ForcingMovingBody.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: ForcingMovingBody.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: Moving Body m_forcing (movement of a body in a domain is
// achieved via a m_forcing term which is the results of a coordinate system
// motion)
//
///////////////////////////////////////////////////////////////////////////////
 
#include <IncNavierStokesSolver/Forcing/ForcingMovingBody.h>
#include <MultiRegions/ExpList.h>
 
using namespace std;
 
namespace Nektar
{
std::string ForcingMovingBody::className =
    SolverUtils::GetForcingFactory().RegisterCreatorFunction(
        "MovingBody", ForcingMovingBody::create, "Moving Body Forcing");
 
ForcingMovingBody::ForcingMovingBody(
    const LibUtilities::SessionReaderSharedPtr &pSession,
    const std::weak_ptr<SolverUtils::EquationSystem> &pEquation)
    : Forcing(pSession, pEquation)
{
}
 
void ForcingMovingBody::v_InitObject(
    const Array<OneD, MultiRegions::ExpListSharedPtr> &pFields,
    [[maybe_unused]] const unsigned int &pNumForcingFields,
    const TiXmlElement *pForce)
{
    // Just 3D homogenous 1D problems can use this techinque
    ASSERTL0(pFields[0]->GetExpType() == MultiRegions::e3DH1D,
             "Moving body implemented just for 3D Homogenous 1D expansions.");
 
    // At this point we know in the xml file where those quantities
    // are declared (equation or file) - via a function name which is now
    // stored in funcNameD etc. We need now to fill in with this info the
    // m_zta and m_eta vectors (actuallythey are matrices) Array to control if
    // the motion is determined by an equation or is from a file.(not Nektar++)
    // check if we need to load a file or we have an equation
    CheckIsFromFile(pForce);
 
    // Initialise movingbody filter
    InitialiseFilter(m_session, pFields, pForce);
 
    // Initialise the cable model
    InitialiseCableModel(m_session, pFields);
 
    // Load mapping
    m_mapping = GlobalMapping::Mapping::Load(m_session, pFields);
    m_mapping->SetTimeDependent(true);
 
    if (m_vdim > 0)
    {
        m_mapping->SetFromFunction(false);
    }
 
    m_zta = Array<OneD, Array<OneD, NekDouble>>(3);
    m_eta = Array<OneD, Array<OneD, NekDouble>>(3);
    // What are this bi-dimensional vectors
    // ------------------------------------------ m_zta[0] = m_zta |  m_eta[0] =
    // m_eta                      | m_zta[1] = d(m_zta)/dt               |
    // m_eta[1] = d(m_eta)/dt                | m_zta[2] = dd(m_zta)/ddtt |
    // m_eta[2] = dd(m_eta)/ddtt             |
    //--------------------------------------------------------------------------------
    size_t phystot = pFields[0]->GetTotPoints();
    for (size_t i = 0; i < m_zta.size(); i++)
    {
        m_zta[i] = Array<OneD, NekDouble>(phystot, 0.0);
        m_eta[i] = Array<OneD, NekDouble>(phystot, 0.0);
    }
}
 
void ForcingMovingBody::v_Apply(
    const Array<OneD, MultiRegions::ExpListSharedPtr> &pFields,
    [[maybe_unused]] const Array<OneD, Array<OneD, NekDouble>> &inarray,
    [[maybe_unused]] Array<OneD, Array<OneD, NekDouble>> &outarray,
    const NekDouble &time)
{
    // Update the forces from the calculation of fluid field, which is
    // implemented in the movingbody filter
    Array<OneD, NekDouble> Hydroforces(2 * m_np, 0.0);
    m_MovBodyfilter->UpdateForce(m_session, pFields, Hydroforces, time);
 
    // for "free" type (m_vdim = 2), the cable vibrates both in streamwise and
    // crossflow dimections, for "constrained" type (m_vdim = 1), the cable only
    // vibrates in crossflow dimection, and for "forced" type (m_vdim = 0), the
    // calbe vibrates specifically along a given function or file
    if (m_vdim == 1 || m_vdim == 2)
    {
        // For free vibration case, displacements, velocities and acceleartions
        // are obtained through solving structure dynamic model
        EvaluateStructDynModel(pFields, Hydroforces, time);
 
        // Convert result to format required by mapping
        size_t physTot = pFields[0]->GetTotPoints();
        Array<OneD, Array<OneD, NekDouble>> coords(3);
        Array<OneD, Array<OneD, NekDouble>> coordsVel(3);
        for (size_t i = 0; i < 3; i++)
        {
            coords[i]    = Array<OneD, NekDouble>(physTot, 0.0);
            coordsVel[i] = Array<OneD, NekDouble>(physTot, 0.0);
        }
        // Get original coordinates
        pFields[0]->GetCoords(coords[0], coords[1], coords[2]);
 
        // Add displacement to coordinates
        Vmath::Vadd(physTot, coords[0], 1, m_zta[0], 1, coords[0], 1);
        Vmath::Vadd(physTot, coords[1], 1, m_eta[0], 1, coords[1], 1);
        // Copy velocities
        Vmath::Vcopy(physTot, m_zta[1], 1, coordsVel[0], 1);
        Vmath::Vcopy(physTot, m_eta[1], 1, coordsVel[1], 1);
 
        // Update mapping
        m_mapping->UpdateMapping(time, coords, coordsVel);
    }
    else if (m_vdim == 0)
    {
        // For forced vibration case, load from specified file or function
        size_t cnt = 0;
        for (size_t j = 0; j < m_funcName.size(); j++)
        {
            if (m_IsFromFile[cnt] && m_IsFromFile[cnt + 1])
            {
                ASSERTL0(false, "Motion loading from file needs specific "
                                "implementation: Work in Progress!");
            }
            else
            {
                GetFunction(pFields, m_session, m_funcName[j], true)
                    ->Evaluate(m_motion[0], m_zta[j], time);
                GetFunction(pFields, m_session, m_funcName[j], true)
                    ->Evaluate(m_motion[1], m_eta[j], time);
                cnt = cnt + 2;
            }
        }
 
        // Update mapping
        m_mapping->UpdateMapping(time);
 
        // Convert result from mapping
        size_t physTot = pFields[0]->GetTotPoints();
        Array<OneD, Array<OneD, NekDouble>> coords(3);
        Array<OneD, Array<OneD, NekDouble>> coordsVel(3);
        for (size_t i = 0; i < 3; i++)
        {
            coords[i]    = Array<OneD, NekDouble>(physTot, 0.0);
            coordsVel[i] = Array<OneD, NekDouble>(physTot, 0.0);
        }
        // Get original coordinates
        pFields[0]->GetCoords(coords[0], coords[1], coords[2]);
 
        // Get Coordinates and coord velocity from mapping
        m_mapping->GetCartesianCoordinates(m_zta[0], m_eta[0], coords[2]);
        m_mapping->GetCoordVelocity(coordsVel);
 
        // Calculate displacement
        Vmath::Vsub(physTot, m_zta[0], 1, coords[0], 1, m_zta[0], 1);
        Vmath::Vsub(physTot, m_eta[0], 1, coords[1], 1, m_eta[0], 1);
 
        Vmath::Vcopy(physTot, coordsVel[0], 1, m_zta[1], 1);
        Vmath::Vcopy(physTot, coordsVel[1], 1, m_eta[1], 1);
 
        for (size_t var = 0; var < 3; var++)
        {
            for (size_t plane = 0; plane < m_np; plane++)
            {
                size_t n      = pFields[0]->GetPlane(plane)->GetTotPoints();
                size_t offset = plane * n;
                size_t Offset = var * m_np + plane;
 
                m_MotionVars[0][Offset] = m_zta[var][offset];
                m_MotionVars[1][Offset] = m_eta[var][offset];
            }
        }
    }
    else
    {
        ASSERTL0(false, "Unrecogized vibration type for cable's dynamic model");
    }
 
    LibUtilities::CommSharedPtr vcomm = pFields[0]->GetComm();
    size_t colrank                    = vcomm->GetColumnComm()->GetRank();
    // Pass the variables of the cable's motion to the movingbody filter
    if (colrank == 0)
    {
        size_t n = m_MotionVars[0].size();
        Array<OneD, NekDouble> tmpArray(2 * n), tmp(n);
        Vmath::Vcopy(n, m_MotionVars[0], 1, tmpArray, 1);
        Vmath::Vcopy(n, m_MotionVars[1], 1, tmp = tmpArray + n, 1);
        m_MovBodyfilter->UpdateMotion(m_session, pFields, tmpArray, time);
    }
}
 
/**
 *
 */
void ForcingMovingBody::EvaluateStructDynModel(
    const Array<OneD, MultiRegions::ExpListSharedPtr> &pFields,
    Array<OneD, NekDouble> &Hydroforces, [[maybe_unused]] NekDouble time)
{
    LibUtilities::CommSharedPtr vcomm = pFields[0]->GetComm();
    size_t colrank                    = vcomm->GetColumnComm()->GetRank();
    size_t nproc                      = vcomm->GetColumnComm()->GetSize();
 
    bool homostrip;
    m_session->MatchSolverInfo("HomoStrip", "True", homostrip, false);
 
    // number of structral modes and number of strips
    size_t npts, nstrips;
    if (!homostrip) // full resolutions
    {
        npts = m_session->GetParameter("HomModesZ");
    }
    else
    {
        m_session->LoadParameter("HomStructModesZ", npts);
        m_session->LoadParameter("Strip_Z", nstrips);
 
        // ASSERTL0(nstrips < = npts,
        //     "the number of struct. modes must be larger than that of the
        //     strips.");
    }
 
    // the hydrodynamic forces
    Array<OneD, Array<OneD, NekDouble>> fces(2);
    // forces in x-direction
    fces[0] = Array<OneD, NekDouble>(npts, 0.0);
    // forces in y-direction
    fces[1] = Array<OneD, NekDouble>(npts, 0.0);
 
    // fill the force vectors
    if (colrank == 0)
    {
        if (!homostrip) // full resolutions
        {
            Vmath::Vcopy(m_np, Hydroforces, 1, fces[0], 1);
            Vmath::Vcopy(m_np, Hydroforces + m_np, 1, fces[1], 1);
        }
        else // strip modelling
        {
            fces[0][0] = Hydroforces[0];
            fces[1][0] = Hydroforces[m_np];
        }
 
        if (!homostrip) // full resolutions
        {
            Array<OneD, NekDouble> tmp(2 * m_np);
            for (size_t i = 1; i < nproc; ++i)
            {
                vcomm->GetColumnComm()->Recv(i, tmp);
                for (size_t n = 0; n < m_np; n++)
                {
                    for (size_t j = 0; j < 2; ++j)
                    {
                        fces[j][i * m_np + n] = tmp[j * m_np + n];
                    }
                }
            }
        }
        else // strip modelling
        // if the body is submerged partly, the fces are filled partly
        // by the flow induced forces
        {
            Array<OneD, NekDouble> tmp(2);
            for (size_t i = 1; i < nstrips; ++i)
            {
                vcomm->GetColumnComm()->Recv(i, tmp);
 
                for (size_t j = 0; j < 2; ++j)
                {
                    fces[j][i] = tmp[j];
                }
            }
        }
    }
    else
    {
        if (!homostrip) // full resolutions
        {
            vcomm->GetColumnComm()->Send(0, Hydroforces);
        }
        else // strip modelling
        {
            for (size_t i = 1; i < nstrips; ++i)
            {
                if (colrank == i)
                {
                    Array<OneD, NekDouble> tmp(2);
                    tmp[0] = Hydroforces[0];
                    tmp[1] = Hydroforces[m_np];
                    vcomm->GetColumnComm()->Send(0, tmp);
                }
            }
        }
    }
 
    if (colrank == 0)
    {
        // Fictitious mass method used to stablize the explicit coupling at
        // relatively lower mass ratio
        bool fictmass;
        m_session->MatchSolverInfo("FictitiousMassMethod", "True", fictmass,
                                   false);
        if (fictmass)
        {
            NekDouble fictrho, fictdamp;
            m_session->LoadParameter("FictMass", fictrho);
            m_session->LoadParameter("FictDamp", fictdamp);
 
            static NekDouble Betaq_Coeffs[2][2] = {{1.0, 0.0}, {2.0, -1.0}};
 
            // only consider second order approximation for fictitious variables
            size_t intOrder = 2;
            size_t nint     = min(m_movingBodyCalls + 1, intOrder);
            size_t nlevels  = m_fV[0].size();
 
            for (size_t i = 0; i < m_motion.size(); ++i)
            {
                RollOver(m_fV[i]);
                RollOver(m_fA[i]);
 
                size_t Voffset = npts;
                size_t Aoffset = 2 * npts;
 
                Vmath::Vcopy(npts, m_MotionVars[i] + Voffset, 1, m_fV[i][0], 1);
                Vmath::Vcopy(npts, m_MotionVars[i] + Aoffset, 1, m_fA[i][0], 1);
 
                // Extrapolate to n+1
                Vmath::Smul(npts, Betaq_Coeffs[nint - 1][nint - 1],
                            m_fV[i][nint - 1], 1, m_fV[i][nlevels - 1], 1);
                Vmath::Smul(npts, Betaq_Coeffs[nint - 1][nint - 1],
                            m_fA[i][nint - 1], 1, m_fA[i][nlevels - 1], 1);
 
                for (size_t n = 0; n < nint - 1; ++n)
                {
                    Vmath::Svtvp(npts, Betaq_Coeffs[nint - 1][n], m_fV[i][n], 1,
                                 m_fV[i][nlevels - 1], 1, m_fV[i][nlevels - 1],
                                 1);
                    Vmath::Svtvp(npts, Betaq_Coeffs[nint - 1][n], m_fA[i][n], 1,
                                 m_fA[i][nlevels - 1], 1, m_fA[i][nlevels - 1],
                                 1);
                }
 
                // Add the fictitious forces on the RHS of the equation
                Vmath::Svtvp(npts, fictdamp, m_fV[i][nlevels - 1], 1, fces[i],
                             1, fces[i], 1);
                Vmath::Svtvp(npts, fictrho, m_fA[i][nlevels - 1], 1, fces[i], 1,
                             fces[i], 1);
            }
        }
    }
    // structural solver is implemented on the root process
    if (colrank == 0)
    {
        // Tensioned cable model is evaluated in wave space
        for (size_t n = 0, cn = 1; n < m_vdim; n++, cn--)
        {
            Newmark_betaSolver(pFields, fces[cn], m_MotionVars[cn]);
        }
    }
 
    Array<OneD, NekDouble> Motvars(2 * 2 * m_np);
    // send physical coeffients to all planes of each processor
    if (!homostrip) // full resolutions
    {
        Array<OneD, NekDouble> tmp(2 * 2 * m_np);
 
        if (colrank != 0)
        {
            vcomm->GetColumnComm()->Recv(0, tmp);
            Vmath::Vcopy(2 * 2 * m_np, tmp, 1, Motvars, 1);
        }
        else
        {
            for (size_t i = 1; i < nproc; ++i)
            {
                for (size_t j = 0; j < 2; j++) // moving dimensions
                {
                    for (size_t k = 0; k < 2; k++) // disp. and vel.
                    {
                        for (size_t n = 0; n < m_np; n++)
                        {
                            tmp[j * 2 * m_np + k * m_np + n] =
                                m_MotionVars[j][k * npts + i * m_np + n];
                        }
                    }
                }
                vcomm->GetColumnComm()->Send(i, tmp);
            }
 
            for (size_t j = 0; j < 2; j++)
            {
                for (size_t k = 0; k < 2; k++)
                {
                    for (size_t n = 0; n < m_np; n++)
                    {
                        tmp[j * 2 * m_np + k * m_np + n] =
                            m_MotionVars[j][k * npts + n];
                    }
                    Vmath::Vcopy(2 * 2 * m_np, tmp, 1, Motvars, 1);
                }
            }
        }
    }
    else // strip modelling
    {
        Array<OneD, NekDouble> tmp(2 * 2);
 
        if (colrank != 0)
        {
            for (size_t j = 1; j < nproc / nstrips; j++)
            {
                if (colrank == j * nstrips)
                {
                    vcomm->GetColumnComm()->Recv(0, tmp);
 
                    for (size_t plane = 0; plane < m_np; plane++)
                    {
                        for (size_t var = 0; var < 2; var++)
                        {
                            for (size_t k = 0; k < 2; k++)
                            {
                                Motvars[var * 2 * m_np + k * m_np + plane] =
                                    tmp[var * 2 + k];
                            }
                        }
                    }
                }
            }
 
            for (size_t i = 1; i < nstrips; i++)
            {
                for (size_t j = 0; j < nproc / nstrips; j++)
                {
                    if (colrank == i + j * nstrips)
                    {
                        vcomm->GetColumnComm()->Recv(0, tmp);
 
                        for (size_t plane = 0; plane < m_np; plane++)
                        {
                            for (size_t var = 0; var < 2; var++)
                            {
                                for (size_t k = 0; k < 2; k++)
                                {
                                    Motvars[var * 2 * m_np + k * m_np + plane] =
                                        tmp[var * 2 + k];
                                }
                            }
                        }
                    }
                }
            }
        }
        else
        {
            for (size_t j = 0; j < 2; ++j)
            {
                for (size_t k = 0; k < 2; ++k)
                {
                    tmp[j * 2 + k] = m_MotionVars[j][k * npts];
                }
            }
 
            for (size_t j = 1; j < nproc / nstrips; j++)
            {
                vcomm->GetColumnComm()->Send(j * nstrips, tmp);
            }
 
            for (size_t plane = 0; plane < m_np; plane++)
            {
                for (size_t j = 0; j < 2; j++)
                {
                    for (size_t k = 0; k < 2; ++k)
                    {
                        Motvars[j * 2 * m_np + k * m_np + plane] =
                            m_MotionVars[j][k * npts];
                    }
                }
            }
 
            for (size_t i = 1; i < nstrips; ++i)
            {
                for (size_t j = 0; j < 2; ++j)
                {
                    for (size_t k = 0; k < 2; ++k)
                    {
                        tmp[j * 2 + k] = m_MotionVars[j][i + k * npts];
                    }
                }
 
                for (size_t j = 0; j < nproc / nstrips; j++)
                {
                    vcomm->GetColumnComm()->Send(i + j * nstrips, tmp);
                }
            }
        }
    }
 
    // Set the m_forcing term based on the motion of the cable
    for (size_t var = 0; var < 2; var++)
    {
        for (size_t plane = 0; plane < m_np; plane++)
        {
            size_t n = pFields[0]->GetPlane(plane)->GetTotPoints();
 
            Array<OneD, NekDouble> tmp;
 
            size_t offset  = plane * n;
            size_t xoffset = var * m_np + plane;
            size_t yoffset = 2 * m_np + xoffset;
 
            Vmath::Fill(n, Motvars[xoffset], tmp = m_zta[var] + offset, 1);
            Vmath::Fill(n, Motvars[yoffset], tmp = m_eta[var] + offset, 1);
        }
    }
}
 
/**
 *
 */
void ForcingMovingBody::Newmark_betaSolver(
    [[maybe_unused]] const Array<OneD, MultiRegions::ExpListSharedPtr> &pFields,
    Array<OneD, NekDouble> &HydroForces, Array<OneD, NekDouble> &BodyMotions)
{
    std::string supptype = m_session->GetSolverInfo("SupportType");
 
    size_t npts = HydroForces.size();
 
    Array<OneD, Array<OneD, NekDouble>> fft_i(4);
    Array<OneD, Array<OneD, NekDouble>> fft_o(4);
 
    for (size_t i = 0; i < 4; i++)
    {
        fft_i[i] = Array<OneD, NekDouble>(npts, 0.0);
        fft_o[i] = Array<OneD, NekDouble>(npts, 0.0);
    }
 
    Vmath::Vcopy(npts, HydroForces, 1, fft_i[0], 1);
    for (size_t i = 0; i < 3; i++)
    {
        Vmath::Vcopy(npts, BodyMotions + i * npts, 1, fft_i[i + 1], 1);
    }
 
    // Implement Fourier transformation of the motion variables
    if (boost::iequals(supptype, "Free-Free"))
    {
        for (size_t j = 0; j < 4; ++j)
        {
            m_FFT->FFTFwdTrans(fft_i[j], fft_o[j]);
        }
    }
    else if (boost::iequals(supptype, "Pinned-Pinned"))
    {
        // TODO:
        size_t N = fft_i[0].size();
 
        for (size_t var = 0; var < 4; var++)
        {
            for (size_t i = 0; i < N; i++)
            {
                fft_o[var][i] = 0;
 
                for (size_t k = 0; k < N; k++)
                {
                    fft_o[var][i] +=
                        fft_i[var][k] * sin(M_PI / (N) * (k + 1 / 2) * (i + 1));
                }
            }
        }
    }
    else
    {
        ASSERTL0(false, "Unrecognized support type for cable's motion");
    }
 
    // solve the ODE in the wave space
    for (size_t i = 0; i < npts; ++i)
    {
        size_t nrows = 3;
 
        Array<OneD, NekDouble> tmp0, tmp1, tmp2;
        tmp0 = Array<OneD, NekDouble>(3, 0.0);
        tmp1 = Array<OneD, NekDouble>(3, 0.0);
        tmp2 = Array<OneD, NekDouble>(3, 0.0);
 
        for (size_t var = 0; var < 3; var++)
        {
            tmp0[var] = fft_o[var + 1][i];
        }
 
        tmp2[0] = fft_o[0][i];
 
        Blas::Dgemv('N', nrows, nrows, 1.0, &(m_CoeffMat_B[i]->GetPtr())[0],
                    nrows, &tmp0[0], 1, 0.0, &tmp1[0], 1);
        Blas::Dgemv('N', nrows, nrows, 1.0 / m_structrho,
                    &(m_CoeffMat_A[i]->GetPtr())[0], nrows, &tmp2[0], 1, 1.0,
                    &tmp1[0], 1);
 
        for (size_t var = 0; var < 3; var++)
        {
            fft_i[var][i] = tmp1[var];
        }
    }
 
    // get physical coeffients via Backward fourier transformation of wave
    // coefficients
    if (boost::iequals(supptype, "Free-Free"))
    {
        for (size_t var = 0; var < 3; var++)
        {
            m_FFT->FFTBwdTrans(fft_i[var], fft_o[var]);
        }
    }
    else if (boost::iequals(supptype, "Pinned-Pinned"))
    {
        // TODO:
        size_t N = fft_i[0].size();
 
        for (size_t var = 0; var < 3; var++)
        {
            for (size_t i = 0; i < N; i++)
            {
                fft_o[var][i] = 0;
 
                for (size_t k = 0; k < N; k++)
                {
                    fft_o[var][i] += fft_i[var][k] *
                                     sin(M_PI / (N) * (k + 1) * (i + 1 / 2)) *
                                     2 / N;
                }
            }
        }
    }
    else
    {
        ASSERTL0(false, "Unrecognized support type for cable's motion");
    }
 
    for (size_t i = 0; i < 3; i++)
    {
        Array<OneD, NekDouble> tmp(npts, 0.0);
        Vmath::Vcopy(npts, fft_o[i], 1, tmp = BodyMotions + i * npts, 1);
    }
}
 
/**
 *
 */
void ForcingMovingBody::InitialiseCableModel(
    [[maybe_unused]] const LibUtilities::SessionReaderSharedPtr &pSession,
    [[maybe_unused]] const Array<OneD, MultiRegions::ExpListSharedPtr> &pFields)
{
    m_movingBodyCalls = 0;
    m_session->LoadParameter("Kinvis", m_kinvis);
    m_session->LoadParameter("TimeStep", m_timestep, 0.01);
 
    LibUtilities::CommSharedPtr vcomm = pFields[0]->GetComm();
    size_t colrank                    = vcomm->GetColumnComm()->GetRank();
    size_t nproc                      = vcomm->GetColumnComm()->GetSize();
 
    // number of structral modes
    size_t npts;
    bool homostrip;
    m_session->MatchSolverInfo("HomoStrip", "True", homostrip, false);
 
    if (!homostrip) // full resolutions
    {
        npts = m_session->GetParameter("HomModesZ");
    }
    else
    {
        m_session->LoadParameter("HomStructModesZ", npts);
    }
 
    m_MotionVars    = Array<OneD, Array<OneD, NekDouble>>(2);
    m_MotionVars[0] = Array<OneD, NekDouble>(3 * npts, 0.0);
    m_MotionVars[1] = Array<OneD, NekDouble>(3 * npts, 0.0);
 
    Array<OneD, unsigned int> ZIDs;
    ZIDs = pFields[0]->GetZIDs();
    m_np = ZIDs.size();
 
    std::string vibtype = m_session->GetSolverInfo("VibrationType");
 
    if (boost::iequals(vibtype, "Constrained"))
    {
        m_vdim = 1;
    }
    else if (boost::iequals(vibtype, "Free"))
    {
        m_vdim = 2;
    }
    else if (boost::iequals(vibtype, "Forced"))
    {
        m_vdim = 0;
        return;
    }
 
    if (!homostrip)
    {
        m_session->LoadParameter("LZ", m_lhom);
        int nplanes = m_session->GetParameter("HomModesZ");
        m_FFT = LibUtilities::GetNektarFFTFactory().CreateInstance("NekFFTW",
                                                                   nplanes);
    }
    else
    {
        int nstrips;
        NekDouble DistStrip;
 
        m_session->LoadParameter("DistStrip", DistStrip);
        m_session->LoadParameter("Strip_Z", nstrips);
        m_lhom = nstrips * DistStrip;
        m_FFT  = LibUtilities::GetNektarFFTFactory().CreateInstance("NekFFTW",
                                                                    nstrips);
    }
 
    // load the structural dynamic parameters from xml file
    m_session->LoadParameter("StructRho", m_structrho);
    m_session->LoadParameter("StructDamp", m_structdamp, 0.0);
 
    // Identify whether the fictitious mass method is active for explicit
    // coupling of fluid solver and structural dynamics solver
    bool fictmass;
    m_session->MatchSolverInfo("FictitiousMassMethod", "True", fictmass, false);
    if (fictmass)
    {
        NekDouble fictrho, fictdamp;
        m_session->LoadParameter("FictMass", fictrho);
        m_session->LoadParameter("FictDamp", fictdamp);
        m_structrho += fictrho;
        m_structdamp += fictdamp;
 
        // Storage array of Struct Velocity and Acceleration used for
        // extrapolation of fictitious force
        m_fV = Array<OneD, Array<OneD, Array<OneD, NekDouble>>>(2);
        m_fA = Array<OneD, Array<OneD, Array<OneD, NekDouble>>>(2);
        for (size_t i = 0; i < m_motion.size(); ++i)
        {
            m_fV[i] = Array<OneD, Array<OneD, NekDouble>>(2);
            m_fA[i] = Array<OneD, Array<OneD, NekDouble>>(2);
 
            for (size_t n = 0; n < 2; ++n)
            {
                m_fV[i][n] = Array<OneD, NekDouble>(npts, 0.0);
                m_fA[i][n] = Array<OneD, NekDouble>(npts, 0.0);
            }
        }
    }
 
    // Setting the coefficient matrices for solving structural dynamic ODEs
    SetDynEqCoeffMatrix(pFields);
 
    // Set initial condition for cable's motion
    size_t cnt = 0;
 
    for (size_t j = 0; j < m_funcName.size(); j++)
    {
        // loading from the specified files through inputstream
        if (m_IsFromFile[cnt] && m_IsFromFile[cnt + 1])
        {
            std::ifstream inputStream;
            size_t nzpoints;
 
            if (homostrip)
            {
                m_session->LoadParameter("HomStructModesZ", nzpoints);
            }
            else
            {
                nzpoints = pFields[0]->GetHomogeneousBasis()->GetNumModes();
            }
 
            if (vcomm->GetRank() == 0)
            {
                std::string filename =
                    m_session->GetFunctionFilename(m_funcName[j], m_motion[0]);
 
                // Open intputstream for cable motions
                inputStream.open(filename.c_str());
 
                // Import the head string from the file
                Array<OneD, std::string> tmp(9);
                for (size_t n = 0; n < tmp.size(); n++)
                {
                    inputStream >> tmp[n];
                }
 
                NekDouble time, z_cds;
                // Import the motion variables from the file
                for (size_t n = 0; n < nzpoints; n++)
                {
                    inputStream >> setprecision(6) >> time;
                    inputStream >> setprecision(6) >> z_cds;
                    inputStream >> setprecision(8) >> m_MotionVars[0][n];
                    inputStream >> setprecision(8) >>
                        m_MotionVars[0][n + nzpoints];
                    inputStream >> setprecision(8) >>
                        m_MotionVars[0][n + 2 * nzpoints];
                    inputStream >> setprecision(8) >> m_MotionVars[1][n];
                    inputStream >> setprecision(8) >>
                        m_MotionVars[1][n + nzpoints];
                    inputStream >> setprecision(8) >>
                        m_MotionVars[1][n + 2 * nzpoints];
                }
                // Close inputstream for cable motions
                inputStream.close();
            }
            cnt = cnt + 2;
        }
        else // Evaluate from the functions specified in xml file
        {
            if (!homostrip)
            {
                size_t nzpoints =
                    pFields[0]->GetHomogeneousBasis()->GetNumModes();
                Array<OneD, NekDouble> z_coords(nzpoints, 0.0);
                Array<OneD, const NekDouble> pts =
                    pFields[0]->GetHomogeneousBasis()->GetZ();
 
                Vmath::Smul(nzpoints, m_lhom / 2.0, pts, 1, z_coords, 1);
                Vmath::Sadd(nzpoints, m_lhom / 2.0, z_coords, 1, z_coords, 1);
 
                Array<OneD, NekDouble> x0(m_np, 0.0);
                Array<OneD, NekDouble> x1(m_np, 0.0);
                Array<OneD, NekDouble> x2(m_np, 0.0);
                for (size_t plane = 0; plane < m_np; plane++)
                {
                    x2[plane] = z_coords[ZIDs[plane]];
                }
 
                Array<OneD, NekDouble> tmp(m_np, 0.0);
                Array<OneD, NekDouble> tmp0(m_np, 0.0);
                Array<OneD, NekDouble> tmp1(m_np, 0.0);
                LibUtilities::EquationSharedPtr ffunc0, ffunc1;
 
                ffunc0 = m_session->GetFunction(m_funcName[j], m_motion[0]);
                ffunc1 = m_session->GetFunction(m_funcName[j], m_motion[1]);
                ffunc0->Evaluate(x0, x1, x2, 0.0, tmp0);
                ffunc1->Evaluate(x0, x1, x2, 0.0, tmp1);
 
                size_t offset = j * npts;
                Vmath::Vcopy(m_np, tmp0, 1, tmp = m_MotionVars[0] + offset, 1);
                Vmath::Vcopy(m_np, tmp1, 1, tmp = m_MotionVars[1] + offset, 1);
 
                if (colrank == 0)
                {
                    for (size_t i = 1; i < nproc; ++i)
                    {
                        vcomm->GetColumnComm()->Recv(i, tmp0);
                        vcomm->GetColumnComm()->Recv(i, tmp1);
                        Vmath::Vcopy(m_np, tmp0, 1,
                                     tmp = m_MotionVars[0] + offset + i * m_np,
                                     1);
                        Vmath::Vcopy(m_np, tmp1, 1,
                                     tmp = m_MotionVars[1] + offset + i * m_np,
                                     1);
                    }
                }
                else
                {
                    vcomm->GetColumnComm()->Send(0, tmp0);
                    vcomm->GetColumnComm()->Send(0, tmp1);
                }
            }
            else
            {
                if (colrank == 0)
                {
                    size_t nstrips;
                    m_session->LoadParameter("Strip_Z", nstrips);
 
                    ASSERTL0(
                        m_session->DefinesSolverInfo("USEFFT"),
                        "Fourier transformation of cable motion is currently "
                        "implemented only for FFTW module.");
 
                    NekDouble DistStrip;
                    m_session->LoadParameter("DistStrip", DistStrip);
 
                    Array<OneD, NekDouble> x0(npts, 0.0);
                    Array<OneD, NekDouble> x1(npts, 0.0);
                    Array<OneD, NekDouble> x2(npts, 0.0);
                    Array<OneD, NekDouble> tmp(npts, 0.0);
                    Array<OneD, NekDouble> tmp0(npts, 0.0);
                    Array<OneD, NekDouble> tmp1(npts, 0.0);
                    for (size_t plane = 0; plane < npts; plane++)
                    {
                        x2[plane] = plane * DistStrip;
                    }
                    LibUtilities::EquationSharedPtr ffunc0, ffunc1;
                    ffunc0 = m_session->GetFunction(m_funcName[j], m_motion[0]);
                    ffunc1 = m_session->GetFunction(m_funcName[j], m_motion[1]);
                    ffunc0->Evaluate(x0, x1, x2, 0.0, tmp0);
                    ffunc1->Evaluate(x0, x1, x2, 0.0, tmp1);
 
                    size_t offset = j * npts;
                    Vmath::Vcopy(npts, tmp0, 1, tmp = m_MotionVars[0] + offset,
                                 1);
                    Vmath::Vcopy(npts, tmp1, 1, tmp = m_MotionVars[1] + offset,
                                 1);
                }
            }
 
            cnt = cnt + 2;
        }
    }
}
 
/**
 *
 */
void ForcingMovingBody::SetDynEqCoeffMatrix(
    [[maybe_unused]] const Array<OneD, MultiRegions::ExpListSharedPtr> &pFields)
{
    size_t nplanes;
 
    bool homostrip;
    m_session->MatchSolverInfo("HomoStrip", "True", homostrip, false);
 
    if (!homostrip)
    {
        nplanes = m_session->GetParameter("HomModesZ");
    }
    else
    {
        m_session->LoadParameter("Strip_Z", nplanes);
    }
 
    m_CoeffMat_A = Array<OneD, DNekMatSharedPtr>(nplanes);
    m_CoeffMat_B = Array<OneD, DNekMatSharedPtr>(nplanes);
 
    NekDouble tmp1, tmp2, tmp3;
    NekDouble tmp4, tmp5, tmp6, tmp7;
 
    // load the structural dynamic parameters from xml file
    NekDouble cabletension;
    NekDouble bendingstiff;
    NekDouble structstiff;
    m_session->LoadParameter("StructStiff", structstiff, 0.0);
    m_session->LoadParameter("CableTension", cabletension, 0.0);
    m_session->LoadParameter("BendingStiff", bendingstiff, 0.0);
 
    tmp1 = m_timestep * m_timestep;
    tmp2 = structstiff / m_structrho;
    tmp3 = m_structdamp / m_structrho;
    tmp4 = cabletension / m_structrho;
    tmp5 = bendingstiff / m_structrho;
 
    // solve the ODE in the wave space for cable motion to obtain disp, vel and
    // accel
 
    std::string supptype = m_session->GetSolverInfo("SupportType");
 
    for (size_t plane = 0; plane < nplanes; plane++)
    {
        int nel = 3;
        m_CoeffMat_A[plane] =
            MemoryManager<DNekMat>::AllocateSharedPtr(nel, nel);
        m_CoeffMat_B[plane] =
            MemoryManager<DNekMat>::AllocateSharedPtr(nel, nel);
 
        // Initialised to avoid compiler warnings.
        unsigned int K = 0;
        NekDouble beta = 0.0;
 
        if (boost::iequals(supptype, "Free-Free"))
        {
            K    = plane / 2;
            beta = 2.0 * M_PI / m_lhom;
        }
        else if (boost::iequals(supptype, "Pinned-Pinned"))
        {
            K    = plane + 1;
            beta = M_PI / m_lhom;
        }
        else
        {
            ASSERTL0(false, "Unrecognized support type for cable's motion");
        }
 
        tmp6 = beta * K;
        tmp6 = tmp6 * tmp6;
        tmp7 = tmp6 * tmp6;
        tmp7 = tmp2 + tmp4 * tmp6 + tmp5 * tmp7;
 
        (*m_CoeffMat_A[plane])(0, 0) = tmp7;
        (*m_CoeffMat_A[plane])(0, 1) = tmp3;
        (*m_CoeffMat_A[plane])(0, 2) = 1.0;
        (*m_CoeffMat_A[plane])(1, 0) = 0.0;
        (*m_CoeffMat_A[plane])(1, 1) = 1.0;
        (*m_CoeffMat_A[plane])(1, 2) = -m_timestep / 2.0;
        (*m_CoeffMat_A[plane])(2, 0) = 1.0;
        (*m_CoeffMat_A[plane])(2, 1) = 0.0;
        (*m_CoeffMat_A[plane])(2, 2) = -tmp1 / 4.0;
        (*m_CoeffMat_B[plane])(0, 0) = 0.0;
        (*m_CoeffMat_B[plane])(0, 1) = 0.0;
        (*m_CoeffMat_B[plane])(0, 2) = 0.0;
        (*m_CoeffMat_B[plane])(1, 0) = 0.0;
        (*m_CoeffMat_B[plane])(1, 1) = 1.0;
        (*m_CoeffMat_B[plane])(1, 2) = m_timestep / 2.0;
        (*m_CoeffMat_B[plane])(2, 0) = 1.0;
        (*m_CoeffMat_B[plane])(2, 1) = m_timestep;
        (*m_CoeffMat_B[plane])(2, 2) = tmp1 / 4.0;
 
        m_CoeffMat_A[plane]->Invert();
        (*m_CoeffMat_B[plane]) =
            (*m_CoeffMat_A[plane]) * (*m_CoeffMat_B[plane]);
    }
}
 
/**
 * Function to roll time-level storages to the next step layout.
 * The stored data associated with the oldest time-level
 * (not required anymore) are moved to the top, where they will
 * be overwritten as the solution process progresses.
 */
void ForcingMovingBody::RollOver(Array<OneD, Array<OneD, NekDouble>> &input)
{
    size_t nlevels = input.size();
 
    Array<OneD, NekDouble> tmp;
    tmp = input[nlevels - 1];
 
    for (size_t n = nlevels - 1; n > 0; --n)
    {
        input[n] = input[n - 1];
    }
 
    input[0] = tmp;
}
 
/**
 *
 */
void ForcingMovingBody::CheckIsFromFile(const TiXmlElement *pForce)
{
 
    m_funcName  = Array<OneD, std::string>(3);
    m_motion    = Array<OneD, std::string>(2);
    m_motion[0] = "x";
    m_motion[1] = "y";
 
    m_IsFromFile = Array<OneD, bool>(6);
    // Loading the x-dispalcement (m_zta) and the y-displacement (m_eta)
    // Those two variables are bith functions of z and t and the may come
    // from an equation (forced vibration) or from another solver which, given
    // the aerodynamic forces at the previous step, calculates the
    // displacements.
 
    // Get the body displacement: m_zta and m_eta
    const TiXmlElement *funcNameElmt_D =
        pForce->FirstChildElement("DISPLACEMENTS");
    ASSERTL0(funcNameElmt_D,
             "MOVINGBODYFORCE tag has to specify a function name which "
             "prescribes the body displacement as d(z,t).");
 
    m_funcName[0] = funcNameElmt_D->GetText();
    ASSERTL0(m_session->DefinesFunction(m_funcName[0]),
             "Function '" + m_funcName[0] + "' not defined.");
 
    // Get the body velocity of movement: d(m_zta)/dt and d(m_eta)/dt
    const TiXmlElement *funcNameElmt_V =
        pForce->FirstChildElement("VELOCITIES");
    ASSERTL0(funcNameElmt_D,
             "MOVINGBODYFORCE tag has to specify a function name which "
             "prescribes the body velocity of movement as v(z,t).");
 
    m_funcName[1] = funcNameElmt_V->GetText();
    ASSERTL0(m_session->DefinesFunction(m_funcName[1]),
             "Function '" + m_funcName[1] + "' not defined.");
 
    // Get the body acceleration: dd(m_zta)/ddt and dd(m_eta)/ddt
    const TiXmlElement *funcNameElmt_A =
        pForce->FirstChildElement("ACCELERATIONS");
    ASSERTL0(funcNameElmt_A,
             "MOVINGBODYFORCE tag has to specify a function name which "
             "prescribes the body acceleration as a(z,t).");
 
    m_funcName[2] = funcNameElmt_A->GetText();
    ASSERTL0(m_session->DefinesFunction(m_funcName[2]),
             "Function '" + m_funcName[2] + "' not defined.");
 
    LibUtilities::FunctionType vType;
 
    // Check Displacement x
    vType = m_session->GetFunctionType(m_funcName[0], m_motion[0]);
    if (vType == LibUtilities::eFunctionTypeExpression)
    {
        m_IsFromFile[0] = false;
    }
    else if (vType == LibUtilities::eFunctionTypeFile)
    {
        m_IsFromFile[0] = true;
    }
    else
    {
        ASSERTL0(false, "The displacements in x must be specified via an "
                        "equation <E> or a file <F>");
    }
 
    // Check Displacement y
    vType = m_session->GetFunctionType(m_funcName[0], m_motion[1]);
    if (vType == LibUtilities::eFunctionTypeExpression)
    {
        m_IsFromFile[1] = false;
    }
    else if (vType == LibUtilities::eFunctionTypeFile)
    {
        m_IsFromFile[1] = true;
    }
    else
    {
        ASSERTL0(false, "The displacements in y must be specified via an "
                        "equation <E> or a file <F>");
    }
 
    // Check Velocity x
    vType = m_session->GetFunctionType(m_funcName[1], m_motion[0]);
    if (vType == LibUtilities::eFunctionTypeExpression)
    {
        m_IsFromFile[2] = false;
    }
    else if (vType == LibUtilities::eFunctionTypeFile)
    {
        m_IsFromFile[2] = true;
    }
    else
    {
        ASSERTL0(false, "The velocities in x must be specified via an equation "
                        "<E> or a file <F>");
    }
 
    // Check Velocity y
    vType = m_session->GetFunctionType(m_funcName[1], m_motion[1]);
    if (vType == LibUtilities::eFunctionTypeExpression)
    {
        m_IsFromFile[3] = false;
    }
    else if (vType == LibUtilities::eFunctionTypeFile)
    {
        m_IsFromFile[3] = true;
    }
    else
    {
        ASSERTL0(false, "The velocities in y must be specified via an equation "
                        "<E> or a file <F>");
    }
 
    // Check Acceleration x
    vType = m_session->GetFunctionType(m_funcName[2], m_motion[0]);
    if (vType == LibUtilities::eFunctionTypeExpression)
    {
        m_IsFromFile[4] = false;
    }
    else if (vType == LibUtilities::eFunctionTypeFile)
    {
        m_IsFromFile[4] = true;
    }
    else
    {
        ASSERTL0(false, "The accelerations in x must be specified via an "
                        "equation <E> or a file <F>");
    }
 
    // Check Acceleration y
    vType = m_session->GetFunctionType(m_funcName[2], m_motion[1]);
    if (vType == LibUtilities::eFunctionTypeExpression)
    {
        m_IsFromFile[5] = false;
    }
    else if (vType == LibUtilities::eFunctionTypeFile)
    {
        m_IsFromFile[5] = true;
    }
    else
    {
        ASSERTL0(false, "The accelerations in y must be specified via an "
                        "equation <E> or a file <F>");
    }
}
 
/**
 *
 */
void ForcingMovingBody::InitialiseFilter(
    const LibUtilities::SessionReaderSharedPtr &pSession,
    const Array<OneD, MultiRegions::ExpListSharedPtr> &pFields,
    const TiXmlElement *pForce)
{
    // Get the outputfile name, output frequency and
    // the boundary's ID for the cable's wall
    std::string typeStr = pForce->Attribute("TYPE");
    std::map<std::string, std::string> vParams;
 
    const TiXmlElement *param = pForce->FirstChildElement("PARAM");
    while (param)
    {
        ASSERTL0(param->Attribute("NAME"),
                 "Missing attribute 'NAME' for parameter in filter " + typeStr +
                     "'.");
        std::string nameStr = param->Attribute("NAME");
 
        ASSERTL0(param->GetText(), "Empty value string for param.");
        std::string valueStr = param->GetText();
 
        vParams[nameStr] = valueStr;
 
        param = param->NextSiblingElement("PARAM");
    }
 
    // Creat the filter for MovingBody, where we performed the calculation of
    // fluid forces and write both the aerodynamic forces and motion variables
    // into the output files
    m_MovBodyfilter = MemoryManager<FilterMovingBody>::AllocateSharedPtr(
        pSession, m_equ.lock(), vParams);
 
    // Initialise the object of MovingBody filter
    m_MovBodyfilter->Initialise(pFields, 0.0);
}
 
} // namespace Nektar