RinglebFlow.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: RinglebFlow.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
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// DEALINGS IN THE SOFTWARE.
//
// Description: Euler equations for Ringleb flow
//
///////////////////////////////////////////////////////////////////////////////
 
#include <boost/core/ignore_unused.hpp>
 
#include <CompressibleFlowSolver/EquationSystems/RinglebFlow.h>
 
using namespace std;
 
namespace Nektar
{
string RinglebFlow::className =
    SolverUtils::GetEquationSystemFactory().RegisterCreatorFunction(
        "RinglebFlow", RinglebFlow::create,
        "Euler equations for Ringleb flow.");
 
RinglebFlow::RinglebFlow(const LibUtilities::SessionReaderSharedPtr &pSession,
                         const SpatialDomains::MeshGraphSharedPtr &pGraph)
    : UnsteadySystem(pSession, pGraph), EulerCFE(pSession, pGraph)
{
}
 
/**
 * @brief Destructor for EulerCFE class.
 */
RinglebFlow::~RinglebFlow()
{
}
 
/**
 * @brief Print out a summary with some relevant information.
 */
void RinglebFlow::v_GenerateSummary(SolverUtils::SummaryList &s)
{
    CompressibleFlowSystem::v_GenerateSummary(s);
    SolverUtils::AddSummaryItem(s, "Problem Type", "RinglebFlow");
}
 
/**
 * @brief Get the exact solutions for isentropic vortex and Ringleb
 * flow problems.
 */
void RinglebFlow::v_EvaluateExactSolution(unsigned int field,
                                          Array<OneD, NekDouble> &outfield,
                                          const NekDouble time)
{
    boost::ignore_unused(time);
    GetExactRinglebFlow(field, outfield);
}
 
/**
 * @brief Compute the exact solution for the Ringleb flow problem.
 */
void RinglebFlow::GetExactRinglebFlow(int field,
                                      Array<OneD, NekDouble> &outarray)
{
    int nTotQuadPoints = GetTotPoints();
 
    Array<OneD, NekDouble> rho(nTotQuadPoints, 100.0);
    Array<OneD, NekDouble> rhou(nTotQuadPoints);
    Array<OneD, NekDouble> rhov(nTotQuadPoints);
    Array<OneD, NekDouble> E(nTotQuadPoints);
    Array<OneD, NekDouble> x(nTotQuadPoints);
    Array<OneD, NekDouble> y(nTotQuadPoints);
    Array<OneD, NekDouble> z(nTotQuadPoints);
 
    m_fields[0]->GetCoords(x, y, z);
 
    // Flow parameters
    NekDouble c, k, phi, r, J, VV, pp, sint, P, ss;
    NekDouble J11, J12, J21, J22, det;
    NekDouble Fx, Fy;
    NekDouble xi, yi;
    NekDouble dV;
    NekDouble dtheta;
    NekDouble par1;
    NekDouble theta     = M_PI / 4.0;
    NekDouble kExt      = 0.7;
    NekDouble V         = kExt * sin(theta);
    NekDouble toll      = 1.0e-8;
    NekDouble errV      = 1.0;
    NekDouble errTheta  = 1.0;
    NekDouble gamma     = m_gamma;
    NekDouble gamma_1_2 = (gamma - 1.0) / 2.0;
 
    for (int i = 0; i < nTotQuadPoints; ++i)
    {
        while ((abs(errV) > toll) || (abs(errTheta) > toll))
        {
            VV   = V * V;
            sint = sin(theta);
            c    = sqrt(1.0 - gamma_1_2 * VV);
            k    = V / sint;
            phi  = 1.0 / k;
            pp   = phi * phi;
            J    = 1.0 / c + 1.0 / (3.0 * c * c * c) +
                1.0 / (5.0 * c * c * c * c * c) -
                0.5 * log((1.0 + c) / (1.0 - c));
 
            r    = pow(c, 1.0 / gamma_1_2);
            xi   = 1.0 / (2.0 * r) * (1.0 / VV - 2.0 * pp) + J / 2.0;
            yi   = phi / (r * V) * sqrt(1.0 - VV * pp);
            par1 = 25.0 - 5.0 * VV;
            ss   = sint * sint;
 
            Fx = xi - x[i];
            Fy = yi - y[i];
 
            J11 =
                39062.5 / pow(par1, 3.5) * (1.0 / VV - 2.0 / VV * ss) * V +
                1562.5 / pow(par1, 2.5) *
                    (-2.0 / (VV * V) + 4.0 / (VV * V) * ss) +
                12.5 / pow(par1, 1.5) * V + 312.5 / pow(par1, 2.5) * V +
                7812.5 / pow(par1, 3.5) * V -
                0.25 *
                    (-1.0 / pow(par1, 0.5) * V / (1.0 - 0.2 * pow(par1, 0.5)) -
                     (1.0 + 0.2 * pow(par1, 0.5)) /
                         pow((1.0 - 0.2 * pow(par1, 0.5)), 2.0) /
                         pow(par1, 0.5) * V) /
                    (1.0 + 0.2 * pow(par1, 0.5)) * (1.0 - 0.2 * pow(par1, 0.5));
 
            J12 = -6250.0 / pow(par1, 2.5) / VV * sint * cos(theta);
            J21 = -6250.0 / (VV * V) * sint / pow(par1, 2.5) *
                      pow((1.0 - ss), 0.5) +
                  78125.0 / V * sint / pow(par1, 3.5) * pow((1.0 - ss), 0.5);
 
            // the matrix is singular when theta = pi/2
            if (abs(y[i]) < toll && abs(cos(theta)) < toll)
            {
                J22 = -39062.5 / pow(par1, 3.5) / V +
                      3125 / pow(par1, 2.5) / (VV * V) +
                      12.5 / pow(par1, 1.5) * V + 312.5 / pow(par1, 2.5) * V +
                      7812.5 / pow(par1, 3.5) * V -
                      0.25 *
                          (-1.0 / pow(par1, 0.5) * V /
                               (1.0 - 0.2 * pow(par1, 0.5)) -
                           (1.0 + 0.2 * pow(par1, 0.5)) /
                               pow((1.0 - 0.2 * pow(par1, 0.5)), 2.0) /
                               pow(par1, 0.5) * V) /
                          (1.0 + 0.2 * pow(par1, 0.5)) *
                          (1.0 - 0.2 * pow(par1, 0.5));
 
                // dV = -dV/dx * Fx
                dV     = -1.0 / J22 * Fx;
                dtheta = 0.0;
                theta  = M_PI / 2.0;
            }
            else
            {
                J22 = 3125.0 / VV * cos(theta) / pow(par1, 2.5) *
                          pow((1.0 - ss), 0.5) -
                      3125.0 / VV * ss / pow(par1, 2.5) / pow((1.0 - ss), 0.5) *
                          cos(theta);
 
                det = -1.0 / (J11 * J22 - J12 * J21);
 
                // [dV dtheta]' = -[invJ]*[Fx Fy]'
                dV     = det * (J22 * Fx - J12 * Fy);
                dtheta = det * (-J21 * Fx + J11 * Fy);
            }
 
            V     = V + dV;
            theta = theta + dtheta;
 
            errV     = abs(dV);
            errTheta = abs(dtheta);
        }
 
        c = sqrt(1.0 - gamma_1_2 * VV);
        r = pow(c, 1.0 / gamma_1_2);
 
        rho[i]  = r;
        rhou[i] = rho[i] * V * cos(theta);
        rhov[i] = rho[i] * V * sin(theta);
        P       = (c * c) * rho[i] / gamma;
        E[i]    = P / (gamma - 1.0) +
               0.5 * (rhou[i] * rhou[i] / rho[i] + rhov[i] * rhov[i] / rho[i]);
 
        // Resetting the guess value
        errV     = 1.0;
        errTheta = 1.0;
        theta    = M_PI / 4.0;
        V        = kExt * sin(theta);
    }
 
    switch (field)
    {
        case 0:
            outarray = rho;
            break;
        case 1:
            outarray = rhou;
            break;
        case 2:
            outarray = rhov;
            break;
        case 3:
            outarray = E;
            break;
        default:
            ASSERTL0(false, "Error in variable number!");
            break;
    }
}
} // namespace Nektar