IncNavierStokes.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File IncNavierStokes.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: Incompressible Navier Stokes class definition built on
// ADRBase class
//
///////////////////////////////////////////////////////////////////////////////
 
#include <iomanip>
#include <boost/algorithm/string.hpp>
 
#include <IncNavierStokesSolver/EquationSystems/IncNavierStokes.h>
#include <LibUtilities/BasicUtils/Timer.h>
#include <LibUtilities/Communication/Comm.h>
#include <SolverUtils/Filters/Filter.h>
#include <LocalRegions/Expansion2D.h>
#include <LocalRegions/Expansion3D.h>
 
#include <LibUtilities/Polylib/Polylib.h>
#include <LibUtilities/BasicUtils/FileSystem.h>
#include <LibUtilities/BasicUtils/PtsIO.h>
#include <algorithm>
#include <iostream>
#include <fstream>
#include <sstream>
 
#include <tinyxml.h>
#include <LibUtilities/BasicUtils/ParseUtils.h>
#include <SolverUtils/Forcing/ForcingMovingReferenceFrame.h>
 
using namespace std;
 
namespace Nektar
{
 
    /**
     * Constructor. Creates ...
     *
     * \param
     * \param
     */
    IncNavierStokes::IncNavierStokes(
        const LibUtilities::SessionReaderSharedPtr& pSession,
        const SpatialDomains::MeshGraphSharedPtr &pGraph):
        UnsteadySystem(pSession, pGraph),
        AdvectionSystem(pSession, pGraph),
        m_SmoothAdvection(false)
    {
    }
 
    void IncNavierStokes::v_InitObject()
    {
        AdvectionSystem::v_InitObject();
 
        int i,j;
        int numfields = m_fields.size();
        std::string velids[] = {"u","v","w"};
 
        // Set up Velocity field to point to the first m_expdim of m_fields;
        m_velocity = Array<OneD,int>(m_spacedim);
 
        for(i = 0; i < m_spacedim; ++i)
        {
            for(j = 0; j < numfields; ++j)
            {
                std::string var = m_boundaryConditions->GetVariable(j);
                if(boost::iequals(velids[i], var))
                {
                    m_velocity[i] = j;
                    break;
                }
 
                ASSERTL0(j != numfields, "Failed to find field: " + var);
            }
        }
 
        // Set up equation type enum using kEquationTypeStr
        for(i = 0; i < (int) eEquationTypeSize; ++i)
        {
            bool match;
            m_session->MatchSolverInfo("EQTYPE",
                            kEquationTypeStr[i],match,false);
            if(match)
            {
                m_equationType = (EquationType)i;
                break;
            }
        }
        ASSERTL0(i != eEquationTypeSize,
                "EQTYPE not found in SOLVERINFO section");
 
        // This probably should to into specific implementations
        // Equation specific Setups
        switch(m_equationType)
        {
        case eSteadyStokes:
        case eSteadyOseen:
        case eSteadyNavierStokes:
        case eSteadyLinearisedNS:
        case eUnsteadyNavierStokes:
        case eUnsteadyStokes:
            break;
        case eNoEquationType:
        default:
            ASSERTL0(false,"Unknown or undefined equation type");
        }
 
        m_session->LoadParameter("Kinvis", m_kinvis);
 
        // Default advection type per solver
        std::string vConvectiveType;
        switch(m_equationType)
        {
        case eUnsteadyStokes:
        case eSteadyLinearisedNS:
            vConvectiveType = "NoAdvection";
            break;
        case eUnsteadyNavierStokes:
        case eSteadyNavierStokes:
            vConvectiveType = "Convective";
            break;
        case eUnsteadyLinearisedNS:
            vConvectiveType = "Linearised";
            break;
        default:
            break;
        }
 
        // Check if advection type overridden
        if (m_session->DefinesTag("AdvectiveType") &&
            m_equationType != eUnsteadyStokes &&
            m_equationType != eSteadyLinearisedNS)
        {
            vConvectiveType = m_session->GetTag("AdvectiveType");
        }
 
        // Initialise advection
        m_advObject = SolverUtils::GetAdvectionFactory().CreateInstance(
                        vConvectiveType, vConvectiveType);
        m_advObject->InitObject( m_session, m_fields);
 
        // Forcing terms
        m_forcing = SolverUtils::Forcing::Load(m_session, shared_from_this(),
                                            m_fields, v_GetForceDimension());
 
        // check to see if any Robin boundary conditions and if so set
        // up m_field to boundary condition maps;
        m_fieldsBCToElmtID  = Array<OneD, Array<OneD, int> >(numfields);
        m_fieldsBCToTraceID = Array<OneD, Array<OneD, int> >(numfields);
        m_fieldsRadiationFactor  =
                Array<OneD, Array<OneD, NekDouble> > (numfields);
 
        for (i = 0; i < m_fields.size(); ++i)
        {
            bool Set = false;
 
            Array<OneD, const SpatialDomains::BoundaryConditionShPtr > BndConds;
            Array<OneD, MultiRegions::ExpListSharedPtr>  BndExp;
            int radpts = 0;
 
            BndConds = m_fields[i]->GetBndConditions();
            BndExp   = m_fields[i]->GetBndCondExpansions();
            for(int n = 0; n < BndConds.size(); ++n)
            {
                if(boost::iequals(BndConds[n]->GetUserDefined(),"Radiation"))
                {
                    ASSERTL0(BndConds[n]->GetBoundaryConditionType() ==
                        SpatialDomains::eRobin,
                        "Radiation boundary condition must be of type Robin <R>");
 
                    if(Set == false)
                    {
                        m_fields[i]->GetBoundaryToElmtMap(
                            m_fieldsBCToElmtID[i],m_fieldsBCToTraceID[i]);
                        Set = true;
                    }
                    radpts += BndExp[n]->GetTotPoints();
                }
                if(boost::iequals(BndConds[n]->GetUserDefined(),
                        "ZeroNormalComponent"))
                {
                    ASSERTL0(BndConds[n]->GetBoundaryConditionType() ==
                            SpatialDomains::eDirichlet,
                            "Zero Normal Component boundary condition option must be of type Dirichlet <D>");
 
                    if(Set == false)
                    {
                        m_fields[i]->GetBoundaryToElmtMap(
                            m_fieldsBCToElmtID[i],m_fieldsBCToTraceID[i]);
                        Set = true;
                    }
                }
            }
 
            m_fieldsRadiationFactor[i] = Array<OneD, NekDouble>(radpts);
 
            radpts = 0; // reset to use as a counter
 
            for(int n = 0; n < BndConds.size(); ++n)
            {
                if(boost::iequals(BndConds[n]->GetUserDefined(),"Radiation"))
                {
 
                    int npoints    = BndExp[n]->GetNpoints();
                    Array<OneD, NekDouble> x0(npoints,0.0);
                    Array<OneD, NekDouble> x1(npoints,0.0);
                    Array<OneD, NekDouble> x2(npoints,0.0);
                    Array<OneD, NekDouble> tmpArray;
 
                    BndExp[n]->GetCoords(x0,x1,x2);
 
                    LibUtilities::Equation coeff =
                        std::static_pointer_cast<
                    SpatialDomains::RobinBoundaryCondition
                        >(BndConds[n])->m_robinPrimitiveCoeff;
 
                    coeff.Evaluate(x0,x1,x2,m_time,
                                   tmpArray = m_fieldsRadiationFactor[i]+ radpts);
                    //Vmath::Neg(npoints,tmpArray = m_fieldsRadiationFactor[i]+ radpts,1);
                    radpts += npoints;
                }
            }
        }
 
        // Set up maping for womersley BC - and load variables
        for (int i = 0; i < m_fields.size(); ++i)
        {
            for(int n = 0; n < m_fields[i]->GetBndConditions().size(); ++n)
            {
                if(boost::istarts_with(m_fields[i]->GetBndConditions()[n]->GetUserDefined(),"Womersley"))
                {
                    // assumes that boundary condition is applied in normal direction
                    // and is decomposed for each direction. There could be a
                    // unique file for each direction
                    m_womersleyParams[i][n] = MemoryManager<WomersleyParams>::AllocateSharedPtr(m_spacedim);
                    // Read in fourier coeffs and precompute coefficients
                    SetUpWomersley(i, n,
                                   m_fields[i]->GetBndConditions()[n]->GetUserDefined());
 
                    m_fields[i]->GetBoundaryToElmtMap(m_fieldsBCToElmtID[i],m_fieldsBCToTraceID[i]);
 
                }
            }
        }
 
        // Set up Field Meta Data for output files
        m_fieldMetaDataMap["Kinvis"]   = boost::lexical_cast<std::string>(m_kinvis);
        m_fieldMetaDataMap["TimeStep"] = boost::lexical_cast<std::string>(m_timestep);
    }
 
    /**
     * Destructor
     */
    IncNavierStokes::~IncNavierStokes(void)
    {
    }
 
    /**
     * Evaluation -N(V) for all fields except pressure using m_velocity
     */
    void IncNavierStokes::EvaluateAdvectionTerms(
                const Array<OneD, const Array<OneD, NekDouble> > &inarray,
                Array<OneD, Array<OneD, NekDouble> > &outarray,
                const NekDouble time)
    {
        int i;
        int VelDim     = m_velocity.size();
        Array<OneD, Array<OneD, NekDouble> > velocity(VelDim);
 
        int  npoints = m_fields[0]->GetNpoints();
        for (i = 0; i < VelDim; ++i)
        {
            velocity[i] = Array<OneD, NekDouble>(npoints);
            Vmath::Vcopy(npoints, inarray[m_velocity[i]], 1, velocity[i], 1);
        }
        for (auto &x : m_forcing)
        {
            x->PreApply(m_fields, velocity, velocity, time);
        }
 
        m_advObject->Advect(m_nConvectiveFields, m_fields,
                            velocity, inarray, outarray, time);
    }
 
    /**
     * Time dependent boundary conditions updating
     */
    void IncNavierStokes::SetBoundaryConditions(NekDouble time)
    {
        int i, n;
        std::string varName;
        int nvariables = m_fields.size();
 
        for (i = 0; i < nvariables; ++i)
        {
            for(n = 0; n < m_fields[i]->GetBndConditions().size(); ++n)
            {
                if(m_fields[i]->GetBndConditions()[n]->IsTimeDependent())
                {
                    varName = m_session->GetVariable(i);
                    m_fields[i]->EvaluateBoundaryConditions(time, varName);
                }
                else if(boost::istarts_with(
                          m_fields[i]->GetBndConditions()[n]->GetUserDefined(),
                          "Womersley"))
                {
                    SetWomersleyBoundary(i,n);
                }
            }
 
            // Set Radiation conditions if required
            SetRadiationBoundaryForcing(i);
        }
 
        SetZeroNormalVelocity();
    }
 
    /**
     * Probably should be pushed back into ContField?
     */
    void IncNavierStokes::SetRadiationBoundaryForcing(int fieldid)
    {
        int  i,n;
 
        Array<OneD, const SpatialDomains::BoundaryConditionShPtr > BndConds;
        Array<OneD, MultiRegions::ExpListSharedPtr>                BndExp;
 
        BndConds = m_fields[fieldid]->GetBndConditions();
        BndExp   = m_fields[fieldid]->GetBndCondExpansions();
 
        LocalRegions::ExpansionSharedPtr elmt;
        StdRegions::StdExpansionSharedPtr Bc;
 
        int cnt;
        int elmtid,nq,offset, boundary;
        Array<OneD, NekDouble> Bvals, U;
        int cnt1 = 0;
 
        for(cnt = n = 0; n < BndConds.size(); ++n)
        {
            std::string type = BndConds[n]->GetUserDefined();
 
            if((BndConds[n]->GetBoundaryConditionType() ==
                    SpatialDomains::eRobin) &&
                (boost::iequals(type,"Radiation")))
            {
                for(i = 0; i < BndExp[n]->GetExpSize(); ++i,cnt++)
                {
                    elmtid = m_fieldsBCToElmtID[m_velocity[fieldid]][cnt];
                    elmt   = m_fields[fieldid]->GetExp(elmtid);
                    offset = m_fields[fieldid]->GetPhys_Offset(elmtid);
 
                    U = m_fields[fieldid]->UpdatePhys() + offset;
                    Bc = BndExp[n]->GetExp(i);
 
                    boundary = m_fieldsBCToTraceID[fieldid][cnt];
 
                    // Get edge values and put into ubc
                    nq = Bc->GetTotPoints();
                    Array<OneD, NekDouble> ubc(nq);
                    elmt->GetTracePhysVals(boundary,Bc,U,ubc);
 
                    Vmath::Vmul(nq,&m_fieldsRadiationFactor[fieldid][cnt1 +
                                BndExp[n]->GetPhys_Offset(i)],1,
                                &ubc[0],1,&ubc[0],1);
 
                    Bvals = BndExp[n]->UpdateCoeffs()+BndExp[n]->
                                GetCoeff_Offset(i);
 
                    Bc->IProductWRTBase(ubc,Bvals);
                }
                cnt1 += BndExp[n]->GetTotPoints();
            }
            else
            {
                cnt += BndExp[n]->GetExpSize();
            }
        }
    }
 
 
    void IncNavierStokes::SetZeroNormalVelocity()
    {
        // use static trip since cannot use UserDefinedTag for zero
        // velocity and have time dependent conditions
        static bool Setup  = false;
 
        if(Setup == true)
        {
            return;
        }
        Setup = true;
 
        int  i,n;
 
        Array<OneD, Array<OneD, const SpatialDomains::BoundaryConditionShPtr > >
            BndConds(m_spacedim);
        Array<OneD, Array<OneD, MultiRegions::ExpListSharedPtr> >
            BndExp(m_spacedim);
 
 
        for(i = 0; i < m_spacedim; ++i)
        {
            BndConds[i] = m_fields[m_velocity[i]]->GetBndConditions();
            BndExp[i]   = m_fields[m_velocity[i]]->GetBndCondExpansions();
        }
 
        LocalRegions::ExpansionSharedPtr elmt,Bc;
 
        int cnt;
        int elmtid,nq, boundary;
 
        Array<OneD, Array<OneD, NekDouble> > normals;
        Array<OneD, NekDouble> Bphys,Bcoeffs;
 
        int fldid = m_velocity[0];
 
        for(cnt = n = 0; n < BndConds[0].size(); ++n)
        {
            if((BndConds[0][n]->GetBoundaryConditionType() ==
                    SpatialDomains::eDirichlet) &&
                (boost::iequals(BndConds[0][n]->GetUserDefined(),
                    "ZeroNormalComponent")))
            {
                for(i = 0; i < BndExp[0][n]->GetExpSize(); ++i,cnt++)
                {
                    elmtid   = m_fieldsBCToElmtID[fldid][cnt];
                    elmt     = m_fields[0]->GetExp(elmtid);
                    boundary = m_fieldsBCToTraceID[fldid][cnt];
 
                    normals = elmt->GetTraceNormal(boundary);
 
                    nq = BndExp[0][n]->GetExp(i)->GetTotPoints();
                    Array<OneD, NekDouble> normvel(nq,0.0);
 
                    for(int k = 0; k < m_spacedim; ++k)
                    {
                        Bphys  = BndExp[k][n]->UpdatePhys()+
                            BndExp[k][n]->GetPhys_Offset(i);
                        Bc  = BndExp[k][n]->GetExp(i);
                        Vmath::Vvtvp(nq,normals[k],1,Bphys,1,normvel,1,
                                     normvel,1);
                    }
 
                    // negate normvel for next step
                    Vmath::Neg(nq,normvel,1);
 
                    for(int k = 0; k < m_spacedim; ++k)
                    {
                        Bphys  = BndExp[k][n]->UpdatePhys()+
                            BndExp[k][n]->GetPhys_Offset(i);
                        Bcoeffs = BndExp[k][n]->UpdateCoeffs()+
                            BndExp[k][n]->GetCoeff_Offset(i);
                        Bc  = BndExp[k][n]->GetExp(i);
                        Vmath::Vvtvp(nq,normvel,1,normals[k],1,Bphys,1,
                                     Bphys,1);
                        Bc->FwdTrans_BndConstrained(Bphys,Bcoeffs);
                    }
                }
            }
            else
            {
                cnt += BndExp[0][n]->GetExpSize();
            }
        }
    }
 
 
    /**
     *  Womersley boundary condition defintion
     */
    void IncNavierStokes::SetWomersleyBoundary(const int fldid, const int bndid)
    {
        ASSERTL1(m_womersleyParams.count(bndid) == 1,
                "Womersley parameters for this boundary have not been set up");
 
        WomersleyParamsSharedPtr WomParam = m_womersleyParams[fldid][bndid];
        NekComplexDouble zvel;
        int  i,j,k;
 
        int M_coeffs = WomParam->m_wom_vel.size();
 
        NekDouble T = WomParam->m_period;
        NekDouble axis_normal = WomParam->m_axisnormal[fldid];
 
        // Womersley Number
        NekComplexDouble omega_c (2.0*M_PI/T, 0.0);
        NekComplexDouble k_c (0.0, 0.0);
        NekComplexDouble m_time_c (m_time, 0.0);
        NekComplexDouble zi (0.0,1.0);
        NekComplexDouble i_pow_3q2 (-1.0/sqrt(2.0),1.0/sqrt(2.0));
 
        MultiRegions::ExpListSharedPtr  BndCondExp;
        BndCondExp   = m_fields[fldid]->GetBndCondExpansions()[bndid];
 
        StdRegions::StdExpansionSharedPtr bc;
        int cnt=0;
        int nfq;
        Array<OneD, NekDouble> Bvals;
        int exp_npts = BndCondExp->GetExpSize();
        Array<OneD, NekDouble> wbc(exp_npts,0.0);
 
        Array<OneD, NekComplexDouble> zt(M_coeffs);
 
        // preallocate the exponent
        for (k=1; k < M_coeffs; k++)
        {
            k_c  = NekComplexDouble((NekDouble) k, 0.0);
            zt[k] = std::exp(zi * omega_c * k_c * m_time_c);
        }
 
        // Loop over each element in an expansion
        for(i = 0; i < exp_npts; ++i,cnt++)
        {
            // Get Boundary and trace expansion
            bc = BndCondExp->GetExp(i);
            nfq = bc->GetTotPoints();
            Array<OneD, NekDouble> wbc(nfq,0.0);
 
            // Compute womersley solution
            for (j=0; j < nfq; j++)
            {
                wbc[j] = WomParam->m_poiseuille[i][j];
                for (k=1; k < M_coeffs; k++)
                {
                    zvel =  WomParam->m_zvel[i][j][k] * zt[k];
                    wbc[j] = wbc[j] + zvel.real();
                }
            }
 
            // Multiply w by normal to get u,v,w component of velocity
            Vmath::Smul(nfq,axis_normal,wbc,1,wbc,1);
            // get the offset
            Bvals = BndCondExp->UpdateCoeffs()+
                    BndCondExp->GetCoeff_Offset(i);
 
            // Push back to Coeff space
            bc->FwdTrans(wbc,Bvals);
        }
    }
 
 
    void IncNavierStokes::SetUpWomersley(const int fldid, const int bndid, std::string womStr)
    {
        std::string::size_type indxBeg = womStr.find_first_of(':') + 1;
        string filename = womStr.substr(indxBeg,string::npos);
 
        TiXmlDocument doc(filename);
 
        bool loadOkay = doc.LoadFile();
        ASSERTL0(loadOkay,(std::string("Failed to load file: ") +
                           filename).c_str());
 
        TiXmlHandle docHandle(&doc);
 
        int err;    /// Error value returned by TinyXML.
 
        TiXmlElement *nektar = doc.FirstChildElement("NEKTAR");
        ASSERTL0(nektar, "Unable to find NEKTAR tag in file.");
 
        TiXmlElement *wombc = nektar->FirstChildElement("WOMERSLEYBC");
        ASSERTL0(wombc, "Unable to find WOMERSLEYBC tag in file.");
 
        // read womersley parameters
        TiXmlElement *womparam = wombc->FirstChildElement("WOMPARAMS");
        ASSERTL0(womparam, "Unable to find WOMPARAMS tag in file.");
 
        // Input coefficients
        TiXmlElement *params = womparam->FirstChildElement("W");
        map<std::string,std::string> Wparams;
 
        // read parameter list
        while (params)
        {
 
            std::string propstr;
            propstr = params->Attribute("PROPERTY");
 
            ASSERTL0(!propstr.empty(),
                    "Failed to read PROPERTY value Womersley BC Parameter");
 
 
            std::string valstr;
            valstr = params->Attribute("VALUE");
 
            ASSERTL0(!valstr.empty(),
                    "Failed to read VALUE value Womersley BC Parameter");
 
            std::transform(propstr.begin(),propstr.end(),propstr.begin(),
                           ::toupper);
            Wparams[propstr] = valstr;
 
            params = params->NextSiblingElement("W");
        }
        bool parseGood;
 
        // Read parameters
 
        ASSERTL0(Wparams.count("RADIUS") == 1,
          "Failed to find Radius parameter in Womersley boundary conditions");
        std::vector<NekDouble> rad;
        ParseUtils::GenerateVector(Wparams["RADIUS"],rad);
        m_womersleyParams[fldid][bndid]->m_radius = rad[0];
 
        ASSERTL0(Wparams.count("PERIOD") == 1,
          "Failed to find period parameter in Womersley boundary conditions");
        std::vector<NekDouble> period;
        parseGood = ParseUtils::GenerateVector(Wparams["PERIOD"],period);
        m_womersleyParams[fldid][bndid]->m_period = period[0];
 
 
        ASSERTL0(Wparams.count("AXISNORMAL") == 1,
          "Failed to find axisnormal parameter in Womersley boundary conditions");
        std::vector<NekDouble> anorm;
        parseGood = ParseUtils::GenerateVector(Wparams["AXISNORMAL"],anorm);
        m_womersleyParams[fldid][bndid]->m_axisnormal[0] = anorm[0];
        m_womersleyParams[fldid][bndid]->m_axisnormal[1] = anorm[1];
        m_womersleyParams[fldid][bndid]->m_axisnormal[2] = anorm[2];
 
 
        ASSERTL0(Wparams.count("AXISPOINT") == 1,
          "Failed to find axispoint parameter in Womersley boundary conditions");
        std::vector<NekDouble> apt;
        parseGood = ParseUtils::GenerateVector(Wparams["AXISPOINT"],apt);
        m_womersleyParams[fldid][bndid]->m_axispoint[0] = apt[0];
        m_womersleyParams[fldid][bndid]->m_axispoint[1] = apt[1];
        m_womersleyParams[fldid][bndid]->m_axispoint[2] = apt[2];
 
        // Read Temporal Fourier Coefficients.
 
        // Find the FourierCoeff tag
        TiXmlElement *coeff = wombc->FirstChildElement("FOURIERCOEFFS");
 
        // Input coefficients
        TiXmlElement *fval = coeff->FirstChildElement("F");
 
        int indx;
        int nextFourierCoeff = -1;
 
        while (fval)
        {
            nextFourierCoeff++;
 
            TiXmlAttribute *fvalAttr = fval->FirstAttribute();
            std::string attrName(fvalAttr->Name());
 
            ASSERTL0(attrName == "ID",
                (std::string("Unknown attribute name: ") + attrName).c_str());
 
            err = fvalAttr->QueryIntValue(&indx);
            ASSERTL0(err == TIXML_SUCCESS, "Unable to read attribute ID.");
 
            std::string coeffStr = fval->FirstChild()->ToText()->ValueStr();
            vector<NekDouble> coeffvals;
 
            parseGood = ParseUtils::GenerateVector(coeffStr, coeffvals);
            ASSERTL0(parseGood,
                    (std::string("Problem reading value of fourier coefficient, ID=") +
                    boost::lexical_cast<string>(indx)).c_str());
            ASSERTL1(coeffvals.size() == 2,
                    (std::string("Have not read two entries of Fourier coefficicent from ID="+
                    boost::lexical_cast<string>(indx)).c_str()));
 
            m_womersleyParams[fldid][bndid]->m_wom_vel.push_back(NekComplexDouble (coeffvals[0], coeffvals[1]));
 
            fval = fval->NextSiblingElement("F");
        }
 
        // starting point of precalculation
        int  i,j,k;
        // M fourier coefficients
        int M_coeffs = m_womersleyParams[fldid][bndid]->m_wom_vel.size();
        NekDouble R = m_womersleyParams[fldid][bndid]->m_radius;
        NekDouble T = m_womersleyParams[fldid][bndid]->m_period;
        Array<OneD, NekDouble > x0 = m_womersleyParams[fldid][bndid]->m_axispoint;
 
        NekComplexDouble rqR;
        // Womersley Number
        NekComplexDouble omega_c (2.0*M_PI/T, 0.0);
        NekComplexDouble alpha_c (R*sqrt(omega_c.real()/m_kinvis), 0.0);
        NekComplexDouble z1 (1.0,0.0);
        NekComplexDouble i_pow_3q2 (-1.0/sqrt(2.0),1.0/sqrt(2.0));
 
        MultiRegions::ExpListSharedPtr  BndCondExp;
        BndCondExp   = m_fields[fldid]->GetBndCondExpansions()[bndid];
 
        StdRegions::StdExpansionSharedPtr bc;
        int cnt = 0;
        int nfq;
        Array<OneD, NekDouble> Bvals;
 
        int exp_npts = BndCondExp->GetExpSize();
        Array<OneD, NekDouble> wbc(exp_npts,0.0);
 
        // allocate time indepedent variables
        m_womersleyParams[fldid][bndid]->m_poiseuille = Array<OneD, Array<OneD, NekDouble> > (exp_npts);
        m_womersleyParams[fldid][bndid]->m_zvel = Array<OneD, Array<OneD, Array<OneD, NekComplexDouble> > > (exp_npts);
        // could use M_coeffs - 1 but need to avoid complicating things
        Array<OneD, NekComplexDouble> zJ0(M_coeffs);
        Array<OneD, NekComplexDouble> lamda_n(M_coeffs);
        Array<OneD, NekComplexDouble> k_c(M_coeffs);
        NekComplexDouble zJ0r;
 
        for (k=1; k < M_coeffs; k++)
        {
            k_c[k]  = NekComplexDouble((NekDouble) k, 0.0);
            lamda_n[k] = i_pow_3q2 * alpha_c * sqrt(k_c[k]);
            zJ0[k]  = Polylib::ImagBesselComp(0,lamda_n[k]);
        }
 
        // Loop over each element in an expansion
        for(i = 0; i < exp_npts; ++i,cnt++)
        {
            // Get Boundary and trace expansion
            bc = BndCondExp->GetExp(i);
            nfq = bc->GetTotPoints();
 
            Array<OneD, NekDouble> x(nfq,0.0);
            Array<OneD, NekDouble> y(nfq,0.0);
            Array<OneD, NekDouble> z(nfq,0.0);
            bc->GetCoords(x,y,z);
 
            m_womersleyParams[fldid][bndid]->m_poiseuille[i] =
                    Array<OneD, NekDouble> (nfq);
            m_womersleyParams[fldid][bndid]->m_zvel[i] =
                    Array<OneD, Array<OneD, NekComplexDouble> > (nfq);
 
            // Compute coefficients
            for (j=0; j < nfq; j++)
            {
                rqR = NekComplexDouble (sqrt((x[j]-x0[0])*(x[j]-x0[0]) +
                         (y[j]-x0[1])*(y[j]-x0[1]) +
                         (z[j]-x0[2])*(z[j]-x0[2]))/R, 0.0);
 
                // Compute Poiseulle Flow
                m_womersleyParams[fldid][bndid]->m_poiseuille[i][j] =
                        m_womersleyParams[fldid][bndid]->m_wom_vel[0].real() *
                        (1. - rqR.real()*rqR.real());
 
 
                m_womersleyParams[fldid][bndid]->m_zvel[i][j] =
                        Array<OneD, NekComplexDouble> (M_coeffs);
 
                // compute the velocity information
                for (k=1; k < M_coeffs; k++)
                {
                    zJ0r = Polylib::ImagBesselComp(0,rqR * lamda_n[k]);
                    m_womersleyParams[fldid][bndid]->m_zvel[i][j][k] =
                            m_womersleyParams[fldid][bndid]->m_wom_vel[k] *
                            (z1 - (zJ0r / zJ0[k]));
                }
            }
        }
    }
 
    /**
    * Add an additional forcing term programmatically.
    */
    void IncNavierStokes::AddForcing(
        const SolverUtils::ForcingSharedPtr& pForce)
    {
        m_forcing.push_back(pForce);
    }
 
    /**
     *
     */
    Array<OneD, NekDouble> IncNavierStokes::v_GetMaxStdVelocity(
        const NekDouble SpeedSoundFactor)
    {
        boost::ignore_unused(SpeedSoundFactor);
        int nvel  = m_velocity.size();
        int nelmt = m_fields[0]->GetExpSize();
 
        Array<OneD, NekDouble> stdVelocity(nelmt, 0.0);
        Array<OneD, Array<OneD, NekDouble> > velfields;
 
        if(m_HomogeneousType == eHomogeneous1D) // just do check on 2D info
        {
            velfields = Array<OneD, Array<OneD, NekDouble> >(2);
 
            for(int i = 0; i < 2; ++i)
            {
                velfields[i] = m_fields[m_velocity[i]]->UpdatePhys();
            }
        }
        else
        {
            velfields = Array<OneD, Array<OneD, NekDouble> >(nvel);
 
            for(int i = 0; i < nvel; ++i)
            {
                velfields[i] = m_fields[m_velocity[i]]->UpdatePhys();
            }
        }
 
        stdVelocity = m_extrapolation->GetMaxStdVelocity(velfields);
 
        return stdVelocity;
    }
 
    /**
     *
     */
    void IncNavierStokes::GetPressure(
        const Array<OneD, const Array<OneD, NekDouble> > &physfield,
              Array<OneD, NekDouble>                     &pressure)
    {
        pressure = physfield[m_nConvectiveFields];
    }
 
    /**
     *
     */
    void IncNavierStokes::GetDensity(
        const Array<OneD, const Array<OneD, NekDouble> > &physfield,
              Array<OneD, NekDouble>                     &density)
    {
        int nPts  = physfield[0].size();
        Vmath::Fill(nPts, 1.0, density, 1);
    }
 
    /**
     *
     */
    void IncNavierStokes::GetVelocity(
        const Array<OneD, const Array<OneD, NekDouble> > &physfield,
              Array<OneD, Array<OneD, NekDouble> >       &velocity)
    {
        for(int i = 0; i < m_spacedim; ++i)
        {
            velocity[i] = physfield[i];
        }
    }
 
    /**
     * Perform the extrapolation.
     */
    bool IncNavierStokes::v_PreIntegrate(int step)
    {
        m_extrapolation->SubStepSaveFields(step);
        m_extrapolation->SubStepAdvance(step,m_time);
        SetBoundaryConditions(m_time+m_timestep);
        return false;
    }
 
} //end of namespace