APEUpwindSolver.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: APEUpwindSolver.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).
//
// 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: Upwind Riemann solver for the APE equations.
//
///////////////////////////////////////////////////////////////////////////////
 
#include <AcousticSolver/RiemannSolvers/APEUpwindSolver.h>
 
using namespace std;
 
namespace Nektar
{
 
std::string APEUpwindSolver::solverName =
    SolverUtils::GetRiemannSolverFactory().RegisterCreatorFunction(
        "APEUpwind", APEUpwindSolver::create,
        "Upwind solver for the APE equation");
 
APEUpwindSolver::APEUpwindSolver(
    const LibUtilities::SessionReaderSharedPtr &pSession)
    : AcousticSolver(pSession)
{
}
 
/**
 * @brief Upwind Riemann solver
 *
 * The fluxes are straight out of sympy, so lets just hope the compiler
 * optimizes them for us.
 *
 * @param pL     Perturbation pressure left state
 * @param rhoL   Perturbation density left state
 * @param pR     Perturbation pressure right state
 * @param rhoR   Perturbation density right state
 * @param uL     x perturbation velocity component left state
 * @param uR     x perturbation velocity component right state
 * @param vL     y perturbation velocity component left state
 * @param vR     y perturbation velocity component right state
 * @param wL     z perturbation velocity component left state
 * @param wR     z perturbation velocity component right state
 * @param c0sqL  Base pressure left state
 * @param c0sqR  Base pressure right state
 * @param rho0L  Base density left state
 * @param rho0R  Base density right state
 * @param u0L    Base x velocity component left state
 * @param u0R    Base x velocity component right state
 * @param v0L    Base y velocity component left state
 * @param v0R    Base y velocity component right state
 * @param w0L    Base z velocity component left state
 * @param w0R    Base z velocity component right state
 * @param pF     Computed Riemann flux for perturbation pressure
 * @param rhoF   Computed Riemann flux for perturbation density
 * @param uF     Computed Riemann flux for x perturbation velocity component
 * @param vF     Computed Riemann flux for y perturbation velocity component
 * @param wF     Computed Riemann flux for z perturbation velocity component
 */
void APEUpwindSolver::v_PointSolve(
    NekDouble pL, [[maybe_unused]] NekDouble rhoL, NekDouble uL, NekDouble vL,
    NekDouble wL, NekDouble pR, [[maybe_unused]] NekDouble rhoR, NekDouble uR,
    NekDouble vR, NekDouble wR, NekDouble c0sqL, NekDouble rho0L, NekDouble u0L,
    NekDouble v0L, NekDouble w0L, NekDouble c0sqR, NekDouble rho0R,
    NekDouble u0R, NekDouble v0R, NekDouble w0R, NekDouble &pF,
    [[maybe_unused]] NekDouble &rhoF, NekDouble &uF, NekDouble &vF,
    NekDouble &wF)
{
    // Speed of sound
    NekDouble c0L = sqrt(c0sqL);
    NekDouble c0R = sqrt(c0sqR);
    NekDouble c0M = (c0L + c0R) / 2.0;
 
    NekDouble u0M = (u0L + u0R) / 2.0;
 
    pF = 0.0;
    uF = 0.0;
    vF = 0.0;
    wF = 0.0;
 
    // lambda_3
    if (u0M - c0M > 0)
    {
        pF = pF + 0.5 * (c0L - u0L) *
                      (-rho0L * v0L * vL * (c0L * u0L + c0sqL) -
                       rho0L * w0L * wL * (c0L * u0L + c0sqL) +
                       (c0sqL - pow(u0L, 2)) * (rho0L * c0L * uL - pL)) /
                      (c0sqL - pow(u0L, 2));
 
        uF = uF +
             0.5 * (c0L - u0L) *
                 (rho0L * c0L * (c0L * u0L + c0sqL) * (v0L * vL + w0L * wL) -
                  rho0L * c0sqL * uL * (c0sqL - pow(u0L, 2)) +
                  c0L * pL * (c0sqL - pow(u0L, 2))) /
                 (rho0L * c0sqL * (c0sqL - pow(u0L, 2)));
    }
    else
    {
        pF = pF + 0.5 * (c0R - u0R) *
                      (-rho0R * v0R * vR * (c0R * u0R + c0sqR) -
                       rho0R * w0R * wR * (c0R * u0R + c0sqR) +
                       (c0sqR - pow(u0R, 2)) * (rho0R * c0R * uR - pR)) /
                      (c0sqR - pow(u0R, 2));
 
        uF = uF +
             0.5 * (c0R - u0R) *
                 (rho0R * c0R * (c0R * u0R + c0sqR) * (v0R * vR + w0R * wR) -
                  rho0R * c0sqR * uR * (c0sqR - pow(u0R, 2)) +
                  c0R * pR * (c0sqR - pow(u0R, 2))) /
                 (rho0R * c0sqR * (c0sqR - pow(u0R, 2)));
    }
 
    // lambda_4
    if (u0M + c0M > 0)
    {
        pF = pF + 0.5 * (c0L + u0L) *
                      (-rho0L * v0L * vL * (c0L * u0L - c0sqL) -
                       rho0L * w0L * wL * (c0L * u0L - c0sqL) +
                       (c0sqL - pow(u0L, 2)) * (rho0L * c0L * uL + pL)) /
                      (c0sqL - pow(u0L, 2));
 
        uF = uF +
             0.5 * (c0L + u0L) *
                 (-rho0L * c0L * (c0L * u0L - c0sqL) * (v0L * vL + w0L * wL) +
                  rho0L * c0sqL * uL * (c0sqL - pow(u0L, 2)) +
                  c0L * pL * (c0sqL - pow(u0L, 2))) /
                 (rho0L * c0sqL * (c0sqL - pow(u0L, 2)));
    }
    else
    {
        pF = pF + 0.5 * (c0R + u0R) *
                      (-rho0R * v0R * vR * (c0R * u0R - c0sqR) -
                       rho0R * w0R * wR * (c0R * u0R - c0sqR) +
                       (c0sqR - pow(u0R, 2)) * (rho0R * c0R * uR + pR)) /
                      (c0sqR - pow(u0R, 2));
 
        uF = uF +
             0.5 * (c0R + u0R) *
                 (-rho0R * c0R * (c0R * u0R - c0sqR) * (v0R * vR + w0R * wR) +
                  rho0R * c0sqR * uR * (c0sqR - pow(u0R, 2)) +
                  c0R * pR * (c0sqR - pow(u0R, 2))) /
                 (rho0R * c0sqR * (c0sqR - pow(u0R, 2)));
    }
}
 
} // namespace Nektar