RiemannSolver.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: RiemannSolver.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.
//
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// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
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// DEALINGS IN THE SOFTWARE.
//
// Description: Abstract base class for Riemann solvers with factory.
//
///////////////////////////////////////////////////////////////////////////////
 
#include <boost/core/ignore_unused.hpp>
 
#include <LibUtilities/BasicUtils/VmathArray.hpp>
#include <SolverUtils/RiemannSolvers/RiemannSolver.h>
 
#define EPSILON 0.000001
 
#define CROSS(dest, v1, v2)                                                    \
    {                                                                          \
        dest[0] = v1[1] * v2[2] - v1[2] * v2[1];                               \
        dest[1] = v1[2] * v2[0] - v1[0] * v2[2];                               \
        dest[2] = v1[0] * v2[1] - v1[1] * v2[0];                               \
    }
 
#define DOT(v1, v2) (v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2])
 
#define SUB(dest, v1, v2)                                                      \
    {                                                                          \
        dest[0] = v1[0] - v2[0];                                               \
        dest[1] = v1[1] - v2[1];                                               \
        dest[2] = v1[2] - v2[2];                                               \
    }
 
using namespace std;
 
namespace Nektar
{
namespace SolverUtils
{
/**
 * Retrieves the singleton instance of the Riemann solver factory.
 */
RiemannSolverFactory &GetRiemannSolverFactory()
{
    static RiemannSolverFactory instance;
    return instance;
}
 
/**
 * @class RiemannSolver
 *
 * @brief The RiemannSolver class provides an abstract interface under
 * which solvers for various Riemann problems can be implemented.
 */
 
RiemannSolver::RiemannSolver() : m_requiresRotation(false), m_rotStorage(3)
{
}
 
RiemannSolver::RiemannSolver(
    const LibUtilities::SessionReaderSharedPtr &pSession)
    : m_requiresRotation(false), m_rotStorage(3)
{
    boost::ignore_unused(pSession);
}
 
/**
 * @brief Perform the Riemann solve given the forwards and backwards
 * spaces.
 *
 * This routine calls the virtual function #v_Solve to perform the
 * Riemann solve. If the flag #m_requiresRotation is set, then the
 * velocity field is rotated to the normal direction to perform
 * dimensional splitting, and the resulting fluxes are rotated back to
 * the Cartesian directions before being returned. For the Rotation to
 * work, the normal vectors "N" and the location of the vector
 * components in Fwd "vecLocs"must be set via the SetAuxVec() method.
 *
 * @param Fwd   Forwards trace space.
 * @param Bwd   Backwards trace space.
 * @param flux  Resultant flux along trace space.
 */
void RiemannSolver::Solve(const int nDim,
                          const Array<OneD, const Array<OneD, NekDouble>> &Fwd,
                          const Array<OneD, const Array<OneD, NekDouble>> &Bwd,
                          Array<OneD, Array<OneD, NekDouble>> &flux)
{
    if (m_requiresRotation)
    {
        ASSERTL1(CheckVectors("N"), "N not defined.");
        ASSERTL1(CheckAuxVec("vecLocs"), "vecLocs not defined.");
        const Array<OneD, const Array<OneD, NekDouble>> normals =
            m_vectors["N"]();
        const Array<OneD, const Array<OneD, NekDouble>> vecLocs =
            m_auxVec["vecLocs"]();
 
        int nFields = Fwd.size();
        int nPts    = Fwd[0].size();
 
        if (m_rotStorage[0].size() != nFields ||
            m_rotStorage[0][0].size() != nPts)
        {
            for (int i = 0; i < 3; ++i)
            {
                m_rotStorage[i] = Array<OneD, Array<OneD, NekDouble>>(nFields);
                for (int j = 0; j < nFields; ++j)
                {
                    m_rotStorage[i][j] = Array<OneD, NekDouble>(nPts);
                }
            }
        }
 
        rotateToNormal(Fwd, normals, vecLocs, m_rotStorage[0]);
        rotateToNormal(Bwd, normals, vecLocs, m_rotStorage[1]);
        v_Solve(nDim, m_rotStorage[0], m_rotStorage[1], m_rotStorage[2]);
        rotateFromNormal(m_rotStorage[2], normals, vecLocs, flux);
    }
    else
    {
        v_Solve(nDim, Fwd, Bwd, flux);
    }
}
 
/**
 * @brief Rotate a vector field to trace normal.
 *
 * This function performs a rotation of a vector so that the first
 * component aligns with the trace normal direction.
 *
 * The vectors  components are stored in inarray. Their locations must
 * be specified in the "vecLocs" array. vecLocs[0] contains the locations
 * of the first vectors components, vecLocs[1] those of the second and
 * so on.
 *
 * In 2D, this is accomplished through the transform:
 *
 * \f[ (u_x, u_y) = (n_x u_x + n_y u_y, -n_x v_x + n_y v_y) \f]
 *
 * In 3D, we generate a (non-unique) transformation using
 * RiemannSolver::fromToRotation.
 *
 */
void RiemannSolver::rotateToNormal(
    const Array<OneD, const Array<OneD, NekDouble>> &inarray,
    const Array<OneD, const Array<OneD, NekDouble>> &normals,
    const Array<OneD, const Array<OneD, NekDouble>> &vecLocs,
    Array<OneD, Array<OneD, NekDouble>> &outarray)
{
    for (int i = 0; i < inarray.size(); ++i)
    {
        Vmath::Vcopy(inarray[i].size(), inarray[i], 1, outarray[i], 1);
    }
 
    for (int i = 0; i < vecLocs.size(); i++)
    {
        ASSERTL1(vecLocs[i].size() == normals.size(),
                 "vecLocs[i] element count mismatch");
 
        switch (normals.size())
        {
            case 1:
            { // do nothing
                const int nq = inarray[0].size();
                const int vx = (int)vecLocs[i][0];
                Vmath::Vmul(nq, inarray[vx], 1, normals[0], 1, outarray[vx], 1);
                break;
            }
            case 2:
            {
                const int nq = inarray[0].size();
                const int vx = (int)vecLocs[i][0];
                const int vy = (int)vecLocs[i][1];
 
                Vmath::Vmul(nq, inarray[vx], 1, normals[0], 1, outarray[vx], 1);
                Vmath::Vvtvp(nq, inarray[vy], 1, normals[1], 1, outarray[vx], 1,
                             outarray[vx], 1);
                Vmath::Vmul(nq, inarray[vx], 1, normals[1], 1, outarray[vy], 1);
                Vmath::Vvtvm(nq, inarray[vy], 1, normals[0], 1, outarray[vy], 1,
                             outarray[vy], 1);
                break;
            }
 
            case 3:
            {
                const int nq = inarray[0].size();
                const int vx = (int)vecLocs[i][0];
                const int vy = (int)vecLocs[i][1];
                const int vz = (int)vecLocs[i][2];
 
                // Generate matrices if they don't already exist.
                if (m_rotMat.size() == 0)
                {
                    GenerateRotationMatrices(normals);
                }
 
                // Apply rotation matrices.
                Vmath::Vvtvvtp(nq, inarray[vx], 1, m_rotMat[0], 1, inarray[vy],
                               1, m_rotMat[1], 1, outarray[vx], 1);
                Vmath::Vvtvp(nq, inarray[vz], 1, m_rotMat[2], 1, outarray[vx],
                             1, outarray[vx], 1);
                Vmath::Vvtvvtp(nq, inarray[vx], 1, m_rotMat[3], 1, inarray[vy],
                               1, m_rotMat[4], 1, outarray[vy], 1);
                Vmath::Vvtvp(nq, inarray[vz], 1, m_rotMat[5], 1, outarray[vy],
                             1, outarray[vy], 1);
                Vmath::Vvtvvtp(nq, inarray[vx], 1, m_rotMat[6], 1, inarray[vy],
                               1, m_rotMat[7], 1, outarray[vz], 1);
                Vmath::Vvtvp(nq, inarray[vz], 1, m_rotMat[8], 1, outarray[vz],
                             1, outarray[vz], 1);
                break;
            }
 
            default:
                ASSERTL1(false, "Invalid space dimension.");
                break;
        }
    }
}
 
/**
 * @brief Rotate a vector field from trace normal.
 *
 * This function performs a rotation of the triad of vector components
 * provided in inarray so that the first component aligns with the
 * Cartesian components; it performs the inverse operation of
 * RiemannSolver::rotateToNormal.
 */
void RiemannSolver::rotateFromNormal(
    const Array<OneD, const Array<OneD, NekDouble>> &inarray,
    const Array<OneD, const Array<OneD, NekDouble>> &normals,
    const Array<OneD, const Array<OneD, NekDouble>> &vecLocs,
    Array<OneD, Array<OneD, NekDouble>> &outarray)
{
    for (int i = 0; i < inarray.size(); ++i)
    {
        Vmath::Vcopy(inarray[i].size(), inarray[i], 1, outarray[i], 1);
    }
 
    for (int i = 0; i < vecLocs.size(); i++)
    {
        ASSERTL1(vecLocs[i].size() == normals.size(),
                 "vecLocs[i] element count mismatch");
 
        switch (normals.size())
        {
            case 1:
            { // do nothing
                const int nq = normals[0].size();
                const int vx = (int)vecLocs[i][0];
                Vmath::Vmul(nq, inarray[vx], 1, normals[0], 1, outarray[vx], 1);
                break;
            }
            case 2:
            {
                const int nq = normals[0].size();
                const int vx = (int)vecLocs[i][0];
                const int vy = (int)vecLocs[i][1];
 
                Vmath::Vmul(nq, inarray[vy], 1, normals[1], 1, outarray[vx], 1);
                Vmath::Vvtvm(nq, inarray[vx], 1, normals[0], 1, outarray[vx], 1,
                             outarray[vx], 1);
                Vmath::Vmul(nq, inarray[vx], 1, normals[1], 1, outarray[vy], 1);
                Vmath::Vvtvp(nq, inarray[vy], 1, normals[0], 1, outarray[vy], 1,
                             outarray[vy], 1);
                break;
            }
 
            case 3:
            {
                const int nq = normals[0].size();
                const int vx = (int)vecLocs[i][0];
                const int vy = (int)vecLocs[i][1];
                const int vz = (int)vecLocs[i][2];
 
                Vmath::Vvtvvtp(nq, inarray[vx], 1, m_rotMat[0], 1, inarray[vy],
                               1, m_rotMat[3], 1, outarray[vx], 1);
                Vmath::Vvtvp(nq, inarray[vz], 1, m_rotMat[6], 1, outarray[vx],
                             1, outarray[vx], 1);
                Vmath::Vvtvvtp(nq, inarray[vx], 1, m_rotMat[1], 1, inarray[vy],
                               1, m_rotMat[4], 1, outarray[vy], 1);
                Vmath::Vvtvp(nq, inarray[vz], 1, m_rotMat[7], 1, outarray[vy],
                             1, outarray[vy], 1);
                Vmath::Vvtvvtp(nq, inarray[vx], 1, m_rotMat[2], 1, inarray[vy],
                               1, m_rotMat[5], 1, outarray[vz], 1);
                Vmath::Vvtvp(nq, inarray[vz], 1, m_rotMat[8], 1, outarray[vz],
                             1, outarray[vz], 1);
                break;
            }
 
            default:
                ASSERTL1(false, "Invalid space dimension.");
                break;
        }
    }
}
 
/**
 * @brief Determine whether a scalar has been defined in #m_scalars.
 *
 * @param name  Scalar name.
 */
bool RiemannSolver::CheckScalars(std::string name)
{
    return m_scalars.find(name) != m_scalars.end();
}
 
/**
 * @brief Determine whether a vector has been defined in #m_vectors.
 *
 * @param name  Vector name.
 */
bool RiemannSolver::CheckVectors(std::string name)
{
    return m_vectors.find(name) != m_vectors.end();
}
 
/**
 * @brief Determine whether a parameter has been defined in #m_params.
 *
 * @param name  Parameter name.
 */
bool RiemannSolver::CheckParams(std::string name)
{
    return m_params.find(name) != m_params.end();
}
 
/**
 * @brief Determine whether a scalar has been defined in #m_auxScal.
 *
 * @param name  Scalar name.
 */
bool RiemannSolver::CheckAuxScal(std::string name)
{
    return m_auxScal.find(name) != m_auxScal.end();
}
 
/**
 * @brief Determine whether a vector has been defined in #m_auxVec.
 *
 * @param name  Vector name.
 */
bool RiemannSolver::CheckAuxVec(std::string name)
{
    return m_auxVec.find(name) != m_auxVec.end();
}
 
/**
 * @brief Generate rotation matrices for 3D expansions.
 */
void RiemannSolver::GenerateRotationMatrices(
    const Array<OneD, const Array<OneD, NekDouble>> &normals)
{
    Array<OneD, NekDouble> xdir(3, 0.0);
    Array<OneD, NekDouble> tn(3);
    NekDouble tmp[9];
    const int nq = normals[0].size();
    int i, j;
    xdir[0] = 1.0;
 
    // Allocate storage for rotation matrices.
    m_rotMat = Array<OneD, Array<OneD, NekDouble>>(9);
 
    for (i = 0; i < 9; ++i)
    {
        m_rotMat[i] = Array<OneD, NekDouble>(nq);
    }
    for (i = 0; i < normals[0].size(); ++i)
    {
        // Generate matrix which takes us from (1,0,0) vector to trace
        // normal.
        tn[0] = normals[0][i];
        tn[1] = normals[1][i];
        tn[2] = normals[2][i];
        FromToRotation(tn, xdir, tmp);
 
        for (j = 0; j < 9; ++j)
        {
            m_rotMat[j][i] = tmp[j];
        }
    }
}
 
/**
 * @brief A function for creating a rotation matrix that rotates a
 * vector @a from into another vector @a to.
 *
 * Authors: Tomas Möller, John Hughes
 *          "Efficiently Building a Matrix to Rotate One Vector to
 *          Another" Journal of Graphics Tools, 4(4):1-4, 1999
 *
 * @param from  Normalised 3-vector to rotate from.
 * @param to    Normalised 3-vector to rotate to.
 * @param out   Resulting 3x3 rotation matrix (row-major order).
 */
void RiemannSolver::FromToRotation(Array<OneD, const NekDouble> &from,
                                   Array<OneD, const NekDouble> &to,
                                   NekDouble *mat)
{
    NekDouble v[3];
    NekDouble e, h, f;
 
    CROSS(v, from, to);
    e = DOT(from, to);
    f = (e < 0) ? -e : e;
    if (f > 1.0 - EPSILON)
    {
        NekDouble u[3], v[3];
        NekDouble x[3];
        NekDouble c1, c2, c3;
        int i, j;
 
        x[0] = (from[0] > 0.0) ? from[0] : -from[0];
        x[1] = (from[1] > 0.0) ? from[1] : -from[1];
        x[2] = (from[2] > 0.0) ? from[2] : -from[2];
 
        if (x[0] < x[1])
        {
            if (x[0] < x[2])
            {
                x[0] = 1.0;
                x[1] = x[2] = 0.0;
            }
            else
            {
                x[2] = 1.0;
                x[0] = x[1] = 0.0;
            }
        }
        else
        {
            if (x[1] < x[2])
            {
                x[1] = 1.0;
                x[0] = x[2] = 0.0;
            }
            else
            {
                x[2] = 1.0;
                x[0] = x[1] = 0.0;
            }
        }
 
        u[0] = x[0] - from[0];
        u[1] = x[1] - from[1];
        u[2] = x[2] - from[2];
        v[0] = x[0] - to[0];
        v[1] = x[1] - to[1];
        v[2] = x[2] - to[2];
 
        c1 = 2.0 / DOT(u, u);
        c2 = 2.0 / DOT(v, v);
        c3 = c1 * c2 * DOT(u, v);
 
        for (i = 0; i < 3; i++)
        {
            for (j = 0; j < 3; j++)
            {
                mat[3 * i + j] =
                    -c1 * u[i] * u[j] - c2 * v[i] * v[j] + c3 * v[i] * u[j];
            }
            mat[i + 3 * i] += 1.0;
        }
    }
    else
    {
        NekDouble hvx, hvz, hvxy, hvxz, hvyz;
        h      = 1.0 / (1.0 + e);
        hvx    = h * v[0];
        hvz    = h * v[2];
        hvxy   = hvx * v[1];
        hvxz   = hvx * v[2];
        hvyz   = hvz * v[1];
        mat[0] = e + hvx * v[0];
        mat[1] = hvxy - v[2];
        mat[2] = hvxz + v[1];
        mat[3] = hvxy + v[2];
        mat[4] = e + h * v[1] * v[1];
        mat[5] = hvyz - v[0];
        mat[6] = hvxz - v[1];
        mat[7] = hvyz + v[0];
        mat[8] = e + hvz * v[2];
    }
}
 
/**
 * @brief Calculate the flux jacobian of Fwd and Bwd
 *
 * @param Fwd   Forwards trace space.
 * @param Bwd   Backwards trace space.
 * @param flux  Resultant flux along trace space.
 */
void RiemannSolver::CalcFluxJacobian(
    const int nDim, const Array<OneD, const Array<OneD, NekDouble>> &Fwd,
    const Array<OneD, const Array<OneD, NekDouble>> &Bwd,
    DNekBlkMatSharedPtr &FJac, DNekBlkMatSharedPtr &BJac)
{
    int nPts = Fwd[0].size();
 
    if (m_requiresRotation)
    {
        ASSERTL1(CheckVectors("N"), "N not defined.");
        ASSERTL1(CheckAuxVec("vecLocs"), "vecLocs not defined.");
        const Array<OneD, const Array<OneD, NekDouble>> normals =
            m_vectors["N"]();
        const Array<OneD, const Array<OneD, NekDouble>> vecLocs =
            m_auxVec["vecLocs"]();
 
        v_CalcFluxJacobian(nDim, Fwd, Bwd, normals, FJac, BJac);
    }
    else
    {
        Array<OneD, Array<OneD, NekDouble>> normals(nDim);
        for (int i = 0; i < nDim; i++)
        {
            normals[i] = Array<OneD, NekDouble>(nPts, 0.0);
        }
        Vmath::Fill(nPts, 1.0, normals[0], 1);
 
        v_CalcFluxJacobian(nDim, Fwd, Bwd, normals, FJac, BJac);
    }
}
 
void RiemannSolver::v_CalcFluxJacobian(
    const int nDim, const Array<OneD, const Array<OneD, NekDouble>> &Fwd,
    const Array<OneD, const Array<OneD, NekDouble>> &Bwd,
    const Array<OneD, const Array<OneD, NekDouble>> &normals,
    DNekBlkMatSharedPtr &FJac, DNekBlkMatSharedPtr &BJac)
{
    boost::ignore_unused(nDim, Fwd, Bwd, normals, FJac, BJac);
    NEKERROR(ErrorUtil::efatal, "v_CalcFluxJacobian not specified.");
}
 
} // namespace SolverUtils
} // namespace Nektar