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).
//
// License for the specific language governing rights and limitations under
// 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
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// 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() : CompressibleSolver()
    {

    }

    /**
     * @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)
    {        
        static NekDouble gamma = m_params["gamma"]();
        
        // 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;

        // Left and right pressures
        NekDouble pL = (gamma - 1.0) *
            (EL - 0.5 * (rhouL * uL + rhovL * vL + rhowL * wL));
        NekDouble pR = (gamma - 1.0) *
            (ER - 0.5 * (rhouR * uR + rhovR * vR + rhowR * wR));
        NekDouble cL = sqrt(gamma * pL / rhoL);
        NekDouble cR = sqrt(gamma * pR / rhoR);
        
        // 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;
    }
}