
        {
            m_diffusion->SetFluxVectorNS(&NavierStokesCFE::
                                          v_GetViscousFluxVector, this);
        }

        // Set up penalty term for LDGNS
        m_diffusion->SetFluxPenaltyNS(&NavierStokesCFE::
            v_GetFluxPenalty, this);

        // Concluding initialisation of diffusion operator
        m_diffusion->InitObject         (m_session, m_fields);
    }

    void NavierStokesCFE::v_DoDiffusion(
        const Array<OneD, const Array<OneD, NekDouble> > &inarray,
              Array<OneD,       Array<OneD, NekDouble> > &outarray,
            const Array<OneD, Array<OneD, NekDouble> >   &pFwd,
            const Array<OneD, Array<OneD, NekDouble> >   &pBwd)
    {
        int i;
        int nvariables = inarray.num_elements();
        int npoints    = GetNpoints();
        int nTracePts  = GetTraceTotPoints();

        Array<OneD, Array<OneD, NekDouble> > outarrayDiff(nvariables);

        Array<OneD, Array<OneD, NekDouble> > inarrayDiff(nvariables-1);
        Array<OneD, Array<OneD, NekDouble> > inFwd(nvariables-1);
        Array<OneD, Array<OneD, NekDouble> > inBwd(nvariables-1);

        for (i = 0; i < nvariables; ++i)
        {
            outarrayDiff[i] = Array<OneD, NekDouble>(npoints);
        }

        for (i = 0; i < nvariables-1; ++i)
        {
            inarrayDiff[i] = Array<OneD, NekDouble>(npoints);
            inFwd[i]       = Array<OneD, NekDouble>(nTracePts);
            inBwd[i]       = Array<OneD, NekDouble>(nTracePts);
        }

        // Extract pressure
        //    (use inarrayDiff[0] as a temporary storage for the pressure)
        m_varConv->GetPressure(inarray, inarrayDiff[0]);

        // Extract temperature
        m_varConv->GetTemperature(inarray, inarrayDiff[nvariables-2]);

        // Extract velocities
        m_varConv->GetVelocityVector(inarray, inarrayDiff);

        // Repeat calculation for trace space
        if (pFwd == NullNekDoubleArrayofArray ||
            pBwd == NullNekDoubleArrayofArray)
        {
            inFwd = NullNekDoubleArrayofArray;
            inBwd = NullNekDoubleArrayofArray;
        }
        else
        {
            m_varConv->GetPressure(pFwd,    inFwd[0]);
            m_varConv->GetPressure(pBwd,    inBwd[0]);

            m_varConv->GetTemperature(pFwd, inFwd[nvariables-2]);
            m_varConv->GetTemperature(pBwd, inBwd[nvariables-2]);

            m_varConv->GetVelocityVector(pFwd, inFwd);
            m_varConv->GetVelocityVector(pBwd, inBwd);
        }

        // Diffusion term in physical rhs form
        m_diffusion->Diffuse(nvariables, m_fields, inarrayDiff, outarrayDiff,
                             inFwd, inBwd);

        for (i = 0; i < nvariables; ++i)
        {
            Vmath::Vadd(npoints,
                        outarrayDiff[i], 1,
                        outarray[i], 1,
                        outarray[i], 1);
        }
    }

    /**
     * @brief Return the flux vector for the LDG diffusion problem.
     * \todo Complete the viscous flux vector
     */
    void NavierStokesCFE::v_GetViscousFluxVector(
        const Array<OneD, Array<OneD, NekDouble> >               &physfield,
              Array<OneD, Array<OneD, Array<OneD, NekDouble> > > &derivativesO1,
              Array<OneD, Array<OneD, Array<OneD, NekDouble> > > &viscousTensor)
    {
        // Auxiliary variables
        int nScalar    = physfield.num_elements();
        int nPts       = physfield[0].num_elements();
        Array<OneD, NekDouble > divVel             (nPts, 0.0);

        // Stokes hypothesis
        const NekDouble lambda = -2.0/3.0;

        // Update viscosity and thermal conductivity
        GetViscosityAndThermalCondFromTemp(physfield[nScalar-1], m_mu,
            m_thermalConductivity);

        // Velocity divergence
        for (int j = 0; j < m_spacedim; ++j)
        {
            Vmath::Vadd(nPts, divVel, 1, derivativesO1[j][j], 1,
                        divVel, 1);
        }

        // Velocity divergence scaled by lambda * mu
        Vmath::Smul(nPts, lambda, divVel, 1, divVel, 1);
        Vmath::Vmul(nPts, m_mu,  1, divVel, 1, divVel, 1);

        // Viscous flux vector for the rho equation = 0
        for (int i = 0; i < m_spacedim; ++i)
        {
            Vmath::Zero(nPts, viscousTensor[i][0], 1);
        }

        // Viscous stress tensor (for the momentum equations)
        for (int i = 0; i < m_spacedim; ++i)
        {
            for (int j = i; j < m_spacedim; ++j)
            {
                Vmath::Vadd(nPts, derivativesO1[i][j], 1,
                                  derivativesO1[j][i], 1,
                                  viscousTensor[i][j+1], 1);

                Vmath::Vmul(nPts, m_mu, 1,
                                  viscousTensor[i][j+1], 1,
                                  viscousTensor[i][j+1], 1);

                if (i == j)
                {
                    // Add divergence term to diagonal
                    Vmath::Vadd(nPts, viscousTensor[i][j+1], 1,
                                  divVel, 1,
                                  viscousTensor[i][j+1], 1);
                }
                else
                {
                    // Copy to make symmetric
                    Vmath::Vcopy(nPts, viscousTensor[i][j+1], 1,
                                       viscousTensor[j][i+1], 1);
                }
            }
        }

        // Terms for the energy equation
        for (int i = 0; i < m_spacedim; ++i)
        {
            Vmath::Zero(nPts, viscousTensor[i][m_spacedim+1], 1);
            // u_j * tau_ij
            for (int j = 0; j < m_spacedim; ++j)
            {
                Vmath::Vvtvp(nPts, physfield[j], 1,
                               viscousTensor[i][j+1], 1,
                               viscousTensor[i][m_spacedim+1], 1,
                               viscousTensor[i][m_spacedim+1], 1);
            }
            // Add k*T_i
            Vmath::Vvtvp(nPts, m_thermalConductivity, 1,
                               derivativesO1[i][m_spacedim], 1,
                               viscousTensor[i][m_spacedim+1], 1,
                               viscousTensor[i][m_spacedim+1], 1);
        }
    }

    /**
     * @brief Return the flux vector for the LDG diffusion problem.
     * \todo Complete the viscous flux vector
     */
    void NavierStokesCFE::v_GetViscousFluxVectorDeAlias(
        const Array<OneD, Array<OneD, NekDouble> >               &physfield,
              Array<OneD, Array<OneD, Array<OneD, NekDouble> > > &derivativesO1,
              Array<OneD, Array<OneD, Array<OneD, NekDouble> > > &viscousTensor)
    {
        // Factor to rescale 1d points in dealiasing.
        NekDouble OneDptscale = 2;
        // Get number of points to dealias a cubic non-linearity
        int nScalar   = physfield.num_elements();
        int nPts      = m_fields[0]->Get1DScaledTotPoints(OneDptscale);
        int nPts_orig = physfield[0].num_elements();

        // Auxiliary variables
        Array<OneD, NekDouble > divVel             (nPts, 0.0);

        // Stokes hypothesis
        const NekDouble lambda = -2.0/3.0;

        // Update viscosity and thermal conductivity
        GetViscosityAndThermalCondFromTemp(physfield[nScalar-1], m_mu,
            m_thermalConductivity);

        // Interpolate inputs and initialise interpolated output
        Array<OneD, Array<OneD, NekDouble> > vel_interp(m_spacedim);
        Array<OneD, Array<OneD, Array<OneD, NekDouble> > >
                                             deriv_interp(m_spacedim);
        Array<OneD, Array<OneD, Array<OneD, NekDouble> > >
                                             out_interp(m_spacedim);
        for (int i = 0; i < m_spacedim; ++i)
        {
            // Interpolate velocity
            vel_interp[i]   = Array<OneD, NekDouble> (nPts);
            m_fields[0]->PhysInterp1DScaled(
                OneDptscale, physfield[i], vel_interp[i]);

            // Interpolate derivatives
            deriv_interp[i] = Array<OneD,Array<OneD,NekDouble> > (m_spacedim+1);
            for (int j = 0; j < m_spacedim+1; ++j)
            {
                deriv_interp[i][j] = Array<OneD, NekDouble> (nPts);
                m_fields[0]->PhysInterp1DScaled(
                    OneDptscale, derivativesO1[i][j], deriv_interp[i][j]);
            }

            // Output (start from j=1 since flux is zero for rho)
            out_interp[i] = Array<OneD,Array<OneD,NekDouble> > (m_spacedim+2);
            for (int j = 1; j < m_spacedim+2; ++j)
            {
                out_interp[i][j] = Array<OneD, NekDouble> (nPts);
            }
        }

        // Velocity divergence
        for (int j = 0; j < m_spacedim; ++j)
        {
            Vmath::Vadd(nPts, divVel, 1, deriv_interp[j][j], 1,
                        divVel, 1);
        }

        // Velocity divergence scaled by lambda * mu
        Vmath::Smul(nPts, lambda, divVel, 1, divVel, 1);
        Vmath::Vmul(nPts, m_mu,  1, divVel, 1, divVel, 1);

        // Viscous flux vector for the rho equation = 0 (no need to dealias)
        for (int i = 0; i < m_spacedim; ++i)
        {
            Vmath::Zero(nPts_orig, viscousTensor[i][0], 1);
        }

        // Viscous stress tensor (for the momentum equations)
        for (int i = 0; i < m_spacedim; ++i)
        {
            for (int j = i; j < m_spacedim; ++j)
            {
                Vmath::Vadd(nPts, deriv_interp[i][j], 1,
                                  deriv_interp[j][i], 1,
                                  out_interp[i][j+1], 1);

                Vmath::Vmul(nPts, m_mu, 1,
                                  out_interp[i][j+1], 1,
                                  out_interp[i][j+1], 1);

                if (i == j)
                {
                    // Add divergence term to diagonal
                    Vmath::Vadd(nPts, out_interp[i][j+1], 1,
                                  divVel, 1,
                                  out_interp[i][j+1], 1);
                }
                else
                {
                    // Make symmetric
                    out_interp[j][i+1] = out_interp[i][j+1];
                }
            }
        }

        // Terms for the energy equation
        for (int i = 0; i < m_spacedim; ++i)
        {
            Vmath::Zero(nPts, out_interp[i][m_spacedim+1], 1);
            // u_j * tau_ij
            for (int j = 0; j < m_spacedim; ++j)
            {
                Vmath::Vvtvp(nPts, vel_interp[j], 1,
                               out_interp[i][j+1], 1,
                               out_interp[i][m_spacedim+1], 1,
                               out_interp[i][m_spacedim+1], 1);
            }
            // Add k*T_i
            Vmath::Vvtvp(nPts, m_thermalConductivity, 1,
                               deriv_interp[i][m_spacedim], 1,
                               out_interp[i][m_spacedim+1], 1,
                               out_interp[i][m_spacedim+1], 1);
        }

        // Project to original space
        for (int i = 0; i < m_spacedim; ++i)
        {
            for (int j = 1; j < m_spacedim+2; ++j)
            {
                m_fields[0]->PhysGalerkinProjection1DScaled(
                    OneDptscale,
                    out_interp[i][j],
                    viscousTensor[i][j]);
            }
        }
    }

    /**
     * @brief Return the penalty vector for the LDGNS diffusion problem.
     */
    void NavierStokesCFE::v_GetFluxPenalty(
        const Array<OneD, Array<OneD, NekDouble> >  &uFwd,
        const Array<OneD, Array<OneD, NekDouble> >  &uBwd,
              Array<OneD, Array<OneD, NekDouble> >  &penaltyCoeff)
    {
        unsigned int nTracePts  = uFwd[0].num_elements();

        // Compute average temperature
        unsigned int nVariables = uFwd.num_elements();
        Array<OneD, NekDouble> tAve{nTracePts, 0.0};
        Vmath::Svtsvtp(nTracePts, 0.5, uFwd[nVariables-1], 1,
            0.5, uBwd[nVariables-1], 1, tAve, 1);

        // Get average viscosity and thermal conductivity
        Array<OneD, NekDouble> muAve{nTracePts, 0.0};
        Array<OneD, NekDouble> tcAve{nTracePts, 0.0};

        GetViscosityAndThermalCondFromTemp(tAve, muAve, tcAve);

        // Compute penalty term
        for (int i = 0; i < nVariables; ++i)
        {
            // Get jump of u variables
            Vmath::Vsub(nTracePts, uFwd[i], 1, uBwd[i], 1, penaltyCoeff[i], 1);
            // Multiply by variable coefficient = {coeff} ( u^+ - u^- )
            if ( i < nVariables-1 )
            {
                Vmath::Vmul(nTracePts, muAve, 1, penaltyCoeff[i], 1,
                    penaltyCoeff[i], 1);
            }
            else
            {
                Vmath::Vmul(nTracePts, tcAve, 1, penaltyCoeff[i], 1,
                    penaltyCoeff[i], 1);
            }
        }
    }


    /**
     * @brief Update viscosity
     * todo: add artificial viscosity here
     */
    void NavierStokesCFE::GetViscosityAndThermalCondFromTemp(
        const Array<OneD, NekDouble> &temperature,
        Array<OneD, NekDouble> &mu,
        Array<OneD, NekDouble> &thermalCond)
    {
        int nPts       = temperature.num_elements();

        // Variable viscosity through the Sutherland's law
        if (m_ViscosityType == "Variable")
        {
            m_varConv->GetDynamicViscosity(temperature, mu);
        }
        else
        {
            Vmath::Fill(nPts, m_muRef, mu, 1);
        }
        NekDouble tRa = m_Cp / m_Prandtl;
        Vmath::Smul(nPts, tRa, mu, 1, thermalCond, 1);

    }

}