NavierStokesCFEAxisym.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: NavierStokesCFEAxisym.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.
//
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// 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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//
// Description: Navier Stokes equations in conservative variables
//
///////////////////////////////////////////////////////////////////////////////
 
#include <CompressibleFlowSolver/EquationSystems/NavierStokesCFEAxisym.h>
 
namespace Nektar
{
 
std::string NavierStokesCFEAxisym::className =
    SolverUtils::GetEquationSystemFactory().RegisterCreatorFunction(
        "NavierStokesCFEAxisym", NavierStokesCFEAxisym::create,
        "Axisymmetric NavierStokes equations in conservative variables.");
 
NavierStokesCFEAxisym::NavierStokesCFEAxisym(
    const LibUtilities::SessionReaderSharedPtr &pSession,
    const SpatialDomains::MeshGraphSharedPtr &pGraph)
    : UnsteadySystem(pSession, pGraph),
      CompressibleFlowSystem(pSession, pGraph),
      NavierStokesCFE(pSession, pGraph)
{
}
 
void NavierStokesCFEAxisym::v_InitObject(bool DeclareFields)
{
    NavierStokesCFE::v_InitObject(DeclareFields);
 
    int nVariables   = m_fields.size();
    int npoints      = GetNpoints();
    m_viscousForcing = Array<OneD, Array<OneD, NekDouble>>(nVariables);
    for (int i = 0; i < nVariables; ++i)
    {
        m_viscousForcing[i] = Array<OneD, NekDouble>(npoints, 0.0);
    }
}
 
void NavierStokesCFEAxisym::v_DoDiffusion(
    const Array<OneD, Array<OneD, NekDouble>> &inarray,
    Array<OneD, Array<OneD, NekDouble>> &outarray,
    const Array<OneD, Array<OneD, NekDouble>> &pFwd,
    const Array<OneD, Array<OneD, NekDouble>> &pBwd)
{
    int npoints    = GetNpoints();
    int nvariables = inarray.size();
 
    NavierStokesCFE::v_DoDiffusion(inarray, outarray, pFwd, pBwd);
 
    for (int i = 0; i < nvariables; ++i)
    {
        Vmath::Vadd(npoints, m_viscousForcing[i], 1, outarray[i], 1,
                    outarray[i], 1);
    }
}
 
/**
 * @brief Return the flux vector for the LDG diffusion problem.
 * \todo Complete the viscous flux vector
 */
void NavierStokesCFEAxisym::v_GetViscousFluxVector(
    const Array<OneD, const Array<OneD, NekDouble>> &physfield,
    TensorOfArray3D<NekDouble> &derivativesO1,
    TensorOfArray3D<NekDouble> &viscousTensor)
{
    int i, j;
    int nVariables = m_fields.size();
    int nPts       = physfield[0].size();
 
    // 1/r
    Array<OneD, Array<OneD, NekDouble>> coords(3);
    Array<OneD, NekDouble> invR(nPts, 0.0);
    for (int i = 0; i < 3; i++)
    {
        coords[i] = Array<OneD, NekDouble>(nPts);
    }
    m_fields[0]->GetCoords(coords[0], coords[1], coords[2]);
    for (int i = 0; i < nPts; ++i)
    {
        if (coords[0][i] < NekConstants::kNekZeroTol)
        {
            invR[i] = 0;
        }
        else
        {
            invR[i] = 1.0 / coords[0][i];
        }
    }
 
    // Stokes hypothesis
    const NekDouble lambda = -2.0 / 3.0;
 
    // Auxiliary variables
    Array<OneD, NekDouble> divVel(nPts, 0.0);
    Array<OneD, NekDouble> tmp(nPts, 0.0);
    Array<OneD, NekDouble> mu(nPts, 0.0);
    Array<OneD, NekDouble> thermalConductivity(nPts, 0.0);
 
    // Update viscosity and thermal conductivity
    GetViscosityAndThermalCondFromTemp(physfield[nVariables - 2], mu,
                                       thermalConductivity);
 
    // Velocity divergence = d(u_r)/dr + d(u_z)/dz + u_r/r
    Vmath::Vadd(nPts, derivativesO1[0][0], 1, derivativesO1[1][1], 1, divVel,
                1);
    Vmath::Vvtvp(nPts, physfield[0], 1, invR, 1, divVel, 1, divVel, 1);
 
    // Velocity divergence scaled by lambda * mu
    Vmath::Smul(nPts, lambda, divVel, 1, divVel, 1);
    Vmath::Vmul(nPts, mu, 1, divVel, 1, divVel, 1);
 
    // Viscous flux vector for the rho equation = 0
    for (i = 0; i < m_spacedim; ++i)
    {
        Vmath::Zero(nPts, viscousTensor[i][0], 1);
    }
 
    // Viscous stress tensor (for the momentum equations)
 
    for (i = 0; i < 2; ++i)
    {
        for (j = i; j < 2; ++j)
        {
            Vmath::Vadd(nPts, derivativesO1[i][j], 1, derivativesO1[j][i], 1,
                        viscousTensor[i][j + 1], 1);
 
            Vmath::Vmul(nPts, mu, 1, viscousTensor[i][j + 1], 1,
                        viscousTensor[i][j + 1], 1);
 
            if (i == j)
            {
                // Add divergence term to diagonal
                Vmath::Vadd(nPts, viscousTensor[i][j + 1], 1, divVel, 1,
                            viscousTensor[i][j + 1], 1);
            }
            else
            {
                // Copy to make symmetric
                Vmath::Vcopy(nPts, viscousTensor[i][j + 1], 1,
                             viscousTensor[j][i + 1], 1);
            }
        }
    }
    // Swirl case
    if (m_spacedim == 3)
    {
        // Tau_theta_theta = mu ( 2*u_r/r - 2/3*div(u))
        Vmath::Vmul(nPts, physfield[0], 1, invR, 1, viscousTensor[2][3], 1);
        Vmath::Smul(nPts, 2.0, viscousTensor[2][3], 1, viscousTensor[2][3], 1);
        Vmath::Vmul(nPts, mu, 1, viscousTensor[2][3], 1, viscousTensor[2][3],
                    1);
        Vmath::Vadd(nPts, viscousTensor[2][3], 1, divVel, 1,
                    viscousTensor[2][3], 1);
 
        // Tau_r_theta = mu (-u_theta/r + d(u_theta)/dr )
        Vmath::Vmul(nPts, physfield[2], 1, invR, 1, viscousTensor[2][1], 1);
        Vmath::Smul(nPts, -1.0, viscousTensor[2][1], 1, viscousTensor[2][1], 1);
        Vmath::Vadd(nPts, derivativesO1[0][2], 1, viscousTensor[2][1], 1,
                    viscousTensor[2][1], 1);
        Vmath::Vmul(nPts, mu, 1, viscousTensor[2][1], 1, viscousTensor[2][1],
                    1);
        Vmath::Vcopy(nPts, viscousTensor[2][1], 1, viscousTensor[0][3], 1);
 
        // Tau_z_theta = mu (d(u_theta)/dz )
        Vmath::Vmul(nPts, mu, 1, derivativesO1[1][2], 1, viscousTensor[2][2],
                    1);
        Vmath::Vcopy(nPts, viscousTensor[2][2], 1, viscousTensor[1][3], 1);
    }
 
    // Terms for the energy equation
    for (i = 0; i < m_spacedim; ++i)
    {
        Vmath::Zero(nPts, viscousTensor[i][m_spacedim + 1], 1);
        // u_j * tau_ij
        for (j = 0; j < m_spacedim; ++j)
        {
            Vmath::Vvtvp(nPts, physfield[j], 1, viscousTensor[i][j + 1], 1,
                         viscousTensor[i][m_spacedim + 1], 1,
                         viscousTensor[i][m_spacedim + 1], 1);
        }
        // Add k*T_i
        if (i != 2)
        {
            Vmath::Vvtvp(nPts, thermalConductivity, 1,
                         derivativesO1[i][m_spacedim], 1,
                         viscousTensor[i][m_spacedim + 1], 1,
                         viscousTensor[i][m_spacedim + 1], 1);
        }
        else
        {
            Vmath::Vmul(nPts, derivativesO1[i][m_spacedim], 1, invR, 1, tmp, 1);
            Vmath::Vvtvp(nPts, thermalConductivity, 1, tmp, 1,
                         viscousTensor[i][m_spacedim + 1], 1,
                         viscousTensor[i][m_spacedim + 1], 1);
        }
    }
 
    // Update viscous forcing
    //   r-momentum: F = 1/r * (tau_rr - tau_theta_theta)
    if (m_spacedim == 3)
    {
        Vmath::Vsub(nPts, viscousTensor[0][1], 1, viscousTensor[2][3], 1,
                    m_viscousForcing[1], 1);
        Vmath::Vmul(nPts, m_viscousForcing[1], 1, invR, 1, m_viscousForcing[1],
                    1);
    }
    else
    {
        Vmath::Vmul(nPts, viscousTensor[0][1], 1, invR, 1, m_viscousForcing[1],
                    1);
    }
 
    //   z-momentum: F = 1/r * tau_r_z
    Vmath::Vmul(nPts, viscousTensor[0][2], 1, invR, 1, m_viscousForcing[2], 1);
 
    //  Theta_momentum: F = 2* tau_r_theta
    if (m_spacedim == 3)
    {
        Vmath::Vmul(nPts, viscousTensor[0][3], 1, invR, 1, m_viscousForcing[3],
                    1);
        Vmath::Smul(nPts, 2.0, m_viscousForcing[3], 1, m_viscousForcing[3], 1);
    }
 
    // Energy: F = 1/r* viscousTensor_T_r
    Vmath::Vmul(nPts, viscousTensor[0][m_spacedim + 1], 1, invR, 1,
                m_viscousForcing[m_spacedim + 1], 1);
}
 
} // namespace Nektar