LinearSWE.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: LinearSWE.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: Linear Shallow water equations in primitive variables
//
///////////////////////////////////////////////////////////////////////////////
 
#include <boost/algorithm/string.hpp>
#include <iomanip>
#include <iostream>
 
#include <MultiRegions/AssemblyMap/AssemblyMapDG.h>
#include <ShallowWaterSolver/EquationSystems/LinearSWE.h>
 
using namespace std;
 
namespace Nektar
{
string LinearSWE::className =
    SolverUtils::GetEquationSystemFactory().RegisterCreatorFunction(
        "LinearSWE", LinearSWE::create,
        "Linear shallow water equation in primitive variables.");
 
LinearSWE::LinearSWE(const LibUtilities::SessionReaderSharedPtr &pSession,
                     const SpatialDomains::MeshGraphSharedPtr &pGraph)
    : ShallowWaterSystem(pSession, pGraph)
{
}
 
void LinearSWE::v_InitObject(bool DeclareFields)
{
    ShallowWaterSystem::v_InitObject(DeclareFields);
 
    if (m_explicitAdvection)
    {
        m_ode.DefineOdeRhs(&LinearSWE::DoOdeRhs, this);
        m_ode.DefineProjection(&LinearSWE::DoOdeProjection, this);
    }
    else
    {
        ASSERTL0(false, "Implicit SWE not set up.");
    }
 
    // Type of advection class to be used
    switch (m_projectionType)
    {
            // Continuous field
        case MultiRegions::eGalerkin:
        {
            //  Do nothing
            break;
        }
            // Discontinuous field
        case MultiRegions::eDiscontinuous:
        {
            string advName;
            string diffName;
            string riemName;
 
            //---------------------------------------------------------------
            // Setting up advection and diffusion operators
            // NB: diffusion not set up for SWE at the moment
            //     but kept here for future use ...
            m_session->LoadSolverInfo("AdvectionType", advName, "WeakDG");
            // m_session->LoadSolverInfo("DiffusionType", diffName, "LDGEddy");
            m_advection = SolverUtils::GetAdvectionFactory().CreateInstance(
                advName, advName);
            // m_diffusion = SolverUtils::GetDiffusionFactory()
            //                             .CreateInstance(diffName, diffName);
 
            m_advection->SetFluxVector(&LinearSWE::GetFluxVector, this);
            // m_diffusion->SetFluxVectorNS(&ShallowWaterSystem::
            //                                  GetEddyViscosityFluxVector,
            //                                  this);
 
            // Setting up Riemann solver for advection operator
            m_session->LoadSolverInfo("UpwindType", riemName, "NoSolver");
            if ((riemName == "LinearHLL") && (m_constantDepth != true))
            {
                ASSERTL0(false, "LinearHLL only valid for constant depth");
            }
            m_riemannSolver =
                SolverUtils::GetRiemannSolverFactory().CreateInstance(
                    riemName, m_session);
 
            // Setting up upwind solver for diffusion operator
            // m_riemannSolverLDG = SolverUtils::GetRiemannSolverFactory()
            //                                 .CreateInstance("UpwindLDG");
 
            // Setting up parameters for advection operator Riemann solver
            m_riemannSolver->SetParam("gravity", &LinearSWE::GetGravity, this);
            m_riemannSolver->SetAuxVec("vecLocs", &LinearSWE::GetVecLocs, this);
            m_riemannSolver->SetVector("N", &LinearSWE::GetNormals, this);
 
            // The numerical flux for linear SWE requires depth information
            int nTracePointsTot = m_fields[0]->GetTrace()->GetTotPoints();
            m_dFwd              = Array<OneD, NekDouble>(nTracePointsTot);
            m_dBwd              = Array<OneD, NekDouble>(nTracePointsTot);
            m_fields[0]->GetFwdBwdTracePhys(m_depth, m_dFwd, m_dBwd);
            CopyBoundaryTrace(m_dFwd, m_dBwd);
            m_riemannSolver->SetScalar("depthFwd", &LinearSWE::GetDepthFwd,
                                       this);
            m_riemannSolver->SetScalar("depthBwd", &LinearSWE::GetDepthBwd,
                                       this);
 
            // Setting up parameters for diffusion operator Riemann solver
            // m_riemannSolverLDG->AddParam (
            //                     "gravity",
            //                     &NonlinearSWE::GetGravity,   this);
            // m_riemannSolverLDG->SetAuxVec(
            //                     "vecLocs",
            //                     &NonlinearSWE::GetVecLocs,  this);
            // m_riemannSolverLDG->AddVector(
            //                     "N",
            //                     &NonlinearSWE::GetNormals, this);
 
            // Concluding initialisation of advection / diffusion operators
            m_advection->SetRiemannSolver(m_riemannSolver);
            // m_diffusion->SetRiemannSolver   (m_riemannSolverLDG);
            m_advection->InitObject(m_session, m_fields);
            // m_diffusion->InitObject         (m_session, m_fields);
            break;
        }
        default:
        {
            ASSERTL0(false, "Unsupported projection type.");
            break;
        }
    }
}
 
LinearSWE::~LinearSWE()
{
}
 
// physarray contains the conservative variables
void LinearSWE::AddCoriolis(
    const Array<OneD, const Array<OneD, NekDouble>> &physarray,
    Array<OneD, Array<OneD, NekDouble>> &outarray)
{
 
    int ncoeffs = GetNcoeffs();
    int nq      = GetTotPoints();
 
    Array<OneD, NekDouble> tmp(nq);
    Array<OneD, NekDouble> mod(ncoeffs);
 
    switch (m_projectionType)
    {
        case MultiRegions::eDiscontinuous:
        {
            // add to u equation
            Vmath::Vmul(nq, m_coriolis, 1, physarray[2], 1, tmp, 1);
            m_fields[0]->IProductWRTBase(tmp, mod);
            m_fields[0]->MultiplyByElmtInvMass(mod, mod);
            m_fields[0]->BwdTrans(mod, tmp);
            Vmath::Vadd(nq, tmp, 1, outarray[1], 1, outarray[1], 1);
 
            // add to v equation
            Vmath::Vmul(nq, m_coriolis, 1, physarray[1], 1, tmp, 1);
            Vmath::Neg(nq, tmp, 1);
            m_fields[0]->IProductWRTBase(tmp, mod);
            m_fields[0]->MultiplyByElmtInvMass(mod, mod);
            m_fields[0]->BwdTrans(mod, tmp);
            Vmath::Vadd(nq, tmp, 1, outarray[2], 1, outarray[2], 1);
        }
        break;
        case MultiRegions::eGalerkin:
        case MultiRegions::eMixed_CG_Discontinuous:
        {
            // add to u equation
            Vmath::Vmul(nq, m_coriolis, 1, physarray[2], 1, tmp, 1);
            Vmath::Vadd(nq, tmp, 1, outarray[1], 1, outarray[1], 1);
 
            // add to v equation
            Vmath::Vmul(nq, m_coriolis, 1, physarray[1], 1, tmp, 1);
            Vmath::Neg(nq, tmp, 1);
            Vmath::Vadd(nq, tmp, 1, outarray[2], 1, outarray[2], 1);
        }
        break;
        default:
            ASSERTL0(false, "Unknown projection scheme for the NonlinearSWE");
            break;
    }
}
 
void LinearSWE::DoOdeRhs(
    const Array<OneD, const Array<OneD, NekDouble>> &inarray,
    Array<OneD, Array<OneD, NekDouble>> &outarray, const NekDouble time)
{
    int i, j;
    int ndim       = m_spacedim;
    int nvariables = inarray.size();
    int nq         = GetTotPoints();
 
    switch (m_projectionType)
    {
        case MultiRegions::eDiscontinuous:
        {
 
            //-------------------------------------------------------
            // Compute the DG advection including the numerical flux
            // by using SolverUtils/Advection
            // Input and output in physical space
            Array<OneD, Array<OneD, NekDouble>> advVel;
 
            m_advection->Advect(nvariables, m_fields, advVel, inarray, outarray,
                                time);
            //-------------------------------------------------------
 
            //-------------------------------------------------------
            // negate the outarray since moving terms to the rhs
            for (i = 0; i < nvariables; ++i)
            {
                Vmath::Neg(nq, outarray[i], 1);
            }
            //-------------------------------------------------------
 
            //-------------------------------------------------
            // Add "source terms"
            // Input and output in physical space
 
            // Coriolis forcing
            if (m_coriolis.size() != 0)
            {
                AddCoriolis(inarray, outarray);
            }
            //-------------------------------------------------
        }
        break;
        case MultiRegions::eGalerkin:
        case MultiRegions::eMixed_CG_Discontinuous:
        {
 
            //-------------------------------------------------------
            // Compute the fluxvector in physical space
            Array<OneD, Array<OneD, Array<OneD, NekDouble>>> fluxvector(
                nvariables);
 
            for (i = 0; i < nvariables; ++i)
            {
                fluxvector[i] = Array<OneD, Array<OneD, NekDouble>>(ndim);
                for (j = 0; j < ndim; ++j)
                {
                    fluxvector[i][j] = Array<OneD, NekDouble>(nq);
                }
            }
 
            LinearSWE::GetFluxVector(inarray, fluxvector);
            //-------------------------------------------------------
 
            //-------------------------------------------------------
            // Take the derivative of the flux terms
            // and negate the outarray since moving terms to the rhs
            Array<OneD, NekDouble> tmp(nq);
            Array<OneD, NekDouble> tmp1(nq);
 
            for (i = 0; i < nvariables; ++i)
            {
                m_fields[i]->PhysDeriv(MultiRegions::DirCartesianMap[0],
                                       fluxvector[i][0], tmp);
                m_fields[i]->PhysDeriv(MultiRegions::DirCartesianMap[1],
                                       fluxvector[i][1], tmp1);
                Vmath::Vadd(nq, tmp, 1, tmp1, 1, outarray[i], 1);
                Vmath::Neg(nq, outarray[i], 1);
            }
 
            //-------------------------------------------------
            // Add "source terms"
            // Input and output in physical space
 
            // Coriolis forcing
            if (m_coriolis.size() != 0)
            {
                AddCoriolis(inarray, outarray);
            }
            //-------------------------------------------------
        }
        break;
        default:
            ASSERTL0(false, "Unknown projection scheme for the NonlinearSWE");
            break;
    }
}
 
void LinearSWE::DoOdeProjection(
    const Array<OneD, const Array<OneD, NekDouble>> &inarray,
    Array<OneD, Array<OneD, NekDouble>> &outarray, const NekDouble time)
{
    int i;
    int nvariables = inarray.size();
 
    switch (m_projectionType)
    {
        case MultiRegions::eDiscontinuous:
        {
 
            // Just copy over array
            int npoints = GetNpoints();
 
            for (i = 0; i < nvariables; ++i)
            {
                Vmath::Vcopy(npoints, inarray[i], 1, outarray[i], 1);
            }
            SetBoundaryConditions(outarray, time);
            break;
        }
        case MultiRegions::eGalerkin:
        case MultiRegions::eMixed_CG_Discontinuous:
        {
 
            EquationSystem::SetBoundaryConditions(time);
            Array<OneD, NekDouble> coeffs(m_fields[0]->GetNcoeffs(), 0.0);
 
            for (i = 0; i < nvariables; ++i)
            {
                m_fields[i]->FwdTrans(inarray[i], coeffs);
                m_fields[i]->BwdTrans(coeffs, outarray[i]);
            }
            break;
        }
        default:
            ASSERTL0(false, "Unknown projection scheme");
            break;
    }
}
 
//----------------------------------------------------
void LinearSWE::SetBoundaryConditions(
    Array<OneD, Array<OneD, NekDouble>> &inarray, NekDouble time)
{
    std::string varName;
    int nvariables = m_fields.size();
    int cnt        = 0;
    int nTracePts  = GetTraceTotPoints();
 
    // Extract trace for boundaries. Needs to be done on all processors to avoid
    // deadlock.
    Array<OneD, Array<OneD, NekDouble>> Fwd(nvariables);
    for (int i = 0; i < nvariables; ++i)
    {
        Fwd[i] = Array<OneD, NekDouble>(nTracePts);
        m_fields[i]->ExtractTracePhys(inarray[i], Fwd[i]);
    }
 
    // loop over Boundary Regions
    for (int n = 0; n < m_fields[0]->GetBndConditions().size(); ++n)
    {
        if (m_fields[0]->GetBndConditions()[n]->GetBoundaryConditionType() ==
            SpatialDomains::ePeriodic)
        {
            continue;
        }
 
        // Wall Boundary Condition
        if (boost::iequals(m_fields[0]->GetBndConditions()[n]->GetUserDefined(),
                           "Wall"))
        {
            WallBoundary2D(n, cnt, Fwd, inarray);
        }
 
        // Time Dependent Boundary Condition (specified in meshfile)
        if (m_fields[0]->GetBndConditions()[n]->IsTimeDependent())
        {
            for (int i = 0; i < nvariables; ++i)
            {
                varName = m_session->GetVariable(i);
                m_fields[i]->EvaluateBoundaryConditions(time, varName);
            }
        }
        cnt += m_fields[0]->GetBndCondExpansions()[n]->GetExpSize();
    }
}
 
//----------------------------------------------------
/**
 * @brief Wall boundary condition.
 */
void LinearSWE::WallBoundary(int bcRegion, int cnt,
                             Array<OneD, Array<OneD, NekDouble>> &Fwd,
                             Array<OneD, Array<OneD, NekDouble>> &physarray)
{
    int i;
    int nvariables = physarray.size();
 
    // Adjust the physical values of the trace to take
    // user defined boundaries into account
    int e, id1, id2, npts;
 
    for (e = 0; e < m_fields[0]->GetBndCondExpansions()[bcRegion]->GetExpSize();
         ++e)
    {
        npts = m_fields[0]
                   ->GetBndCondExpansions()[bcRegion]
                   ->GetExp(e)
                   ->GetTotPoints();
        id1 = m_fields[0]->GetBndCondExpansions()[bcRegion]->GetPhys_Offset(e);
        id2 = m_fields[0]->GetTrace()->GetPhys_Offset(
            m_fields[0]->GetTraceMap()->GetBndCondIDToGlobalTraceID(cnt + e));
 
        // For 2D/3D, define: v* = v - 2(v.n)n
        Array<OneD, NekDouble> tmp(npts, 0.0);
 
        // Calculate (v.n)
        for (i = 0; i < m_spacedim; ++i)
        {
            Vmath::Vvtvp(npts, &Fwd[1 + i][id2], 1, &m_traceNormals[i][id2], 1,
                         &tmp[0], 1, &tmp[0], 1);
        }
 
        // Calculate 2.0(v.n)
        Vmath::Smul(npts, -2.0, &tmp[0], 1, &tmp[0], 1);
 
        // Calculate v* = v - 2.0(v.n)n
        for (i = 0; i < m_spacedim; ++i)
        {
            Vmath::Vvtvp(npts, &tmp[0], 1, &m_traceNormals[i][id2], 1,
                         &Fwd[1 + i][id2], 1, &Fwd[1 + i][id2], 1);
        }
 
        // copy boundary adjusted values into the boundary expansion
        for (i = 0; i < nvariables; ++i)
        {
            Vmath::Vcopy(npts, &Fwd[i][id2], 1,
                         &(m_fields[i]
                               ->GetBndCondExpansions()[bcRegion]
                               ->UpdatePhys())[id1],
                         1);
        }
    }
}
 
void LinearSWE::WallBoundary2D(int bcRegion, int cnt,
                               Array<OneD, Array<OneD, NekDouble>> &Fwd,
                               Array<OneD, Array<OneD, NekDouble>> &physarray)
{
 
    int i;
    int nvariables = physarray.size();
 
    // Adjust the physical values of the trace to take
    // user defined boundaries into account
    int e, id1, id2, npts;
 
    for (e = 0; e < m_fields[0]->GetBndCondExpansions()[bcRegion]->GetExpSize();
         ++e)
    {
        npts = m_fields[0]
                   ->GetBndCondExpansions()[bcRegion]
                   ->GetExp(e)
                   ->GetNumPoints(0);
        id1 = m_fields[0]->GetBndCondExpansions()[bcRegion]->GetPhys_Offset(e);
        id2 = m_fields[0]->GetTrace()->GetPhys_Offset(
            m_fields[0]->GetTraceMap()->GetBndCondIDToGlobalTraceID(cnt + e));
 
        switch (m_expdim)
        {
            case 1:
            {
                // negate the forward flux
                Vmath::Neg(npts, &Fwd[1][id2], 1);
            }
            break;
            case 2:
            {
                Array<OneD, NekDouble> tmp_n(npts);
                Array<OneD, NekDouble> tmp_t(npts);
 
                Vmath::Vmul(npts, &Fwd[1][id2], 1, &m_traceNormals[0][id2], 1,
                            &tmp_n[0], 1);
                Vmath::Vvtvp(npts, &Fwd[2][id2], 1, &m_traceNormals[1][id2], 1,
                             &tmp_n[0], 1, &tmp_n[0], 1);
 
                Vmath::Vmul(npts, &Fwd[1][id2], 1, &m_traceNormals[1][id2], 1,
                            &tmp_t[0], 1);
                Vmath::Vvtvm(npts, &Fwd[2][id2], 1, &m_traceNormals[0][id2], 1,
                             &tmp_t[0], 1, &tmp_t[0], 1);
 
                // negate the normal flux
                Vmath::Neg(npts, tmp_n, 1);
 
                // rotate back to Cartesian
                Vmath::Vmul(npts, &tmp_t[0], 1, &m_traceNormals[1][id2], 1,
                            &Fwd[1][id2], 1);
                Vmath::Vvtvm(npts, &tmp_n[0], 1, &m_traceNormals[0][id2], 1,
                             &Fwd[1][id2], 1, &Fwd[1][id2], 1);
 
                Vmath::Vmul(npts, &tmp_t[0], 1, &m_traceNormals[0][id2], 1,
                            &Fwd[2][id2], 1);
                Vmath::Vvtvp(npts, &tmp_n[0], 1, &m_traceNormals[1][id2], 1,
                             &Fwd[2][id2], 1, &Fwd[2][id2], 1);
            }
            break;
            case 3:
                ASSERTL0(false,
                         "3D not implemented for Shallow Water Equations");
                break;
            default:
                ASSERTL0(false, "Illegal expansion dimension");
        }
 
        // copy boundary adjusted values into the boundary expansion
        for (i = 0; i < nvariables; ++i)
        {
            Vmath::Vcopy(npts, &Fwd[i][id2], 1,
                         &(m_fields[i]
                               ->GetBndCondExpansions()[bcRegion]
                               ->UpdatePhys())[id1],
                         1);
        }
    }
}
 
// Physfield in primitive Form
void LinearSWE::GetFluxVector(
    const Array<OneD, const Array<OneD, NekDouble>> &physfield,
    Array<OneD, Array<OneD, Array<OneD, NekDouble>>> &flux)
{
    int i, j;
    int nq = m_fields[0]->GetTotPoints();
 
    NekDouble g = m_g;
 
    // Flux vector for the mass equation
    for (i = 0; i < m_spacedim; ++i)
    {
        Vmath::Vmul(nq, m_depth, 1, physfield[i + 1], 1, flux[0][i], 1);
    }
 
    // Put (g eta) in tmp
    Array<OneD, NekDouble> tmp(nq);
    Vmath::Smul(nq, g, physfield[0], 1, tmp, 1);
 
    // Flux vector for the momentum equations
    for (i = 0; i < m_spacedim; ++i)
    {
        for (j = 0; j < m_spacedim; ++j)
        {
            // must zero fluxes as not initialised to zero in AdvectionWeakDG
            // ...
            Vmath::Zero(nq, flux[i + 1][j], 1);
        }
 
        // Add (g eta) to appropriate field
        Vmath::Vadd(nq, flux[i + 1][i], 1, tmp, 1, flux[i + 1][i], 1);
    }
}
 
void LinearSWE::ConservativeToPrimitive(
    const Array<OneD, const Array<OneD, NekDouble>> &physin,
    Array<OneD, Array<OneD, NekDouble>> &physout)
{
    int nq = GetTotPoints();
 
    if (physin.get() == physout.get())
    {
        // copy indata and work with tmp array
        Array<OneD, Array<OneD, NekDouble>> tmp(3);
        for (int i = 0; i < 3; ++i)
        {
            // deep copy
            tmp[i] = Array<OneD, NekDouble>(nq);
            Vmath::Vcopy(nq, physin[i], 1, tmp[i], 1);
        }
 
        // \eta = h - d
        Vmath::Vsub(nq, tmp[0], 1, m_depth, 1, physout[0], 1);
 
        // u = hu/h
        Vmath::Vdiv(nq, tmp[1], 1, tmp[0], 1, physout[1], 1);
 
        // v = hv/ v
        Vmath::Vdiv(nq, tmp[2], 1, tmp[0], 1, physout[2], 1);
    }
    else
    {
        // \eta = h - d
        Vmath::Vsub(nq, physin[0], 1, m_depth, 1, physout[0], 1);
 
        // u = hu/h
        Vmath::Vdiv(nq, physin[1], 1, physin[0], 1, physout[1], 1);
 
        // v = hv/ v
        Vmath::Vdiv(nq, physin[2], 1, physin[0], 1, physout[2], 1);
    }
}
 
void LinearSWE::v_ConservativeToPrimitive()
{
    int nq = GetTotPoints();
 
    // u = hu/h
    Vmath::Vdiv(nq, m_fields[1]->GetPhys(), 1, m_fields[0]->GetPhys(), 1,
                m_fields[1]->UpdatePhys(), 1);
 
    // v = hv/ v
    Vmath::Vdiv(nq, m_fields[2]->GetPhys(), 1, m_fields[0]->GetPhys(), 1,
                m_fields[2]->UpdatePhys(), 1);
 
    // \eta = h - d
    Vmath::Vsub(nq, m_fields[0]->GetPhys(), 1, m_depth, 1,
                m_fields[0]->UpdatePhys(), 1);
}
 
void LinearSWE::PrimitiveToConservative(
    const Array<OneD, const Array<OneD, NekDouble>> &physin,
    Array<OneD, Array<OneD, NekDouble>> &physout)
{
 
    int nq = GetTotPoints();
 
    if (physin.get() == physout.get())
    {
        // copy indata and work with tmp array
        Array<OneD, Array<OneD, NekDouble>> tmp(3);
        for (int i = 0; i < 3; ++i)
        {
            // deep copy
            tmp[i] = Array<OneD, NekDouble>(nq);
            Vmath::Vcopy(nq, physin[i], 1, tmp[i], 1);
        }
 
        // h = \eta + d
        Vmath::Vadd(nq, tmp[0], 1, m_depth, 1, physout[0], 1);
 
        // hu = h * u
        Vmath::Vmul(nq, physout[0], 1, tmp[1], 1, physout[1], 1);
 
        // hv = h * v
        Vmath::Vmul(nq, physout[0], 1, tmp[2], 1, physout[2], 1);
    }
    else
    {
        // h = \eta + d
        Vmath::Vadd(nq, physin[0], 1, m_depth, 1, physout[0], 1);
 
        // hu = h * u
        Vmath::Vmul(nq, physout[0], 1, physin[1], 1, physout[1], 1);
 
        // hv = h * v
        Vmath::Vmul(nq, physout[0], 1, physin[2], 1, physout[2], 1);
    }
}
 
void LinearSWE::v_PrimitiveToConservative()
{
    int nq = GetTotPoints();
 
    // h = \eta + d
    Vmath::Vadd(nq, m_fields[0]->GetPhys(), 1, m_depth, 1,
                m_fields[0]->UpdatePhys(), 1);
 
    // hu = h * u
    Vmath::Vmul(nq, m_fields[0]->GetPhys(), 1, m_fields[1]->GetPhys(), 1,
                m_fields[1]->UpdatePhys(), 1);
 
    // hv = h * v
    Vmath::Vmul(nq, m_fields[0]->GetPhys(), 1, m_fields[2]->GetPhys(), 1,
                m_fields[2]->UpdatePhys(), 1);
}
 
/**
 * @brief Compute the velocity field \f$ \mathbf{v} \f$ given the momentum
 * \f$ h\mathbf{v} \f$.
 *
 * @param physfield  Velocity field.
 * @param velocity   Velocity field.
 */
void LinearSWE::GetVelocityVector(
    const Array<OneD, Array<OneD, NekDouble>> &physfield,
    Array<OneD, Array<OneD, NekDouble>> &velocity)
{
    const int npts = physfield[0].size();
 
    for (int i = 0; i < m_spacedim; ++i)
    {
        Vmath::Vcopy(npts, physfield[1 + i], 1, velocity[i], 1);
    }
}
 
void LinearSWE::v_GenerateSummary(SolverUtils::SummaryList &s)
{
    ShallowWaterSystem::v_GenerateSummary(s);
    if (m_session->DefinesSolverInfo("UpwindType"))
    {
        std::string UpwindType;
        UpwindType = m_session->GetSolverInfo("UpwindType");
        if (UpwindType == "LinearAverage")
        {
            SolverUtils::AddSummaryItem(s, "Riemann Solver", "Linear Average");
        }
        if (UpwindType == "LinearHLL")
        {
            SolverUtils::AddSummaryItem(s, "Riemann Solver", "Linear HLL");
        }
    }
    SolverUtils::AddSummaryItem(s, "Variables", "eta  should be in field[0]");
    SolverUtils::AddSummaryItem(s, "", "u    should be in field[1]");
    SolverUtils::AddSummaryItem(s, "", "v    should be in field[2]");
}
 
} // namespace Nektar