EnforceEntropyTotalEnthalpy.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: EnforceEntropyTotalEnthalpy.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
// 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: Modified Riemann invariant boundary condition.
//              Enforce the entropy and total enthalpy at the inflow boundary;
//              Enforce the Riemann invariant at the outflow boundary.
//              The input can be either VALUE or FILE.
//
///////////////////////////////////////////////////////////////////////////////
 
#include "EnforceEntropyTotalEnthalpy.h"
using namespace std;
 
namespace Nektar
{
 
std::string EnforceEntropyTotalEnthalpy::className =
    GetCFSBndCondFactory().RegisterCreatorFunction(
        "EnforceEntropyTotalEnthalpy", EnforceEntropyTotalEnthalpy::create,
        "Riemann invariant boundary condition, \
                        fixing H and S.");
 
EnforceEntropyTotalEnthalpy::EnforceEntropyTotalEnthalpy(
    const LibUtilities::SessionReaderSharedPtr &pSession,
    const Array<OneD, MultiRegions::ExpListSharedPtr> &pFields,
    const Array<OneD, Array<OneD, NekDouble>> &pTraceNormals,
    const Array<OneD, Array<OneD, NekDouble>> &pGridVelocity,
    const int pSpaceDim, const int bcRegion, const int cnt)
    : CFSBndCond(pSession, pFields, pTraceNormals, pGridVelocity, pSpaceDim,
                 bcRegion, cnt)
{
 
    const MultiRegions::ExpListSharedPtr bndexp =
        m_fields[0]->GetBndCondExpansions()[m_bcRegion];
 
    //-> Gather a list of index from trace to this boundary
    m_npts = bndexp->GetTotPoints();
 
    m_bndToTraceMap = Array<OneD, int>(m_npts, -1);
 
    const Array<OneD, const int> &traceBndMap = m_fields[0]->GetTraceBndMap();
 
    // Construct a map for the boundary to trace map for easy acess to
    // phys space points
    int cnt1 = 0;
    for (int e = 0; e < bndexp->GetNumElmts(); ++e)
    {
        int nTracePts = bndexp->GetExp(e)->GetTotPoints();
 
        int id =
            m_fields[0]->GetTrace()->GetPhys_Offset(traceBndMap[m_offset + e]);
 
        // Loop on the points of the m_bcRegion
        for (int i = 0; i < nTracePts; i++)
        {
            // the ith point in region e
            m_bndToTraceMap[cnt1++] = id + i;
        }
    }
 
    Array<OneD, Array<OneD, NekDouble>> BCvals(m_fields.size());
    m_bndPhys = Array<OneD, Array<OneD, NekDouble>>(m_fields.size());
 
    for (int i = 0; i < m_fields.size(); ++i)
    {
        m_bndPhys[i] =
            m_fields[i]->GetBndCondExpansions()[m_bcRegion]->UpdatePhys();
 
        BCvals[i] = Array<OneD, NekDouble>(m_npts);
        Vmath::Vcopy(m_npts, m_bndPhys[i], 1, BCvals[i], 1);
    }
 
    // Set up boudnary required BCs
    m_rhoBC = Array<OneD, NekDouble>(m_npts);
    Vmath::Vcopy(m_npts, BCvals[0], 1, m_rhoBC, 1);
 
    m_velBC = Array<OneD, Array<OneD, NekDouble>>(m_spacedim);
    // Evaluate velocity on boundary
    for (int i = 0; i < m_spacedim; ++i)
    {
        m_velBC[i] = Array<OneD, NekDouble>(m_npts);
        Vmath::Vcopy(m_npts, BCvals[i + 1], 1, m_velBC[i], 1);
        Vmath::Vdiv(m_npts, m_velBC[i], 1, m_rhoBC, 1, m_velBC[i], 1);
    }
    m_pBC = Array<OneD, NekDouble>(m_npts);
    m_varConv->GetPressure(BCvals, m_pBC);
 
    // Computing the normal velocity for characteristics coming
    // from outside the computational domain
    m_VnInf = Array<OneD, NekDouble>(m_npts, 0.0);
    for (int i = 0; i < m_spacedim; i++)
    {
        for (int j = 0; j < m_npts; ++j)
        {
            m_VnInf[j] += m_traceNormals[i][m_bndToTraceMap[j]] * m_velBC[i][j];
        }
    }
}
 
void EnforceEntropyTotalEnthalpy::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 nDimensions = m_spacedim;
 
    Array<OneD, Array<OneD, NekDouble>> FwdBnd(Fwd.size());
    Array<OneD, Array<OneD, NekDouble>> bndPhys(Fwd.size());
 
    // make a local copy of Fwd along boundary of interest
    for (i = 0; i < Fwd.size(); ++i)
    {
        FwdBnd[i] = Array<OneD, NekDouble>(m_npts);
        for (j = 0; j < m_npts; ++j)
        {
            FwdBnd[i][j] = Fwd[i][m_bndToTraceMap[j]];
        }
    }
 
    // Computing the normal velocity for characteristics coming
    // from inside the computational domain
    Array<OneD, NekDouble> Vn(m_npts, 0.0);
 
    for (i = 0; i < nDimensions; ++i)
    {
        for (j = 0; j < m_npts; ++j)
        {
            Vn[j] += m_traceNormals[i][m_bndToTraceMap[j]] * FwdBnd[i + 1][j];
        }
    }
    // divide by density.
    Vmath::Vdiv(m_npts, Vn, 1, FwdBnd[0], 1, Vn, 1);
 
    // Get speed of sound
    Array<OneD, NekDouble> pressure(m_npts);
    Array<OneD, NekDouble> soundSpeed(m_npts);
 
    m_varConv->GetPressure(FwdBnd, pressure);
    m_varConv->GetSoundSpeed(FwdBnd, soundSpeed);
 
    // Get Mach. Note: it is computed by Vn/c
    Array<OneD, NekDouble> Mach(m_npts, 0.0);
    Vmath::Vdiv(m_npts, Vn, 1, soundSpeed, 1, Mach, 1);
    Vmath::Vabs(m_npts, Mach, 1, Mach, 1);
 
    // Auxiliary variables
    Array<OneD, NekDouble> velBC(nDimensions, 0.0);
 
    // L represents properties outside boundary
    // R represents properties inside boundary (numerical state)
    NekDouble rhoL, uL, pL;
    NekDouble EBC, rR, cstar, pstar, rhostar, ustar, Sstar, vn;
 
    NekDouble gamMinOne        = m_gamma - 1.0;
    NekDouble twoOverGamMinOne = 2.0 / gamMinOne;
    NekDouble gamInv           = 1.0 / m_gamma;
 
    NekDouble tmp1, tmp2;
    // Loop on m_bcRegions
    for (int pnt = 0; pnt < m_npts; ++pnt)
    {
        // Impose inflow Riemann invariant
        if (Vn[pnt] <= 0.0)
        {
            // Subsonic flows
            if (Mach[pnt] < 1.00)
            {
                // right characteristic
                rR = -Vn[pnt] - sqrt(m_gamma * pressure[pnt] / FwdBnd[0][pnt]) *
                                    twoOverGamMinOne;
                vn = -m_VnInf[pnt]; // vn BC
 
                // fix total entropy and entropy to be input values
                // compute cstar and ustar using left-pointint characteristic
                // IR^-
                tmp1 = twoOverGamMinOne * rR;
                tmp1 = tmp1 * tmp1;
                tmp2 = rR * rR - vn * vn -
                       twoOverGamMinOne * m_gamma * m_pBC[pnt] / m_rhoBC[pnt];
                tmp2 =
                    (twoOverGamMinOne * twoOverGamMinOne + twoOverGamMinOne) *
                    tmp2;
                cstar   = -twoOverGamMinOne * rR + sqrt(tmp1 - tmp2);
                cstar   = cstar / (twoOverGamMinOne * twoOverGamMinOne +
                                 twoOverGamMinOne);
                ustar   = rR + twoOverGamMinOne * cstar;
                Sstar   = m_pBC[pnt] / pow(m_rhoBC[pnt], m_gamma);
                rhostar = pow(cstar * cstar / (m_gamma * Sstar),
                              0.5 * twoOverGamMinOne);
                pstar   = rhostar * cstar * cstar * gamInv;
 
                // add supplement equation that rhoL=rhostar
                // then pL=pstar, according to IL^0
                // and  uL=ustar, according to IL^+
                rhoL = rhostar;
                pL   = pstar;
                uL   = ustar;
            }
            else // Supersonic inflow
            {
                // all characteristics are from left so just impose
                // star state to left values
                // Note: m_vnInf is the negative of the normal velocity
                // across boundary
                rhoL = m_rhoBC[pnt];
                uL   = -m_VnInf[pnt];
                pL   = m_pBC[pnt];
            }
 
            // Boundary energy
            EBC = pL * twoOverGamMinOne * 0.5;
 
            // evaluate the different between the left state normal
            // velocity and that from the desired condition (note
            // m_VnInf is using an outwards normal definition.
            NekDouble VnDiff = uL + m_VnInf[pnt];
 
            // Boundary velocities & Kinite energy
            // Note: normals are negated since they point outwards in
            // the domain
 
            // Note: Can just use the BC values directly!!
            for (j = 0; j < nDimensions; ++j)
            {
                // Set velocity to the desired conditions modified to
                // take account of the normal state for Riemann
                // problem. (Negative accounts for outwards normal definition)
                // velBC[j] = m_velBC[j][pnt];
                velBC[j] = m_velBC[j][pnt] -
                           VnDiff * m_traceNormals[j][m_bndToTraceMap[pnt]];
 
                EBC += 0.5 * rhoL * velBC[j] * velBC[j];
            }
 
            //-------------------------------------------------------------------------
            // Impose Left hand Riemann Invariant boundary conditions
            m_bndPhys[0][pnt] = rhoL;
            for (j = 0; j < nDimensions; ++j)
            {
                m_bndPhys[j + 1][pnt] = rhoL * velBC[j];
            }
            m_bndPhys[nDimensions + 1][pnt] = EBC;
        }
        else // Outflow
        {
 
            // Note: Allowing the switch can cause worse convergence in this
            // type BC.
            //       So improve it later.
            if (Mach[pnt] < 1.00)
            {
                // subsonic outflow: fix pstar
                rR = -Vn[pnt] - sqrt(m_gamma * pressure[pnt] / FwdBnd[0][pnt]) *
                                    twoOverGamMinOne;
                // vn = -m_VnInf[pnt];
 
                pstar   = m_pBC[pnt];
                rhostar = FwdBnd[0][pnt] * pow((pstar / pressure[pnt]), gamInv);
                cstar   = sqrt(m_gamma * pstar / rhostar);
                ustar   = rR + cstar * twoOverGamMinOne;
 
                rhoL = rhostar;
                uL   = ustar;
                pL   = pstar;
            }
            else
            {
                // supersonic outflow
                // Just set to imposed state and let Riemann BC dictate values
                rhoL = m_rhoBC[pnt];
                uL   = -m_VnInf[pnt];
                pL   = m_pBC[pnt];
            }
 
            // Boundary energy
            EBC = pL * twoOverGamMinOne * 0.5;
 
            // Boundary velocities & Kinite energy
            // Note: normals are negated since they point outwards in
            // the domain
            for (j = 0; j < nDimensions; ++j)
            {
                velBC[j] = -1.0 * uL * m_traceNormals[j][m_bndToTraceMap[pnt]];
                EBC += 0.5 * rhoL * velBC[j] * velBC[j];
            }
 
            // Impose Left hand Riemann Invariant boundary conditions
            m_bndPhys[0][pnt] = rhoL;
            for (j = 0; j < nDimensions; ++j)
            {
                m_bndPhys[j + 1][pnt] = rhoL * velBC[j];
            }
            m_bndPhys[nDimensions + 1][pnt] = EBC;
        }
    }
}
 
} // namespace Nektar