NavierStokesCFE.h

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///////////////////////////////////////////////////////////////////////////////
//
// File NavierStokesCFE.h
//
// 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: NavierStokes equations in conservative variable
//
///////////////////////////////////////////////////////////////////////////////
 
#ifndef NEKTAR_SOLVERS_COMPRESSIBLEFLOWSOLVER_EQUATIONSYSTEMS_NAVIERSTOKESCFE_H
#define NEKTAR_SOLVERS_COMPRESSIBLEFLOWSOLVER_EQUATIONSYSTEMS_NAVIERSTOKESCFE_H
 
#include <CompressibleFlowSolver/EquationSystems/CompressibleFlowSystem.h>
#include <CompressibleFlowSolver/Misc/EquationOfState.h>
#include <LibUtilities/BasicUtils/Smath.hpp>
#include <MultiRegions/ContField.h>
 
namespace Nektar
{
/**
 *
 *
 **/
class NavierStokesCFE : virtual public CompressibleFlowSystem
{
public:
    friend class MemoryManager<NavierStokesCFE>;
 
    // Creates an instance of this class
    static SolverUtils::EquationSystemSharedPtr create(
        const LibUtilities::SessionReaderSharedPtr &pSession,
        const SpatialDomains::MeshGraphSharedPtr &pGraph)
    {
        SolverUtils::EquationSystemSharedPtr p =
            MemoryManager<NavierStokesCFE>::AllocateSharedPtr(pSession, pGraph);
        p->InitObject();
        return p;
    }
    // Name of class
    static std::string className;
 
    virtual ~NavierStokesCFE();
 
protected:
    std::string m_ViscosityType;
    /// flag to switch between constant viscosity and Sutherland
    /// an enum could be added for more options
    bool m_is_mu_variable{false};
    /// flag to switch between IP and LDG
    /// an enum could be added for more options
    bool m_is_diffIP{false};
    /// flag for shock capturing switch on/off
    /// an enum could be added for more options
    bool m_is_shockCaptPhys{false};
 
    NekDouble m_Cp;
    NekDouble m_Cv;
    NekDouble m_Prandtl;
 
    std::string m_physicalSensorType;
    std::string m_smoothing;
    MultiRegions::ContFieldSharedPtr m_C0ProjectExp;
 
    /// Equation of system for computing temperature
    EquationOfStateSharedPtr m_eos;
 
    NekDouble m_Twall;
    NekDouble m_muRef;
    NekDouble m_thermalConductivityRef;
 
    NavierStokesCFE(const LibUtilities::SessionReaderSharedPtr &pSession,
                    const SpatialDomains::MeshGraphSharedPtr &pGraph);
 
    void GetViscousFluxVectorConservVar(
        const int nDim, const Array<OneD, Array<OneD, NekDouble>> &inarray,
        const TensorOfArray3D<NekDouble> &qfields,
        TensorOfArray3D<NekDouble> &outarray,
        Array<OneD, int> &nonZeroIndex = NullInt1DArray,
        const Array<OneD, Array<OneD, NekDouble>> &normal =
            NullNekDoubleArrayOfArray);
 
    void GetViscousSymmtrFluxConservVar(
        const int nSpaceDim, const Array<OneD, Array<OneD, NekDouble>> &inaverg,
        const Array<OneD, Array<OneD, NekDouble>> &inarray,
        TensorOfArray3D<NekDouble> &outarray, Array<OneD, int> &nonZeroIndex,
        const Array<OneD, Array<OneD, NekDouble>> &normals);
 
    void SpecialBndTreat(Array<OneD, Array<OneD, NekDouble>> &consvar);
 
    void GetArtificialViscosity(
        const Array<OneD, Array<OneD, NekDouble>> &inarray,
        Array<OneD, NekDouble> &muav);
 
    void CalcViscosity(const Array<OneD, const Array<OneD, NekDouble>> &inaverg,
                       Array<OneD, NekDouble> &mu);
 
    void InitObject_Explicit();
 
    virtual void v_InitObject(bool DeclareField = true) override;
 
    virtual void v_DoDiffusion(
        const Array<OneD, Array<OneD, NekDouble>> &inarray,
        Array<OneD, Array<OneD, NekDouble>> &outarray,
        const Array<OneD, Array<OneD, NekDouble>> &pFwd,
        const Array<OneD, Array<OneD, NekDouble>> &pBwd) override;
 
    virtual void v_GetViscousFluxVector(
        const Array<OneD, const Array<OneD, NekDouble>> &physfield,
        TensorOfArray3D<NekDouble> &derivatives,
        TensorOfArray3D<NekDouble> &viscousTensor);
 
    virtual void v_GetViscousFluxVectorDeAlias(
        const Array<OneD, const Array<OneD, NekDouble>> &physfield,
        TensorOfArray3D<NekDouble> &derivatives,
        TensorOfArray3D<NekDouble> &viscousTensor);
 
    void GetPhysicalAV(
        const Array<OneD, const Array<OneD, NekDouble>> &physfield);
 
    void Ducros(Array<OneD, NekDouble> &field);
    void C0Smooth(Array<OneD, NekDouble> &field);
 
    virtual void v_GetFluxPenalty(
        const Array<OneD, const Array<OneD, NekDouble>> &uFwd,
        const Array<OneD, const Array<OneD, NekDouble>> &uBwd,
        Array<OneD, Array<OneD, NekDouble>> &penaltyCoeff);
 
    void GetViscosityAndThermalCondFromTemp(
        const Array<OneD, NekDouble> &temperature, Array<OneD, NekDouble> &mu,
        Array<OneD, NekDouble> &thermalCond);
 
    void GetDivCurlSquared(
        const Array<OneD, MultiRegions::ExpListSharedPtr> &fields,
        const Array<OneD, Array<OneD, NekDouble>> &cnsVar,
        Array<OneD, NekDouble> &div, Array<OneD, NekDouble> &curlSquare,
        const Array<OneD, Array<OneD, NekDouble>> &cnsVarFwd,
        const Array<OneD, Array<OneD, NekDouble>> &cnsVarBwd);
 
    void GetDivCurlFromDvelT(const TensorOfArray3D<NekDouble> &pVarDer,
                             Array<OneD, NekDouble> &div,
                             Array<OneD, NekDouble> &curlSquare);
 
    virtual void v_ExtraFldOutput(
        std::vector<Array<OneD, NekDouble>> &fieldcoeffs,
        std::vector<std::string> &variables) override;
 
    template <class T, typename = typename std::enable_if<
                           std::is_floating_point<T>::value ||
                           tinysimd::is_vector_floating_point<T>::value>::type>
    inline void GetViscosityAndThermalCondFromTempKernel(const T &temperature,
                                                         T &mu, T &thermalCond)
    {
        GetViscosityFromTempKernel(temperature, mu);
        NekDouble tRa = m_Cp / m_Prandtl;
        thermalCond   = tRa * mu;
    }
 
    template <class T, typename = typename std::enable_if<
                           std::is_floating_point<T>::value ||
                           tinysimd::is_vector_floating_point<T>::value>::type>
    inline void GetViscosityFromTempKernel(const T &temperature, T &mu)
    {
        // Variable viscosity through the Sutherland's law
        if (m_is_mu_variable)
        {
            mu = m_varConv->GetDynamicViscosity(temperature);
        }
        else
        {
            mu = m_muRef;
        }
    }
 
    /**
     * @brief Calculate diffusion flux using the Jacobian form.
     *
     * @param in
     *
     * @param out
     * outarray[nvars] flux
     */
    template <class T, typename = typename std::enable_if<
                           std::is_floating_point<T>::value ||
                           tinysimd::is_vector_floating_point<T>::value>::type>
    inline void GetViscousFluxBilinearFormKernel(
        const unsigned short nDim, const unsigned short FluxDirection,
        const unsigned short DerivDirection,
        // these need to be a pointers because of the custom allocator of vec_t
        const T *inaverg, const T *injumpp, const T &mu, T *outarray)
    {
        // Constants
        unsigned short nDim_plus_one           = nDim + 1;
        unsigned short FluxDirection_plus_one  = FluxDirection + 1;
        unsigned short DerivDirection_plus_one = DerivDirection + 1;
 
        NekDouble gammaoPr           = m_gamma / m_Prandtl;
        NekDouble one_minus_gammaoPr = 1.0 - gammaoPr;
 
        constexpr NekDouble OneThird  = 1. / 3.;
        constexpr NekDouble TwoThird  = 2. * OneThird;
        constexpr NekDouble FourThird = 4. * OneThird;
 
        if (DerivDirection == FluxDirection)
        {
            // rho flux always zero
            outarray[0] = 0.0; // store 1x
 
            // load 1/rho
            T oneOrho = 1.0 / inaverg[0]; // load 1x
            // get vel, vel^2, sum of vel^2
            std::array<T, 3> u  = {{0.0, 0.0, 0.0}};
            std::array<T, 3> u2 = {{0.0, 0.0, 0.0}};
            T u2sum{};
            for (unsigned short d = 0; d < nDim; ++d)
            {
                u[d]  = inaverg[d + 1] * oneOrho; // load 1x
                u2[d] = u[d] * u[d];
                u2sum += u2[d];
            }
 
            // get E - sum v^2
            T E_minus_u2sum = inaverg[nDim_plus_one]; // load 1x
            E_minus_u2sum *= oneOrho;
            E_minus_u2sum -= u2sum;
 
            // get nu = mu/rho
            T nu = mu * oneOrho; // load 1x
 
            // ^^^^ above is almost the same for both loops
 
            T tmp1 = OneThird * u2[FluxDirection] + u2sum;
            tmp1 += gammaoPr * E_minus_u2sum;
            tmp1 *= injumpp[0]; // load 1x
 
            T tmp2 = gammaoPr * injumpp[nDim_plus_one] - tmp1; // load 1x
 
            // local var for energy output
            T outTmpE = 0.0;
            for (unsigned short d = 0; d < nDim; ++d)
            {
                unsigned short d_plus_one = d + 1;
                // flux[rhou, rhov, rhow]
                T outTmpD = injumpp[d_plus_one] - u[d] * injumpp[0];
                outTmpD *= nu;
                // flux rhoE
                T tmp3 = one_minus_gammaoPr * u[d];
                outTmpE += tmp3 * injumpp[d_plus_one];
 
                if (d == FluxDirection)
                {
                    outTmpD *= FourThird;
                    T tmp4 = OneThird * u[FluxDirection];
                    outTmpE += tmp4 * injumpp[FluxDirection_plus_one];
                }
 
                outarray[d_plus_one] = outTmpD; // store 1x
            }
 
            outTmpE += tmp2;
            outTmpE *= nu;
            outarray[nDim_plus_one] = outTmpE; // store 1x
        }
        else
        {
            // rho flux always zero
            outarray[0] = 0.0; // store 1x
 
            // load 1/rho
            T oneOrho = 1.0 / inaverg[0]; // load 1x
            // get vel, vel^2, sum of vel^2
            std::array<T, 3> u, u2;
            T u2sum{};
            for (unsigned short d = 0; d < nDim; ++d)
            {
                unsigned short d_plus_one = d + 1;
                u[d]  = inaverg[d_plus_one] * oneOrho; // load 1x
                u2[d] = u[d] * u[d];
                u2sum += u2[d];
                // Not all directions are set
                // one could work out the one that is not set
                outarray[d_plus_one] = 0.0; // store 1x
            }
 
            // get E - sum v^2
            T E_minus_u2sum = inaverg[nDim_plus_one]; // load 1x
            E_minus_u2sum *= oneOrho;
            E_minus_u2sum -= u2sum;
 
            // get nu = mu/rho
            T nu = mu * oneOrho; // load 1x
 
            // ^^^^ above is almost the same for both loops
 
            T tmp1 = u[DerivDirection] * injumpp[0] -
                     injumpp[DerivDirection_plus_one]; // load 2x
            tmp1 *= TwoThird;
            outarray[FluxDirection_plus_one] = nu * tmp1; // store 1x
 
            tmp1 =
                injumpp[FluxDirection_plus_one] - u[FluxDirection] * injumpp[0];
            outarray[DerivDirection_plus_one] = nu * tmp1; // store 1x
 
            tmp1 = OneThird * u[FluxDirection] * u[DerivDirection];
            tmp1 *= injumpp[0];
 
            T tmp2 =
                TwoThird * u[FluxDirection] * injumpp[DerivDirection_plus_one];
 
            tmp1 += tmp2;
 
            tmp1 = u[DerivDirection] * injumpp[FluxDirection_plus_one] - tmp1;
            outarray[nDim_plus_one] = nu * tmp1; // store 1x
        }
    }
 
    /**
     * @brief Return the flux vector for the IP diffusion problem, based on
     * conservative variables
     */
    template <bool IS_TRACE>
    void GetViscousFluxVectorConservVar(
        const int nDim, const Array<OneD, Array<OneD, NekDouble>> &inarray,
        const TensorOfArray3D<NekDouble> &qfields,
        TensorOfArray3D<NekDouble> &outarray, Array<OneD, int> &nonZeroIndex,
        const Array<OneD, Array<OneD, NekDouble>> &normal)
    {
        size_t nConvectiveFields = inarray.size();
        size_t nPts              = inarray[0].size();
        size_t n_nonZero         = nConvectiveFields - 1;
 
        // max outfield dimensions
        constexpr unsigned short nOutMax = 3 - 2 * IS_TRACE;
        constexpr unsigned short nVarMax = 5;
        constexpr unsigned short nDimMax = 3;
 
        // Update viscosity and thermal conductivity
        // unfortunately the artificial viscosity is difficult to vectorize
        // with the current implementation
        Array<OneD, NekDouble> temperature(nPts, 0.0);
        Array<OneD, NekDouble> mu(nPts, 0.0);
        Array<OneD, NekDouble> thermalConductivity(nPts, 0.0);
        m_varConv->GetTemperature(inarray, temperature);
        GetViscosityAndThermalCondFromTemp(temperature, mu,
                                           thermalConductivity);
 
        // vector loop
        using namespace tinysimd;
        using vec_t    = simd<NekDouble>;
        size_t sizeVec = (nPts / vec_t::width) * vec_t::width;
        size_t p       = 0;
 
        for (; p < sizeVec; p += vec_t::width)
        {
            // there is a significant penalty to use std::vector
            alignas(vec_t::alignment) std::array<vec_t, nVarMax> inTmp,
                qfieldsTmp, outTmp;
            alignas(vec_t::alignment) std::array<vec_t, nDimMax> normalTmp;
            alignas(vec_t::alignment) std::array<vec_t, nVarMax * nOutMax>
                outArrTmp{{}};
 
            // rearrenge and load data
            for (size_t f = 0; f < nConvectiveFields; ++f)
            {
                inTmp[f].load(&(inarray[f][p]), is_not_aligned);
                // zero output vector
                if (IS_TRACE)
                {
                    outArrTmp[f] = 0.0;
                }
                else
                {
                    for (int d = 0; d < nDim; ++d)
                    {
                        outArrTmp[f + nConvectiveFields * d] = 0.0;
                    }
                }
            }
            if (IS_TRACE)
            {
                for (size_t d = 0; d < nDim; ++d)
                {
                    normalTmp[d].load(&(normal[d][p]), is_not_aligned);
                }
            }
 
            // get viscosity
            vec_t muV{};
            muV.load(&(mu[p]), is_not_aligned);
 
            for (size_t nderiv = 0; nderiv < nDim; ++nderiv)
            {
                // rearrenge and load data
                for (size_t f = 0; f < nConvectiveFields; ++f)
                {
                    qfieldsTmp[f].load(&(qfields[nderiv][f][p]),
                                       is_not_aligned);
                }
 
                for (size_t d = 0; d < nDim; ++d)
                {
                    GetViscousFluxBilinearFormKernel(
                        nDim, d, nderiv, inTmp.data(), qfieldsTmp.data(), muV,
                        outTmp.data());
 
                    if (IS_TRACE)
                    {
                        for (size_t f = 0; f < nConvectiveFields; ++f)
                        {
                            outArrTmp[f] += normalTmp[d] * outTmp[f];
                        }
                    }
                    else
                    {
                        for (size_t f = 0; f < nConvectiveFields; ++f)
                        {
                            outArrTmp[f + nConvectiveFields * d] += outTmp[f];
                        }
                    }
                }
            }
 
            // store data
            if (IS_TRACE)
            {
                for (int f = 0; f < nConvectiveFields; ++f)
                {
                    outArrTmp[f].store(&(outarray[0][f][p]), is_not_aligned);
                }
            }
            else
            {
                for (int d = 0; d < nDim; ++d)
                {
                    for (int f = 0; f < nConvectiveFields; ++f)
                    {
                        outArrTmp[f + nConvectiveFields * d].store(
                            &(outarray[d][f][p]), is_not_aligned);
                    }
                }
            }
        }
 
        // scalar loop
        for (; p < nPts; ++p)
        {
            std::array<NekDouble, nVarMax> inTmp, qfieldsTmp, outTmp;
            std::array<NekDouble, nDimMax> normalTmp;
            std::array<NekDouble, nVarMax * nOutMax> outArrTmp{{}};
            // rearrenge and load data
            for (int f = 0; f < nConvectiveFields; ++f)
            {
                inTmp[f] = inarray[f][p];
                // zero output vector
                if (IS_TRACE)
                {
                    outArrTmp[f] = 0.0;
                }
                else
                {
                    for (int d = 0; d < nDim; ++d)
                    {
                        outArrTmp[f + nConvectiveFields * d] = 0.0;
                    }
                }
            }
 
            if (IS_TRACE)
            {
                for (int d = 0; d < nDim; ++d)
                {
                    normalTmp[d] = normal[d][p];
                }
            }
 
            // get viscosity
            NekDouble muS = mu[p];
 
            for (int nderiv = 0; nderiv < nDim; ++nderiv)
            {
                // rearrenge and load data
                for (int f = 0; f < nConvectiveFields; ++f)
                {
                    qfieldsTmp[f] = qfields[nderiv][f][p];
                }
 
                for (int d = 0; d < nDim; ++d)
                {
                    GetViscousFluxBilinearFormKernel(
                        nDim, d, nderiv, inTmp.data(), qfieldsTmp.data(), muS,
                        outTmp.data());
 
                    if (IS_TRACE)
                    {
                        for (size_t f = 0; f < nConvectiveFields; ++f)
                        {
                            outArrTmp[f] += normalTmp[d] * outTmp[f];
                        }
                    }
                    else
                    {
                        for (size_t f = 0; f < nConvectiveFields; ++f)
                        {
                            outArrTmp[f + nConvectiveFields * d] += outTmp[f];
                        }
                    }
                }
            }
 
            // store data
            if (IS_TRACE)
            {
                for (int f = 0; f < nConvectiveFields; ++f)
                {
                    outarray[0][f][p] = outArrTmp[f];
                }
            }
            else
            {
                for (int d = 0; d < nDim; ++d)
                {
                    for (int f = 0; f < nConvectiveFields; ++f)
                    {
                        outarray[d][f][p] =
                            outArrTmp[f + nConvectiveFields * d];
                    }
                }
            }
        }
 
        // this is always the same, it should be initialized with the IP class
        nonZeroIndex = Array<OneD, int>{n_nonZero, 0};
        for (int i = 1; i < n_nonZero + 1; ++i)
        {
            nonZeroIndex[n_nonZero - i] = nConvectiveFields - i;
        }
    }
};
 
} // namespace Nektar
#endif