RiemannInvariantBC.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: RiemannInvariantBC.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: Riemann invariant boundary condition
//
///////////////////////////////////////////////////////////////////////////////
 
#include "RiemannInvariantBC.h"
 
using namespace std;
 
namespace Nektar
{
 
std::string RiemannInvariantBC::className =
    GetCFSBndCondFactory().RegisterCreatorFunction(
        "RiemannInvariant", RiemannInvariantBC::create,
        "Riemann invariant boundary condition.");
 
RiemannInvariantBC::RiemannInvariantBC(
    const LibUtilities::SessionReaderSharedPtr &pSession,
    const Array<OneD, MultiRegions::ExpListSharedPtr> &pFields,
    const Array<OneD, Array<OneD, NekDouble>> &pTraceNormals,
    const int pSpaceDim, const int bcRegion, const int cnt)
    : CFSBndCond(pSession, pFields, pTraceNormals, pSpaceDim, bcRegion, cnt)
{
    // Calculate VnInf
    int nTracePts = m_fields[0]->GetTrace()->GetNpoints();
    m_VnInf       = Array<OneD, NekDouble>(nTracePts, 0.0);
 
    // Computing the normal velocity for characteristics coming
    // from outside the computational domain
    for (int i = 0; i < m_spacedim; i++)
    {
        Vmath::Svtvp(nTracePts, m_velInf[i], m_traceNormals[i], 1, m_VnInf, 1,
                     m_VnInf, 1);
    }
}
 
void RiemannInvariantBC::v_Apply(
    Array<OneD, Array<OneD, NekDouble>> &Fwd,
    [[maybe_unused]] Array<OneD, Array<OneD, NekDouble>> &physarray,
    [[maybe_unused]] const NekDouble &time)
{
    int i, j;
    int nTracePts   = m_fields[0]->GetTrace()->GetNpoints();
    int nDimensions = m_spacedim;
 
    const Array<OneD, const int> &traceBndMap = m_fields[0]->GetTraceBndMap();
 
    NekDouble gammaInv         = 1.0 / m_gamma;
    NekDouble gammaMinusOne    = m_gamma - 1.0;
    NekDouble gammaMinusOneInv = 1.0 / gammaMinusOne;
 
    // Computing the normal velocity for characteristics coming
    // from inside the computational domain
    Array<OneD, NekDouble> Vn(nTracePts, 0.0);
    Array<OneD, NekDouble> Vel(nTracePts, 0.0);
    for (i = 0; i < nDimensions; ++i)
    {
        Vmath::Vdiv(nTracePts, Fwd[i + 1], 1, Fwd[0], 1, Vel, 1);
        Vmath::Vvtvp(nTracePts, m_traceNormals[i], 1, Vel, 1, Vn, 1, Vn, 1);
    }
 
    // Computing the absolute value of the velocity in order to compute the
    // Mach number to decide whether supersonic or subsonic
    Array<OneD, NekDouble> absVel(nTracePts, 0.0);
    m_varConv->GetAbsoluteVelocity(Fwd, absVel);
 
    // Get speed of sound
    Array<OneD, NekDouble> pressure(nTracePts);
    Array<OneD, NekDouble> soundSpeed(nTracePts);
 
    m_varConv->GetPressure(Fwd, pressure);
    m_varConv->GetSoundSpeed(Fwd, soundSpeed);
 
    // Get Mach
    Array<OneD, NekDouble> Mach(nTracePts, 0.0);
    Vmath::Vdiv(nTracePts, Vn, 1, soundSpeed, 1, Mach, 1);
    Vmath::Vabs(nTracePts, Mach, 1, Mach, 1);
 
    // Auxiliary variables
    int eMax;
    int e, id1, id2, nBCEdgePts, pnt;
    NekDouble cPlus, rPlus, cMinus, rMinus, VDBC, VNBC;
    Array<OneD, NekDouble> velBC(nDimensions, 0.0);
    Array<OneD, NekDouble> rhoVelBC(nDimensions, 0.0);
    NekDouble rhoBC, EBC, cBC, sBC, pBC;
 
    eMax = m_fields[0]->GetBndCondExpansions()[m_bcRegion]->GetExpSize();
 
    // Loop on m_bcRegions
    for (e = 0; e < eMax; ++e)
    {
        nBCEdgePts = m_fields[0]
                         ->GetBndCondExpansions()[m_bcRegion]
                         ->GetExp(e)
                         ->GetTotPoints();
 
        id1 =
            m_fields[0]->GetBndCondExpansions()[m_bcRegion]->GetPhys_Offset(e);
        id2 =
            m_fields[0]->GetTrace()->GetPhys_Offset(traceBndMap[m_offset + e]);
 
        // Loop on the points of the m_bcRegion
        for (i = 0; i < nBCEdgePts; i++)
        {
            pnt = id2 + i;
 
            // Impose inflow Riemann invariant
            if (Vn[pnt] <= 0.0)
            {
                // Subsonic flows
                if (Mach[pnt] < 1.00)
                {
                    // + Characteristic from inside
                    cPlus = sqrt(m_gamma * pressure[pnt] / Fwd[0][pnt]);
                    rPlus = Vn[pnt] + 2.0 * cPlus * gammaMinusOneInv;
 
                    // - Characteristic from boundary
                    cMinus = sqrt(m_gamma * m_pInf / m_rhoInf);
                    rMinus = m_VnInf[pnt] - 2.0 * cMinus * gammaMinusOneInv;
                }
                else
                {
                    // + Characteristic from inside
                    cPlus = sqrt(m_gamma * m_pInf / m_rhoInf);
                    rPlus = m_VnInf[pnt] + 2.0 * cPlus * gammaMinusOneInv;
 
                    // + Characteristic from inside
                    cMinus = sqrt(m_gamma * m_pInf / m_rhoInf);
                    rMinus = m_VnInf[pnt] - 2.0 * cPlus * gammaMinusOneInv;
                }
 
                // Riemann boundary variables
                VNBC = 0.5 * (rPlus + rMinus);
                cBC  = 0.25 * gammaMinusOne * (rPlus - rMinus);
                VDBC = VNBC - m_VnInf[pnt];
 
                // Thermodynamic boundary variables
                sBC   = m_pInf / (pow(m_rhoInf, m_gamma));
                rhoBC = pow((cBC * cBC) / (m_gamma * sBC), gammaMinusOneInv);
                pBC   = rhoBC * cBC * cBC * gammaInv;
 
                // Kinetic energy initialiasation
                NekDouble EkBC = 0.0;
 
                // Boundary velocities
                for (j = 0; j < nDimensions; ++j)
                {
                    velBC[j]    = m_velInf[j] + VDBC * m_traceNormals[j][pnt];
                    rhoVelBC[j] = rhoBC * velBC[j];
                    EkBC += 0.5 * rhoBC * velBC[j] * velBC[j];
                }
 
                // Boundary energy
                EBC = pBC * gammaMinusOneInv + EkBC;
 
                // Imposing Riemann Invariant boundary conditions
                (m_fields[0]
                     ->GetBndCondExpansions()[m_bcRegion]
                     ->UpdatePhys())[id1 + i] = rhoBC;
                for (j = 0; j < nDimensions; ++j)
                {
                    (m_fields[j + 1]
                         ->GetBndCondExpansions()[m_bcRegion]
                         ->UpdatePhys())[id1 + i] = rhoVelBC[j];
                }
                (m_fields[nDimensions + 1]
                     ->GetBndCondExpansions()[m_bcRegion]
                     ->UpdatePhys())[id1 + i] = EBC;
            }
            else // Impose outflow Riemann invariant
            {
                // Subsonic flows
                if (Mach[pnt] < 1.00)
                {
                    // + Characteristic from inside
                    cPlus = sqrt(m_gamma * pressure[pnt] / Fwd[0][pnt]);
                    rPlus = Vn[pnt] + 2.0 * cPlus * gammaMinusOneInv;
 
                    // - Characteristic from boundary
                    cMinus = sqrt(m_gamma * m_pInf / m_rhoInf);
                    rMinus = m_VnInf[pnt] - 2.0 * cMinus * gammaMinusOneInv;
                }
                else
                {
                    // + Characteristic from inside
                    cPlus = sqrt(m_gamma * pressure[pnt] / Fwd[0][pnt]);
                    rPlus = Vn[pnt] + 2.0 * cPlus * gammaMinusOneInv;
 
                    // + Characteristic from inside
                    cMinus = sqrt(m_gamma * pressure[pnt] / Fwd[0][pnt]);
                    rMinus = Vn[pnt] - 2.0 * cPlus * gammaMinusOneInv;
                }
 
                // Riemann boundary variables
                VNBC = 0.5 * (rPlus + rMinus);
                cBC  = 0.25 * gammaMinusOne * (rPlus - rMinus);
                VDBC = VNBC - Vn[pnt];
 
                // Thermodynamic boundary variables
                sBC   = pressure[pnt] / (pow(Fwd[0][pnt], m_gamma));
                rhoBC = pow((cBC * cBC) / (m_gamma * sBC), gammaMinusOneInv);
                pBC   = rhoBC * cBC * cBC * gammaInv;
 
                // Kinetic energy initialiasation
                NekDouble EkBC = 0.0;
 
                // Boundary velocities
                for (j = 0; j < nDimensions; ++j)
                {
                    velBC[j] = Fwd[j + 1][pnt] / Fwd[0][pnt] +
                               VDBC * m_traceNormals[j][pnt];
                    rhoVelBC[j] = rhoBC * velBC[j];
                    EkBC += 0.5 * rhoBC * velBC[j] * velBC[j];
                }
 
                // Boundary energy
                EBC = pBC * gammaMinusOneInv + EkBC;
 
                // Imposing Riemann Invariant boundary conditions
                (m_fields[0]
                     ->GetBndCondExpansions()[m_bcRegion]
                     ->UpdatePhys())[id1 + i] = rhoBC;
                for (j = 0; j < nDimensions; ++j)
                {
                    (m_fields[j + 1]
                         ->GetBndCondExpansions()[m_bcRegion]
                         ->UpdatePhys())[id1 + i] = rhoVelBC[j];
                }
                (m_fields[nDimensions + 1]
                     ->GetBndCondExpansions()[m_bcRegion]
                     ->UpdatePhys())[id1 + i] = EBC;
            }
        }
    }
}
 
} // namespace Nektar