AUSM2Solver.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: AUSM2Solver.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
// 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: AUSM2 Riemann solver.
//
///////////////////////////////////////////////////////////////////////////////
 
#include <CompressibleFlowSolver/RiemannSolvers/AUSM2Solver.h>
 
namespace Nektar
{
std::string AUSM2Solver::solverName =
    SolverUtils::GetRiemannSolverFactory().RegisterCreatorFunction(
        "AUSM2", AUSM2Solver::create, "AUSM2 Riemann solver");
 
AUSM2Solver::AUSM2Solver(const LibUtilities::SessionReaderSharedPtr &pSession)
    : CompressibleSolver(pSession)
{
}
 
/**
 * @brief AUSM2 Riemann solver
 *
 * @param rhoL      Density left state.
 * @param rhoR      Density right state.
 * @param rhouL     x-momentum component left state.
 * @param rhouR     x-momentum component right state.
 * @param rhovL     y-momentum component left state.
 * @param rhovR     y-momentum component right state.
 * @param rhowL     z-momentum component left state.
 * @param rhowR     z-momentum component right state.
 * @param EL        Energy left state.
 * @param ER        Energy right state.
 * @param rhof      Computed Riemann flux for density.
 * @param rhouf     Computed Riemann flux for x-momentum component
 * @param rhovf     Computed Riemann flux for y-momentum component
 * @param rhowf     Computed Riemann flux for z-momentum component
 * @param Ef        Computed Riemann flux for energy.
 */
void AUSM2Solver::v_PointSolve(double rhoL, double rhouL, double rhovL,
                               double rhowL, double EL, double rhoR,
                               double rhouR, double rhovR, double rhowR,
                               double ER, double &rhof, double &rhouf,
                               double &rhovf, double &rhowf, double &Ef)
{
    // Left and Right velocities
    NekDouble uL = rhouL / rhoL;
    NekDouble vL = rhovL / rhoL;
    NekDouble wL = rhowL / rhoL;
    NekDouble uR = rhouR / rhoR;
    NekDouble vR = rhovR / rhoR;
    NekDouble wR = rhowR / rhoR;
 
    // Internal energy (per unit mass)
    NekDouble eL = (EL - 0.5 * (rhouL * uL + rhovL * vL + rhowL * wL)) / rhoL;
    NekDouble eR = (ER - 0.5 * (rhouR * uR + rhovR * vR + rhowR * wR)) / rhoR;
    // Pressure
    NekDouble pL = m_eos->GetPressure(rhoL, eL);
    NekDouble pR = m_eos->GetPressure(rhoR, eR);
    // Speed of sound
    NekDouble cL = m_eos->GetSoundSpeed(rhoL, eL);
    NekDouble cR = m_eos->GetSoundSpeed(rhoR, eR);
 
    // Average speeds of sound
    NekDouble cA = 0.5 * (cL + cR);
 
    // Local Mach numbers
    NekDouble ML = uL / cA;
    NekDouble MR = uR / cA;
 
    // Parameters for specify the upwinding
    NekDouble beta   = 0.125;
    NekDouble alpha  = 0.1875;
    NekDouble sigma  = 1.0;
    NekDouble Kp     = 0.25;
    NekDouble Ku     = 0.75;
    NekDouble Mtilde = 0.5 * (ML * ML + MR * MR);
    NekDouble rhoA   = 0.5 * (rhoL + rhoR);
    NekDouble Mp     = -Kp * ((pR - pL) / (rhoA * cA * cA)) *
                   std::max(1.0 - sigma * Mtilde, 0.0);
 
    NekDouble Mbar = M4Function(0, beta, ML) + M4Function(1, beta, MR) + Mp;
 
    NekDouble pu = -2.0 * Ku * rhoA * cA * cA * (MR - ML) *
                   P5Function(0, alpha, ML) * P5Function(1, alpha, MR);
 
    NekDouble pbar =
        pL * P5Function(0, alpha, ML) + pR * P5Function(1, alpha, MR) + pu;
 
    if (Mbar >= 0.0)
    {
        rhof  = cA * Mbar * rhoL;
        rhouf = cA * Mbar * rhoL * uL + pbar;
        rhovf = cA * Mbar * rhoL * vL;
        rhowf = cA * Mbar * rhoL * wL;
        Ef    = cA * Mbar * (EL + pL);
    }
    else
    {
        rhof  = cA * Mbar * rhoR;
        rhouf = cA * Mbar * rhoR * uR + pbar;
        rhovf = cA * Mbar * rhoR * vR;
        rhowf = cA * Mbar * rhoR * wR;
        Ef    = cA * Mbar * (ER + pR);
    }
}
 
double AUSM2Solver::M1Function(int A, double M)
{
    double out;
 
    if (A == 0)
    {
        out = 0.5 * (M + fabs(M));
    }
    else
    {
        out = 0.5 * (M - fabs(M));
    }
 
    return out;
}
 
double AUSM2Solver::M2Function(int A, double M)
{
    double out;
 
    if (A == 0)
    {
        out = 0.25 * (M + 1.0) * (M + 1.0);
    }
    else
    {
        out = -0.25 * (M - 1.0) * (M - 1.0);
    }
 
    return out;
}
 
double AUSM2Solver::M4Function(int A, double beta, double M)
{
    double out;
 
    if (fabs(M) >= 1.0)
    {
        out = M1Function(A, M);
    }
    else
    {
        out = M2Function(A, M);
 
        if (A == 0)
        {
            out *= 1.0 - 16.0 * beta * M2Function(1, M);
        }
        else
        {
            out *= 1.0 + 16.0 * beta * M2Function(0, M);
        }
    }
 
    return out;
}
 
double AUSM2Solver::P5Function(int A, double alpha, double M)
{
    double out;
 
    if (fabs(M) >= 1.0)
    {
        out = (1.0 / M) * M1Function(A, M);
    }
    else
    {
        out = M2Function(A, M);
 
        if (A == 0)
        {
            out *= (2.0 - M) - 16.0 * alpha * M * M2Function(1, M);
        }
        else
        {
            out *= (-2.0 - M) + 16.0 * alpha * M * M2Function(0, M);
        }
    }
 
    return out;
}
} // namespace Nektar