MappingXYofZ.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: MappingXYofZ.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: Mapping of the type X = x + f(z), Y = y + g(z)
//
///////////////////////////////////////////////////////////////////////////////

#include <GlobalMapping/MappingXYofZ.h>
#include <MultiRegions/ExpList.h>

namespace Nektar
{
namespace GlobalMapping
{

std::string MappingXYofZ::className =
        GetMappingFactory().RegisterCreatorFunction("XYofZ",
                MappingXYofZ::create, "X = x + f(z), Y = y +g(z)");

/**
 * @class MappingXYofZ
 * This class implements a constant-Jacobian mapping defined by
 * \f[ \bar{x} = \bar{x}(x,z) = x + f(z) \f]
 * \f[ \bar{y} = \bar{y}(y,z) = y + g(z) \f]
 * \f[ \bar{z} = z \f]
 * where \f$(\bar{x},\bar{y},\bar{z})\f$ are the Cartesian (physical) 
 * coordinates and \f$(x,y,z)\f$ are the transformed (computational)
 *  coordinates.
 */
MappingXYofZ::MappingXYofZ(
        const LibUtilities::SessionReaderSharedPtr &pSession,
        const Array<OneD, MultiRegions::ExpListSharedPtr>&   pFields)
    : Mapping(pSession, pFields)
{
}

/**
 *
 */
void MappingXYofZ::v_InitObject(
        const Array<OneD, MultiRegions::ExpListSharedPtr> &pFields,
        const TiXmlElement                                *pMapping)
{
    Mapping::v_InitObject(pFields, pMapping);

    m_constantJacobian = true;

    ASSERTL0(m_nConvectiveFields==3,
           "Mapping X = x + f(z), Y = y+g(z) needs 3 velocity components.");
}

void MappingXYofZ::v_ContravarToCartesian(
    const Array<OneD, Array<OneD, NekDouble> >        &inarray,
    Array<OneD, Array<OneD, NekDouble> >              &outarray)
{
    int physTot = m_fields[0]->GetTotPoints();

    // U1 = u1 + fz*u3
    Vmath::Vvtvp(physTot, m_GeometricInfo[0], 1, inarray[2], 1, 
                            inarray[0], 1, outarray[0],1);

    // U2 = u2 + gz*u3
    Vmath::Vvtvp(physTot, m_GeometricInfo[3], 1, inarray[2], 1, 
                            inarray[1], 1, outarray[1],1);

    // U3 = u3
    Vmath::Vcopy(physTot, inarray[2], 1, outarray[2], 1);
}

void MappingXYofZ::v_CovarToCartesian(
    const Array<OneD, Array<OneD, NekDouble> >        &inarray,
    Array<OneD, Array<OneD, NekDouble> >              &outarray)
{
    int physTot = m_fields[0]->GetTotPoints();
    Array<OneD, NekDouble> wk(physTot, 0.0);

    // U1 = u1
    Vmath::Vcopy(physTot, inarray[0], 1, outarray[0], 1);

    // U2 = u2
    Vmath::Vcopy(physTot, inarray[1], 1, outarray[1], 1);

    // U3 = u3 - fz*u1 - gz*u2
    Vmath::Vmul(physTot, m_GeometricInfo[0], 1, inarray[0], 1, wk, 1);
    Vmath::Vsub(physTot, inarray[2], 1, wk, 1, outarray[2], 1);
    Vmath::Vmul(physTot, m_GeometricInfo[3], 1, inarray[1], 1, wk, 1);
    Vmath::Vsub(physTot, inarray[2], 1, wk, 1, outarray[2], 1);
}

void MappingXYofZ::v_ContravarFromCartesian(
    const Array<OneD, Array<OneD, NekDouble> >        &inarray,
    Array<OneD, Array<OneD, NekDouble> >              &outarray)
{
    int physTot = m_fields[0]->GetTotPoints();
    Array<OneD, NekDouble> wk(physTot, 0.0);

    // U1 = u1 - fz * u3
    Vmath::Vmul(physTot, m_GeometricInfo[0], 1, inarray[2], 1, wk, 1);
    Vmath::Vsub(physTot, inarray[0], 1, wk, 1, outarray[0], 1);        

    // U2 = u2 - gz*u3
    Vmath::Vmul(physTot, m_GeometricInfo[3], 1, inarray[2], 1, wk, 1);
    Vmath::Vsub(physTot, inarray[1], 1, wk, 1, outarray[1], 1);

    // U3 = u3
    Vmath::Vcopy(physTot, inarray[2], 1, outarray[2], 1);        
}

void MappingXYofZ::v_CovarFromCartesian(
    const Array<OneD, Array<OneD, NekDouble> >        &inarray,
    Array<OneD, Array<OneD, NekDouble> >              &outarray)
{
    int physTot = m_fields[0]->GetTotPoints();

    // U1 = u1
    Vmath::Vcopy(physTot, inarray[0], 1, outarray[0], 1);

    // U2 = u2
    Vmath::Vcopy(physTot, inarray[1], 1, outarray[1], 1);

    // U3 = u3 + fz*u1 + gz*u2
    Vmath::Vmul(physTot, m_GeometricInfo[0], 1, 
                         inarray[0], 1, outarray[2], 1);
    Vmath::Vvtvp(physTot, m_GeometricInfo[3], 1, inarray[1], 1,
                            outarray[2], 1, outarray[2], 1);        
    Vmath::Vadd(physTot, inarray[2], 1, outarray[2], 1, outarray[2], 1);
}

void MappingXYofZ::v_GetJacobian(
    Array<OneD, NekDouble>               &outarray)
{
    int physTot = m_fields[0]->GetTotPoints();
    Vmath::Fill(physTot, 1.0, outarray, 1);
}

void MappingXYofZ::v_DotGradJacobian(
    const Array<OneD, Array<OneD, NekDouble> >        &inarray,
    Array<OneD, NekDouble>                            &outarray)
{
    int physTot = m_fields[0]->GetTotPoints();        
    Vmath::Zero(physTot, outarray, 1);   
}

void MappingXYofZ::v_GetMetricTensor(
    Array<OneD, Array<OneD, NekDouble> >              &outarray)
{
    int physTot = m_fields[0]->GetTotPoints();
    int nvel = m_nConvectiveFields;

    for (int i=0; i<nvel*nvel; i++)
    {
        outarray[i] = Array<OneD, NekDouble> (physTot, 0.0); 
    }
    // Fill diagonal with 1.0
    for (int i=0; i<nvel; i++)
    {
        Vmath::Sadd(physTot, 1.0, outarray[i*nvel+i], 1,
                                    outarray[i*nvel+i], 1); 
    }            

    // G_{13} and G_{31} = fz
    Vmath::Vcopy(physTot, m_GeometricInfo[0], 1, outarray[0*nvel+2], 1);
    Vmath::Vcopy(physTot, m_GeometricInfo[0], 1, outarray[2*nvel+0], 1);

    // G_{23} and G_{32} = gz
    Vmath::Vcopy(physTot, m_GeometricInfo[3], 1, outarray[1*nvel+2], 1);
    Vmath::Vcopy(physTot, m_GeometricInfo[3], 1, outarray[2*nvel+1], 1);

    // G^{33} = (1+fz^2 + gz^2)
    Vmath::Vadd(physTot, m_GeometricInfo[2], 1, outarray[2*nvel+2], 1, 
                                                outarray[2*nvel+2], 1);
    Vmath::Vadd(physTot, m_GeometricInfo[5], 1, outarray[2*nvel+2], 1, 
                                                outarray[2*nvel+2], 1);
}

void MappingXYofZ::v_GetInvMetricTensor(
    Array<OneD, Array<OneD, NekDouble> >              &outarray)
{
    int physTot = m_fields[0]->GetTotPoints();
    int nvel = m_nConvectiveFields;
    Array<OneD, NekDouble> wk(physTot, 0.0);

    for (int i=0; i<nvel*nvel; i++)
    {
        outarray[i] = Array<OneD, NekDouble> (physTot, 0.0); 
    }
    // Fill diagonal with 1.0
    for (int i=0; i<nvel; i++)
    {
        Vmath::Sadd(physTot, 1.0, outarray[i*nvel+i], 1, 
                                    outarray[i*nvel+i], 1); 
    }            

    // G^{11} = 1+fz^2
    Vmath::Vadd(physTot, outarray[0*nvel+0], 1, m_GeometricInfo[2], 1,
                                                outarray[0*nvel+0], 1);

    // G^{22} = 1+gz^2
    Vmath::Vadd(physTot, outarray[1*nvel+1], 1, m_GeometricInfo[5], 1,
                                                outarray[1*nvel+1], 1);

    // G^{12} and G^{21} = fz*gz
    Vmath::Vcopy(physTot, m_GeometricInfo[6],1, outarray[0*nvel+1], 1);
    Vmath::Vcopy(physTot, outarray[0*nvel+1], 1, outarray[1*nvel+0], 1);

    // G^{13} and G^{31} = -fz
    Vmath::Vcopy(physTot, m_GeometricInfo[0],1,wk,1); // fz
    Vmath::Neg(physTot, wk, 1);
    Vmath::Vcopy(physTot, wk, 1, outarray[0*nvel+2], 1);
    Vmath::Vcopy(physTot, wk, 1, outarray[2*nvel+0], 1);

    // G^{23} and G^{32} = -gz
    Vmath::Vcopy(physTot, m_GeometricInfo[3],1,wk,1); // fz
    Vmath::Neg(physTot, wk, 1);
    Vmath::Vcopy(physTot, wk, 1, outarray[1*nvel+2], 1);
    Vmath::Vcopy(physTot, wk, 1, outarray[2*nvel+1], 1);
}

void MappingXYofZ::v_ApplyChristoffelContravar(
    const Array<OneD, Array<OneD, NekDouble> >        &inarray,
    Array<OneD, Array<OneD, NekDouble> >              &outarray)
{
    int physTot = m_fields[0]->GetTotPoints();
    int nvel = m_nConvectiveFields;

    for (int i = 0; i< nvel; i++)
    {
        for (int j = 0; j< nvel; j++)
        {
            outarray[i*nvel+j] = Array<OneD, NekDouble>(physTot,0.0);
        }            
    }

    // Calculate non-zero terms  

    // outarray(0,2) = U3 * fzz
    Vmath::Vmul(physTot,m_GeometricInfo[1],1,inarray[2],1,
                                            outarray[0*nvel+2],1);

    // outarray(1,2) = U3 * gzz
    Vmath::Vmul(physTot,m_GeometricInfo[4],1,inarray[2],1,
                                            outarray[1*nvel+2],1);

}

void MappingXYofZ::v_ApplyChristoffelCovar(
    const Array<OneD, Array<OneD, NekDouble> >        &inarray,
    Array<OneD, Array<OneD, NekDouble> >              &outarray)
{
    int physTot = m_fields[0]->GetTotPoints();
    int nvel = m_nConvectiveFields;

    for (int i = 0; i< nvel; i++)
    {
        for (int j = 0; j< nvel; j++)
        {
            outarray[i*nvel+j] = Array<OneD, NekDouble>(physTot,0.0);
        }            
    }

    // Calculate non-zero terms

    // outarray(2,2) = U1 * fzz + U^2 * gzz
    Vmath::Vmul(physTot,m_GeometricInfo[1],1,inarray[0],1,outarray[2*nvel+2],1);
    Vmath::Vvtvp(physTot, m_GeometricInfo[4], 1, inarray[1], 1, 
                            outarray[2*nvel+2], 1, outarray[2*nvel+2],1);
}    

void MappingXYofZ::v_UpdateGeomInfo()
{
    int phystot         = m_fields[0]->GetTotPoints();       
    // Allocation of geometry memory
    m_GeometricInfo =  Array<OneD, Array<OneD, NekDouble> >(7);
    for (int i = 0; i < m_GeometricInfo.num_elements(); i++)
    {
        m_GeometricInfo[i] = Array<OneD, NekDouble>(phystot, 0.0);
    }

    bool waveSpace = m_fields[0]->GetWaveSpace();
    m_fields[0]->SetWaveSpace(false);        

    // Calculate derivatives of x transformation --> m_GeometricInfo 0-1
    m_fields[0]->PhysDeriv(MultiRegions::DirCartesianMap[2],
                                m_coords[0],m_GeometricInfo[0]);
    m_fields[0]->PhysDeriv(MultiRegions::DirCartesianMap[2],
                                m_GeometricInfo[0],m_GeometricInfo[1]);
    // m_GeometricInfo[2] = fz^2
    Vmath::Vmul(phystot,m_GeometricInfo[0],1,m_GeometricInfo[0],1,
                                            m_GeometricInfo[2],1);       

    // Calculate derivatives of transformation -> m_GeometricInfo 3-4
    m_fields[0]->PhysDeriv(MultiRegions::DirCartesianMap[2],
                                m_coords[1],m_GeometricInfo[3]);
    m_fields[0]->PhysDeriv(MultiRegions::DirCartesianMap[2],
                                m_GeometricInfo[3],m_GeometricInfo[4]);
    // m_GeometricInfo[5] = gz^2
    Vmath::Vmul(phystot,m_GeometricInfo[3],1,m_GeometricInfo[3],1,
                                            m_GeometricInfo[5],1);

    // m_GeometricInfo[6] = gz*fz
    Vmath::Vmul(phystot,m_GeometricInfo[0],1,m_GeometricInfo[3],1,
                                            m_GeometricInfo[6],1);

    m_fields[0]->SetWaveSpace(waveSpace);
}

}
}