tr1bubblestokes.C

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/*
 *
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 *              ##   ##  ##   ##  ####    ####    ##  #  ##
 *             ##   ##  ##   ##  ##      ##      ##     ##
 *            ##   ##  ##   ##  ##      ##      ##     ##
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 *
 *
 *             OOFEM : Object Oriented Finite Element Code
 *
 *               Copyright (C) 1993 - 2025   Borek Patzak
 *
 *
 *
 *       Czech Technical University, Faculty of Civil Engineering,
 *   Department of Structural Mechanics, 166 29 Prague, Czech Republic
 *
 *  This library is free software; you can redistribute it and/or
 *  modify it under the terms of the GNU Lesser General Public
 *  License as published by the Free Software Foundation; either
 *  version 2.1 of the License, or (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 *  Lesser General Public License for more details.
 *
 *  You should have received a copy of the GNU Lesser General Public
 *  License along with this library; if not, write to the Free Software
 *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 */
 
#include "tr1bubblestokes.h"
#include "node.h"
#include "elementinternaldofman.h"
#include "domain.h"
#include "gaussintegrationrule.h"
#include "gausspoint.h"
#include "bcgeomtype.h"
#include "load.h"
#include "bodyload.h"
#include "boundaryload.h"
#include "mathfem.h"
#include "fm/Materials/fluiddynamicmaterial.h"
#include "fei2dtrlin.h"
#include "masterdof.h"
#include "fluidcrosssection.h"
#include "classfactory.h"
 
namespace oofem {
REGISTER_Element(Tr1BubbleStokes);
 
// Set up interpolation coordinates
FEI2dTrLin Tr1BubbleStokes :: interp(1, 2);
// Set up ordering vectors (for assembling)
IntArray Tr1BubbleStokes :: momentum_ordering = {1, 2, 4, 5, 7, 8, 10, 11};
IntArray Tr1BubbleStokes :: conservation_ordering = {3, 6, 9};
IntArray Tr1BubbleStokes :: edge_ordering [ 3 ] = {
    {1, 2, 4, 5},
    {4, 5, 7, 8},
    {7, 8, 1, 2}
};
 
Tr1BubbleStokes :: Tr1BubbleStokes(int n, Domain *aDomain) : FMElement(n, aDomain), ZZNodalRecoveryModelInterface(this), SpatialLocalizerInterface(this)
{
    this->numberOfDofMans = 3;
    this->numberOfGaussPoints = 7;
 
    this->bubble = std::make_unique<ElementDofManager>(1, aDomain, this);
    this->bubble->appendDof( new MasterDof(this->bubble.get(), V_u) );
    this->bubble->appendDof( new MasterDof(this->bubble.get(), V_v) );
}
 
void Tr1BubbleStokes :: computeGaussPoints()
{
    if ( integrationRulesArray.size() == 0 ) {
        integrationRulesArray.resize(1);
        integrationRulesArray [ 0 ] = std::make_unique<GaussIntegrationRule>(1, this, 1, 3);
        this->giveCrossSection()->setupIntegrationPoints(* integrationRulesArray [ 0 ], this->numberOfGaussPoints, this);
    }
}
 
int Tr1BubbleStokes :: computeNumberOfDofs()
{
    return 11;
}
 
void Tr1BubbleStokes :: giveDofManDofIDMask(int inode, IntArray &answer) const
{
    answer = {V_u, V_v, P_f};
}
 
void Tr1BubbleStokes :: giveInternalDofManDofIDMask(int i, IntArray &answer) const
{
    answer = {V_u, V_v};
}
 
int Tr1BubbleStokes :: giveNumberOfInternalDofManagers() const
{
    return 1;
    
}
 
DofManager *Tr1BubbleStokes :: giveInternalDofManager(int i) const
{
    return this->bubble.get();
}
 
double Tr1BubbleStokes :: computeVolumeAround(GaussPoint *gp)
{
    double detJ = fabs( this->interp.giveTransformationJacobian( gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(this) ) );
    return detJ *gp->giveWeight();
}
 
void Tr1BubbleStokes :: giveCharacteristicVector(FloatArray &answer, CharType mtrx, ValueModeType mode,
                                                 TimeStep *tStep)
{
    // Compute characteristic vector for this element. I.e the load vector(s)
    if ( mtrx == ExternalForcesVector ) {
        this->computeExternalForcesVector(answer, tStep);
    } else if ( mtrx == InternalForcesVector ) {
        this->computeInternalForcesVector(answer, tStep);
    } else {
        OOFEM_ERROR("Unknown Type of characteristic mtrx.");
    }
}
 
void Tr1BubbleStokes :: giveCharacteristicMatrix(FloatMatrix &answer,
                                                 CharType mtrx, TimeStep *tStep)
{
    if ( mtrx == TangentStiffnessMatrix ) {
        this->computeStiffnessMatrix(answer, TangentStiffness, tStep);
    } else {
        OOFEM_ERROR("Unknown Type of characteristic mtrx.");
    }
}
 
void Tr1BubbleStokes :: computeInternalForcesVector(FloatArray &answer, TimeStep *tStep)
{
    FluidDynamicMaterial *mat = static_cast< FluidCrossSection * >( this->giveCrossSection() )->giveFluidMaterial();
 
    FloatArrayF<8> a_velocity = this->computeVectorOfVelocities(VM_Total, tStep);
    FloatArrayF<3> a_pressure = this->computeVectorOfPressures(VM_Total, tStep);
 
    FloatArrayF<8> momentum;
    FloatArrayF<3> conservation;
 
    for ( auto &gp: *integrationRulesArray [ 0 ] ) {
        const auto &lcoords = gp->giveNaturalCoordinates();
 
        auto N = this->interp.evalN( lcoords );
        auto val = this->interp.evaldNdx( FEIElementGeometryWrapper(this) );
        auto detJ = val.first;
        auto dN = val.second;
        auto dA = std::abs(detJ) * gp->giveWeight();
 
        FloatArrayF<8> dNv;
        FloatMatrixF<3,8> B;
        for ( int j = 0, k = 0; j < 3; j++, k += 2 ) {
            dNv[k]     = B(0, k)     = B(2, k + 1) = dN(0, j);
            dNv[k + 1] = B(1, k + 1) = B(2, k)     = dN(1, j);
        }
 
        // Bubble contribution;
        dNv[6] = B(0, 6) = B(2, 7) = 27. * ( dN(0, 0) * N[1] * N[2] + N[0] * dN(1, 0) * N[2] + N[0] * N[1] * dN(2, 0) );
        dNv[7] = B(1, 7) = B(2, 6) = 27. * ( dN(0, 1) * N[1] * N[2] + N[0] * dN(1, 1) * N[2] + N[0] * N[1] * dN(2, 1) );
 
        auto pressure = dot(N, a_pressure);
        auto epsp = dot(B, a_velocity);
 
        auto s_r = mat->computeDeviatoricStress2D(epsp, pressure, gp, tStep);
        auto devStress = s_r.first;
        auto r_vol = s_r.second;
 
        momentum += Tdot(B, devStress * dA) + dNv * (-pressure * dA);
        conservation += N * (r_vol * dA);
    }
 
    answer.resize(11);
    answer.zero();
    answer.assemble(momentum, this->momentum_ordering);
    answer.assemble(conservation, this->conservation_ordering);
}
 
void Tr1BubbleStokes :: computeExternalForcesVector(FloatArray &answer, TimeStep *tStep)
{
    FloatArray vec;
 
    int nLoads = this->boundaryLoadArray.giveSize() / 2;
    answer.resize(11);
    answer.zero();
    for ( int i = 1; i <= nLoads; i++ ) {  // For each Neumann boundary condition
        int load_number = this->boundaryLoadArray.at(2 * i - 1);
        int load_id = this->boundaryLoadArray.at(2 * i);
        Load *load = this->domain->giveLoad(load_number);
        bcGeomType ltype = load->giveBCGeoType();
 
        if ( ltype == EdgeLoadBGT ) {
            this->computeBoundarySurfaceLoadVector(vec, static_cast< BoundaryLoad * >(load), load_id, ExternalForcesVector, VM_Total, tStep);
            answer.add(vec);
        }
    }
 
    nLoads = this->giveBodyLoadArray()->giveSize();
    for ( int i = 1; i <= nLoads; i++ ) {
        Load *load  = domain->giveLoad( bodyLoadArray.at(i) );
        BodyLoad *bLoad;
        if ((bLoad = dynamic_cast<BodyLoad*>(load))) {
            bcGeomType ltype = load->giveBCGeoType();
            if ( ltype == BodyLoadBGT && load->giveBCValType() == ForceLoadBVT ) {
                this->computeLoadVector(vec, bLoad, ExternalForcesVector, VM_Total, tStep);
                answer.add(vec);
            }
        }
    }
}
 
 
void Tr1BubbleStokes :: computeLoadVector(FloatArray &answer, BodyLoad *load, CharType type, ValueModeType mode, TimeStep *tStep)
{
    if ( type != ExternalForcesVector ) {
        answer.clear();
        return;
    }
 
    FloatArray N, gVector, temparray(8);
 
    load->computeComponentArrayAt(gVector, tStep, VM_Total);
    temparray.zero();
    if ( gVector.giveSize() ) {
        for ( auto &gp: *integrationRulesArray [ 0 ] ) {
            const FloatArray &lcoords = gp->giveNaturalCoordinates();
 
            double rho = static_cast< FluidCrossSection * >( this->giveCrossSection() )->giveDensity(gp);
            double detJ = fabs( this->interp.giveTransformationJacobian( lcoords, FEIElementGeometryWrapper(this) ) );
            double dA = detJ * gp->giveWeight();
 
            this->interp.evalN( N, lcoords, FEIElementGeometryWrapper(this) );
            for ( int j = 0; j < 3; j++ ) {
                temparray(2 * j)     += N(j) * rho * gVector(0) * dA;
                temparray(2 * j + 1) += N(j) * rho * gVector(1) * dA;
            }
 
            temparray(6) += N(0) * N(1) * N(2) * rho * gVector(0) * dA;
            temparray(7) += N(0) * N(1) * N(2) * rho * gVector(1) * dA;
        }
    }
 
    answer.resize(11);
    answer.zero();
    answer.assemble(temparray, this->momentum_ordering);
}
 
  void Tr1BubbleStokes :: computeBoundarySurfaceLoadVector(FloatArray &answer, BoundaryLoad *load, int iEdge, CharType type, ValueModeType mode, TimeStep *tStep, bool global)
{
    if ( type != ExternalForcesVector ) {
        answer.clear();
        return;
    }
 
    if ( load->giveType() == TransmissionBC ) { // Neumann boundary conditions (traction)
 
        int numberOfEdgeIPs = ( int ) ceil( ( load->giveApproxOrder() + 2. ) / 2. );
 
        GaussIntegrationRule iRule(1, this, 1, 1);
        FloatArray N, t, f(4);
 
        f.zero();
        iRule.SetUpPointsOnLine(numberOfEdgeIPs, _Unknown);
 
        for ( auto &gp: iRule ) {
            const FloatArray &lcoords = gp->giveNaturalCoordinates();
 
            this->interp.edgeEvalN( N, iEdge, lcoords, FEIElementGeometryWrapper(this) );
            double detJ = fabs( this->interp.boundaryGiveTransformationJacobian( iEdge, lcoords, FEIElementGeometryWrapper(this) ) );
            double dS = gp->giveWeight() * detJ;
 
            if ( load->giveFormulationType() == Load :: FT_Entity ) { // Edge load in xi-eta system
                load->computeValueAt(t, tStep, lcoords, VM_Total);
            } else { // Edge load in x-y system
                FloatArray gcoords;
                this->interp.boundaryLocal2Global( gcoords, iEdge, lcoords, FEIElementGeometryWrapper(this) );
                load->computeValueAt(t, tStep, gcoords, VM_Total);
            }
 
            // Reshape the vector
            for ( int j = 0; j < 2; j++ ) {
                f(2 * j)     += N(j) * t(0) * dS;
                f(2 * j + 1) += N(j) * t(1) * dS;
            }
        }
 
        answer.resize(11);
        answer.zero();
        answer.assemble(f, this->edge_ordering [ iEdge - 1 ]);
    } else {
        OOFEM_ERROR("Strange boundary condition type");
    }
}
 
void Tr1BubbleStokes :: computeStiffnessMatrix(FloatMatrix &answer, MatResponseMode mode, TimeStep *tStep)
{
    // Note: Working with the components; [K, G+Dp; G^T+Dv^T, C] . [v,p]
    FluidDynamicMaterial *mat = static_cast< FluidCrossSection * >( this->giveCrossSection() )->giveFluidMaterial();
    FloatMatrixF<8,8> K;
    FloatMatrixF<8,3> G, Dp;
    FloatMatrixF<3,8> DvT;
    FloatMatrixF<3,3> C;
 
    for ( auto &gp: *integrationRulesArray [ 0 ] ) {
        // Compute Gauss point and determinant at current element
        const auto &lcoords = gp->giveNaturalCoordinates();
 
        auto N = this->interp.evalN( lcoords );
        auto detj_dn = this->interp.evaldNdx( FEIElementGeometryWrapper(this) );
        auto dN = detj_dn.second;
        auto detJ = detj_dn.first;
        auto dA = std::abs(detJ) * gp->giveWeight();
 
        FloatArrayF<8> dN_V;
        FloatMatrixF<3,8> B;
        for ( int j = 0, k = 0; j < 3; j++, k += 2 ) {
            dN_V[k]     = B(0, k)     = B(2, k + 1) = dN(0, j);
            dN_V[k + 1] = B(1, k + 1) = B(2, k)     = dN(1, j);
        }
 
        // Bubble contribution;
        dN_V[6] = B(0, 6) = B(2, 7) = 27. * ( dN(0, 0) * N[1] * N[2] + N[0] * dN(1, 0) * N[2] + N[0] * N[1] * dN(2, 0) );
        dN_V[7] = B(1, 7) = B(2, 6) = 27. * ( dN(0, 1) * N[1] * N[2] + N[0] * dN(1, 1) * N[2] + N[0] * N[1] * dN(2, 1) );
 
        // Computing the internal forces should have been done first.
        // dsigma_dev/deps_dev  dsigma_dev/dp  deps_vol/deps_dev  deps_vol/dp
        //auto [Ed, Ep, Cd, Cp] = mat->computeTangents2D(mode, gp, tStep);
        auto tangents = mat->computeTangents2D(mode, gp, tStep);
 
        K.plusProductSymmUpper(B, dot(tangents.dsdd, B), dA);
        G.plusDyadUnsym(dN_V, N, -dA);
        Dp.plusDyadUnsym(Tdot(B, tangents.dsdp), N, dA);
        DvT.plusDyadUnsym(N, Tdot(B, tangents.dedd), dA);
        C.plusDyadSymmUpper(N, tangents.dedp * dA);
    }
 
    K.symmetrized();
    C.symmetrized();
    auto GTDvT = transpose(G) + DvT;
    auto GDp = G + Dp;
 
    answer.resize(11, 11);
    answer.zero();
    answer.assemble(K, this->momentum_ordering);
    answer.assemble(GTDvT, this->conservation_ordering, this->momentum_ordering);
    answer.assemble(GDp, this->momentum_ordering, this->conservation_ordering);
    answer.assemble(C, this->conservation_ordering);
}
 
FEInterpolation *Tr1BubbleStokes :: giveInterpolation() const
{
    return & interp;
}
 
FEInterpolation *Tr1BubbleStokes :: giveInterpolation(DofIDItem id) const
{
    return & interp;
}
 
void Tr1BubbleStokes :: updateYourself(TimeStep *tStep)
{
    Element :: updateYourself(tStep);
}
 
// Some extension Interfaces to follow:
 
Interface *Tr1BubbleStokes :: giveInterface(InterfaceType it)
{
    switch ( it ) {
    case ZZNodalRecoveryModelInterfaceType:
        return static_cast< ZZNodalRecoveryModelInterface * >(this);
 
    case SpatialLocalizerInterfaceType:
        return static_cast< SpatialLocalizerInterface * >(this);
 
    default:
        return FMElement :: giveInterface(it);
    }
}
 
void Tr1BubbleStokes :: computeField(ValueModeType mode, TimeStep *tStep, const FloatArray &lcoords, FloatArray &answer)
{
    FloatArray n, n_lin, pressures, velocities;
    this->interp.evalN( n, lcoords, FEIElementGeometryWrapper(this) );
    this->interp.evalN( n_lin, lcoords, FEIElementGeometryWrapper(this) );
    this->computeVectorOf({P_f}, mode, tStep, pressures);
    this->computeVectorOf({V_u, V_v}, mode, tStep, velocities);
 
    answer.resize(3);
    answer.zero();
    for ( int i = 1; i <= n.giveSize(); i++ ) {
        answer(0) += n.at(i) * velocities.at(i*2-1);
        answer(1) += n.at(i) * velocities.at(i*2);
    }
    answer(0) += n.at(1) * n.at(2) * n.at(3) * velocities.at(7);
    answer(1) += n.at(1) * n.at(2) * n.at(3) * velocities.at(8);
 
    for ( int i = 1; i <= n_lin.giveSize(); i++ ) {
        answer(2) += n_lin.at(i) * pressures.at(i);
    }
}
 
} // end namespace oofem