LEEUpwindSolver.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: LEEUpwindSolver.cpp
//
// For more information, please see: http://www.nektar.info
//
// The MIT License
//
// Copyright (c) 2017 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: Lax-Friedrichs solver for the LEE equations.
//
///////////////////////////////////////////////////////////////////////////////
 
#include <AcousticSolver/RiemannSolvers/LEEUpwindSolver.h>
 
using namespace std;
 
namespace Nektar
{
 
std::string LEEUpwindSolver::solverName =
    SolverUtils::GetRiemannSolverFactory().RegisterCreatorFunction(
        "LEEUpwind", LEEUpwindSolver::create, "Upwind Solver for LEE");
 
/**
 *
 */
LEEUpwindSolver::LEEUpwindSolver(
    const LibUtilities::SessionReaderSharedPtr &pSession)
    : LEESolver(pSession)
{
}
 
/**
 * @brief Lax-Friedrichs Riemann solver
 *
 * @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 rhouL  x perturbation velocity component left state
 * @param rhouR  x perturbation velocity component right state
 * @param rhovL  y perturbation velocity component left state
 * @param rhovR  y perturbation velocity component right state
 * @param rhowL  z perturbation velocity component left state
 * @param rhowR  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 rhouF  Computed Riemann flux for x perturbation velocity component
 * @param rhovF  Computed Riemann flux for y perturbation velocity component
 * @param rhowF  Computed Riemann flux for z perturbation velocity component
 */
void LEEUpwindSolver::v_PointSolve(
    NekDouble pL, NekDouble rhoL, NekDouble rhouL, NekDouble rhovL,
    NekDouble rhowL, NekDouble pR, NekDouble rhoR, NekDouble rhouR,
    NekDouble rhovR, NekDouble rhowR, NekDouble c0sqL,
    [[maybe_unused]] NekDouble rho0L, NekDouble u0L,
    [[maybe_unused]] NekDouble v0L, [[maybe_unused]] NekDouble w0L,
    NekDouble c0sqR, [[maybe_unused]] NekDouble rho0R, NekDouble u0R,
    [[maybe_unused]] NekDouble v0R, [[maybe_unused]] NekDouble w0R,
    NekDouble &pF, NekDouble &rhoF, NekDouble &rhouF, NekDouble &rhovF,
    NekDouble &rhowF)
{
    // 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;
    rhoF  = 0.0;
    rhouF = 0.0;
    rhovF = 0.0;
    rhowF = 0.0;
 
    // lambda_1,2,3
    if (u0M > 0)
    {
        rhoF  = rhoF + u0L * (c0sqL * rhoL - pL) / c0sqL;
        rhovF = rhovF + rhovL * u0L;
        rhowF = rhowF + rhowL * u0L;
    }
    else
    {
        rhoF  = rhoF + u0R * (c0sqR * rhoR - pR) / c0sqR;
        rhovF = rhovF + rhovR * u0R;
        rhowF = rhowF + rhowR * u0R;
    }
 
    // lambda_4
    if (u0M - c0M > 0)
    {
        pF   = pF + 0.5 * (c0L - u0L) * (rhouL * c0L - pL);
        rhoF = rhoF + 0.5 * (c0L - u0L) * (rhouL * c0sqL - c0L * pL) /
                          pow(c0sqL, 3.0 / 2.0);
        rhouF = rhouF + 0.5 * (c0L - u0L) * (-rhouL * c0L + pL) / c0L;
    }
    else
    {
        pF   = pF + 0.5 * (c0R - u0R) * (rhouR * c0R - pR);
        rhoF = rhoF + 0.5 * (c0R - u0R) * (rhouR * c0sqR - c0R * pR) /
                          pow(c0sqR, 3.0 / 2.0);
        rhouF = rhouF + 0.5 * (c0R - u0R) * (-rhouR * c0R + pR) / c0R;
    }
 
    // lambda_5
    if (u0M + c0M > 0)
    {
        pF   = pF + 0.5 * (c0L + u0L) * (rhouL * c0L + pL);
        rhoF = rhoF + 0.5 * (c0L + u0L) * (rhouL * c0sqL + c0L * pL) /
                          pow(c0sqL, 3.0 / 2.0);
        rhouF = rhouF + 0.5 * (c0L + u0L) * (rhouL * c0L + pL) / c0L;
    }
    else
    {
        pF   = pF + 0.5 * (c0R + u0R) * (rhouR * c0R + pR);
        rhoF = rhoF + 0.5 * (c0R + u0R) * (rhouR * c0sqR + c0R * pR) /
                          pow(c0sqR, 3.0 / 2.0);
        rhouF = rhouF + 0.5 * (c0R + u0R) * (rhouR * c0R + pR) / c0R;
    }
}
} // namespace Nektar