示例#1
0
void
DrivenCavity<Dim>::Jacobian(const vector_ptrtype& X, sparse_matrix_ptrtype& J)
{
    auto U = Vh->element( "(u,p)" );
    auto V = Vh->element( "(v,q)" );
    auto u = U.template element<0>( "u" );
    auto v = V.template element<0>( "u" );
    auto p = U.template element<1>( "p" );
    auto q = V.template element<1>( "p" );
    //#if defined( FEELPP_USE_LM )
    auto lambda = U.template element<2>();
    auto nu = V.template element<2>();

    //#endif

    if (!J) J = backend(_name="newtonns")->newMatrix( Vh, Vh );
    auto a = form2( _test=Vh, _trial=Vh, _matrix=J );
    a = integrate( elements( mesh ), inner(gradt( u ),grad( v ))/Re );
    a += integrate( elements( mesh ), id(q)*divt(u) -idt(p)*div(v) );
    // Convective terms
    a += integrate( elements( mesh ), trans(id(v))*gradv(u)*idt(u));
    a += integrate( elements( mesh ), trans(id(v))*gradt(u)*idv(u));

    //#if defined( FEELPP_USE_LM )
    a += integrate(elements(mesh), id(q)*idt(lambda)+idt(p)*id(nu));
    //#elif
    //a += integrate(elements(mesh), idt(p)*id(nu));

    //Weak Dirichlet conditions
    a += integrate( boundaryfaces( mesh ),-trans( -idt(p)*N()+gradt(u)*N()/Re )*id( v ));//
    a += integrate( boundaryfaces( mesh ),-trans( -id(p)*N()+grad(u)*N()/Re )*idt( u ));//
    a += integrate( boundaryfaces( mesh ), +penalbc*inner( idt( u ),id( v ) )/hFace() );


}
void run()
{

    Environment::changeRepository( boost::format( "/testsuite/feeldiscr/%1%/P%2%/" )
                                   % Environment::about().appName()
                                   % OrderPoly );


    /* change parameters below */
    const int nDim = 2;
    const int nOrderPoly = OrderPoly;
    const int nOrderGeo = 1;

    //------------------------------------------------------------------------------//

    typedef Mesh< Simplex<nDim, 1,nDim> > mesh_type;
    typedef Mesh< Simplex<nDim, 1,nDim> > mesh_bis_type;

    double meshSize = option("hsize").as<double>();
    double meshSizeBis = option("hsize-bis").as<double>();

    // mesh
    GeoTool::Node x1( 0,0 );
    GeoTool::Node x2( 4,1 );
    GeoTool::Rectangle Omega( meshSize,"Omega",x1,x2 );
    Omega.setMarker( _type="line",_name="Entree",_marker4=true );
    Omega.setMarker( _type="line",_name="Sortie",_marker2=true );
    Omega.setMarker( _type="line",_name="Paroi",_marker1=true,_marker3=true );
    Omega.setMarker( _type="surface",_name="Fluid",_markerAll=true );
    auto mesh = Omega.createMesh(_mesh=new mesh_type,_name="omega_"+ mesh_type::shape_type::name() );
    LOG(INFO) << "created mesh\n";

    GeoTool::Rectangle OmegaBis( meshSizeBis,"Omega",x1,x2 );
    OmegaBis.setMarker( _type="line",_name="Entree",_marker4=true );
    OmegaBis.setMarker( _type="line",_name="Sortie",_marker2=true );
    OmegaBis.setMarker( _type="line",_name="Paroi",_marker1=true,_marker3=true );
    OmegaBis.setMarker( _type="surface",_name="Fluid",_markerAll=true );
    auto meshBis = OmegaBis.createMesh(_mesh=new mesh_bis_type,_name="omegaBis_"+ mesh_type::shape_type::name() );

    //auto meshBis= mesh->createP1mesh();
    LOG(INFO) << "created meshBis\n";

    typedef Lagrange<nOrderPoly,Scalar,Continuous,PointSetFekete> basis_type;
    typedef FunctionSpace<mesh_type, bases<basis_type> > space_type;

    auto Xh = space_type::New( mesh );
    auto u = Xh->element();
    auto v = Xh->element();
    auto u2 = Xh->element();
    LOG(INFO) << "created space and elements\n";

    auto mybackend = backend();

    //--------------------------------------------------------------//

    auto A = mybackend->newMatrix( Xh, Xh );
    auto F = mybackend->newVector( Xh );
    auto pi = cst( M_PI );
    auto u_exact = cos( pi*Px() )*sin( pi*Py() );
    auto dudx = -pi*sin( pi*Px() )*sin( pi*Py() );
    auto dudy = pi*cos( pi*Px() )*cos( pi*Py() );
    auto grad_u_uexact = vec( dudx,dudy );
    auto lap = -2*pi*pi*cos( pi*Px() )*sin( pi*Py() );
    //auto lap = -pi*pi*cos(pi*Px())*sin(pi*Py())
    //    -pi*pi*cos(pi*Px())*sin(pi*Py());
    LOG(INFO) << "created exact data and matrix/vector\n";

    auto f = -lap;//cst(1.);
    double gammabc=10;

    // assemblage
    form2( Xh, Xh, A, _init=true ) =
        integrate( elements( mesh ), //_Q<15>(),
                   + gradt( u )*trans( grad( v ) ) );

    form2( Xh, Xh, A ) +=
        integrate( boundaryfaces( mesh ),
                   - gradt( u )*N()*id( v )
                   + gammabc*idt( u )*id( v )/hFace() );

    form1( Xh, F, _init=true ) =
        integrate( elements( mesh ), // _Q<10>(),
                   trans( f )*id( v ) );

    form1( Xh, F ) +=
        integrate( boundaryfaces( mesh ),
                   + gammabc*u_exact*id( v )/hFace() );

    LOG(INFO) << "A,F assembled\n";

    //form2( Xh, Xh, A ) +=
    //    on( boundaryfaces(mesh) , u, F, u_exact );

    // solve system
    mybackend->solve( A,u,F );
    LOG(INFO) << "A u = F solved\n";
    //--------------------------------------------------------------//

    auto a2 = form2( _test=Xh, _trial=Xh );
    auto f2 = form1( _test=Xh );
    LOG(INFO) << "created form2 a2 and form1 F2\n";

    // assemblage

    a2 = integrate( elements( meshBis ),
                    + gradt( u2 )*trans( grad( v ) ),
                    _Q<10>() );
    LOG(INFO) << "a2 grad.grad term\n";
    a2 += integrate( boundaryfaces( meshBis ),
                     - gradt( u2 )*N()*id( v )
                     + gammabc*idt( u2 )*id( v )/hFace(),
                     _Q<10>() );
    LOG(INFO) << "a2 weak dirichlet terms\n";

    f2 = integrate( elements( meshBis ),
                    trans( f )*id( v ),
                    _Q<10>() );
    LOG(INFO) << "f2 source term\n";
    f2 += integrate( boundaryfaces( meshBis ),
                     + gammabc*u_exact*id( v )/hFace(),
                     _Q<10>() );
    LOG(INFO) << "f2 dirichlet terms\n";

    LOG(INFO) << "a2,f2 assembled\n";

    //form2( Xh, Xh, A2 ) +=
    //     on( boundaryfaces(mesh) , u2, F2, u_exact );



#if 0

    for ( size_type i = 0 ; i< F->size() ; ++i )
    {
        auto errOnF = std::abs( ( *F )( i )-( *F2 )( i ) );

        if ( errOnF > 1e-8 )
            std::cout << "\nerrOnF : " << errOnF;
    }

    std::cout << "\nFin errOnF !!!!\n";
#endif

    // solve system
    a2.solve( _rhs=f2, _solution=u2 );


    auto diff = std::sqrt( integrate( elements( mesh ), ( idv( u )-idv( u2 ) )*( idv( u )-idv( u2 ) ) ).evaluate()( 0,0 ) );
#if 0
    auto int1 = integrate( elements( mesh ), abs( idv( u ) ) ).evaluate()( 0,0 );
    auto int2 = integrate( elements( mesh ), abs( idv( u2 ) ) ).evaluate()( 0,0 );

    std::cout << "\nThe diff : " << diff
              << " int1 :" << int1
              << " int2 :" << int2
              << "\n";
#endif
#if USE_BOOST_TEST
    BOOST_CHECK_SMALL( diff,1e-2 );
#endif


    //--------------------------------------------------------------//

    if ( option("exporter.export").as<bool>() )
    {
        // export
        auto ex = exporter( _mesh=mesh );
        ex->add( "u", u );
        ex->add( "ubis", u2 );
        ex->save();
    }
}
示例#3
0
文件: ns.hpp 项目: LANTZT/feelpp
void
NavierStokes::run()
{
    this->init();

    auto U = Xh->element( "(u,p)" );
    auto V = Xh->element( "(u,q)" );
    auto u = U.element<0>( "u" );
    auto v = V.element<0>( "u" );
    auto p = U.element<1>( "p" );
    auto q = V.element<1>( "p" );
#if defined( FEELPP_USE_LM )
    auto lambda = U.element<2>();
    auto nu = V.element<2>();
#endif
    //# endmarker4 #

    LOG(INFO) << "[dof]         number of dof: " << Xh->nDof() << "\n";
    LOG(INFO) << "[dof]    number of dof/proc: " << Xh->nLocalDof() << "\n";
    LOG(INFO) << "[dof]      number of dof(U): " << Xh->functionSpace<0>()->nDof()  << "\n";
    LOG(INFO) << "[dof] number of dof/proc(U): " << Xh->functionSpace<0>()->nLocalDof()  << "\n";
    LOG(INFO) << "[dof]      number of dof(P): " << Xh->functionSpace<1>()->nDof()  << "\n";
    LOG(INFO) << "[dof] number of dof/proc(P): " << Xh->functionSpace<1>()->nLocalDof()  << "\n";

    LOG(INFO) << "Data Summary:\n";
    LOG(INFO) << "   hsize = " << meshSize << "\n";
    LOG(INFO) << "  export = " << this->vm().count( "export" ) << "\n";
    LOG(INFO) << "      mu = " << mu << "\n";
    LOG(INFO) << " bccoeff = " << penalbc << "\n";




    //# marker5 #
    auto deft = gradt( u )+trans(gradt(u));
    auto def = grad( v )+trans(grad(v));
    //# endmarker5 #

    //# marker6 #
    // total stress tensor (trial)
    auto SigmaNt = -idt( p )*N()+mu*deft*N();

    // total stress tensor (test)
    auto SigmaN = -id( p )*N()+mu*def*N();
    //# endmarker6 #

    auto F = M_backend->newVector( Xh );
    auto D =  M_backend->newMatrix( Xh, Xh );

    // right hand side
    auto ns_rhs = form1( _test=Xh, _vector=F );


    LOG(INFO) << "[navier-stokes] vector local assembly done\n";

    // construction of the BDF
    auto bdfns=bdf(_space=Xh);

    /*
     * Construction of the left hand side
     */

    auto navierstokes = form2( _test=Xh, _trial=Xh, _matrix=D );
    mpi::timer chrono;
    navierstokes += integrate( elements( mesh ), mu*inner( deft,def )+ trans(idt( u ))*id( v )*bdfns->polyDerivCoefficient( 0 ) );
    LOG(INFO) << "mu*inner(deft,def)+(bdf(u),v): " << chrono.elapsed() << "\n";
    chrono.restart();
    navierstokes +=integrate( elements( mesh ), - div( v )*idt( p ) + divt( u )*id( q ) );
    LOG(INFO) << "(u,p): " << chrono.elapsed() << "\n";
    chrono.restart();
#if defined( FEELPP_USE_LM )
    navierstokes +=integrate( elements( mesh ), id( q )*idt( lambda ) + idt( p )*id( nu ) );
    LOG(INFO) << "(lambda,p): " << chrono.elapsed() << "\n";
    chrono.restart();
#endif

    std::for_each( inflow_conditions.begin(), inflow_conditions.end(),
                   [&]( BoundaryCondition const&  bc )
                   {
                       // right hand side
                       ns_rhs += integrate( markedfaces( mesh, bc.marker() ), inner( idf(&bc,BoundaryCondition::operator()),-SigmaN+penalbc*id( v )/hFace() ) );

                       navierstokes +=integrate( boundaryfaces( mesh ), -inner( SigmaNt,id( v ) ) );
                       navierstokes +=integrate( boundaryfaces( mesh ), -inner( SigmaN,idt( u ) ) );
                       navierstokes +=integrate( boundaryfaces( mesh ), +penalbc*inner( idt( u ),id( v ) )/hFace() );
                   });
    std::for_each( wall_conditions.begin(), wall_conditions.end(),
                   [&]( BoundaryCondition const&  bc )
                   {
                       navierstokes +=integrate( boundaryfaces( mesh ), -inner( SigmaNt,id( v ) ) );
                       navierstokes +=integrate( boundaryfaces( mesh ), -inner( SigmaN,idt( u ) ) );
                       navierstokes +=integrate( boundaryfaces( mesh ), +penalbc*inner( idt( u ),id( v ) )/hFace() );
                   });
    std::for_each( outflow_conditions.begin(), outflow_conditions.end(),
                   [&]( BoundaryCondition const&  bc )
                   {
                       ns_rhs += integrate( markedfaces( mesh, bc.marker() ), inner( idf(&bc,BoundaryCondition::operator()),N() ) );
                   });

    LOG(INFO) << "bc: " << chrono.elapsed() << "\n";
    chrono.restart();

    u = vf::project( _space=Xh->functionSpace<0>(), _expr=cst(0.) );
    p = vf::project( _space=Xh->functionSpace<1>(), _expr=cst(0.) );

    M_bdf->initialize( U );

    for( bdfns->start(); bdfns->isFinished(); bdfns->next() )
    {
        // add time dependent terms
        auto bdf_poly = bdfns->polyDeriv();
        form1( _test=Xh, _vector=Ft ) =
            integrate( _range=elements(mesh), _expr=trans(idv( bdf_poly ))*id( v ) );
        // add convective terms
        form1( _test=Xh, _vector=Ft ) +=
            integrate( _range=elements(mesh), _expr=trans(gradv(u)*idv( u ))*id(v) );
        // add contrib from time independent terms
        Ft->add( 1., F );

        // add time stepping terms from BDF to right hand side
        backend()->solve( _matrix=D, _solution=U, _rhs=Ft );

        this->exportResults( bdfns->time(), U );
    }





} // NavierNavierstokes::run
示例#4
0
void
DrivenCavity<Dim>::Residual(const vector_ptrtype& X, vector_ptrtype& R)
{
    auto U = Vh->element( "(u,p)" );
    auto V = Vh->element( "(v,q)" );
    auto u = U.template element<0>( "u" );
    //auto u_exact = U.template element<0>( "u_exact" );
    auto v = V.template element<0>( "u" );
    auto p = U.template element<1>( "p" );
    auto q = V.template element<1>( "p" );
    //#if defined( FEELPP_USE_LM )
    auto lambda = U.template element<2>();
    auto nu = V.template element<2>();
    //#endif

    auto uex=unitX();
    auto u_exact=vf::project(Vh->template functionSpace<0>(), markedfaces(mesh, "wall2"), uex );


    U=*X;
    auto r = form1( _test=Vh, _vector=R );
    //r += integrate( elements( mesh ),-inner( f,id( v ) ) );
    r = integrate( elements( mesh ), trans(gradv( u )*idv(u))*id(v));//convective term
    r += integrate( elements( mesh ), inner(gradv( u ),grad( v ))/Re );
    r +=  integrate( elements( mesh ),-idv(p)*div(v) + id(q)*divv(u));
    //#if defined( FEELPP_USE_LM )
    r += integrate ( elements( mesh ), +id( q )*idv( lambda )+idv( p )*id( nu ) );
    //#endif


    //Weak Dirichlet
    auto SigmaNv = ( -idv( p )*N() + gradv( u )*N()/Re );
    auto SigmaN = ( -id( q )*N() + grad( v )*N()/Re );
    r +=integrate ( boundaryfaces(mesh), - trans( SigmaNv )*id( v ) - trans( SigmaN )*( idv( u ) -idv(u_exact) ) + penalbc*trans( idv( u ) - idv(u_exact) )*id( v )/hFace() );


}
示例#5
0
文件: beam.cpp 项目: LANTZT/feelpp
void
Beam<nDim,nOrder>::run()
{

    this->changeRepository( boost::format( "doc/manual/solid/%1%/%2%/P%3%/h_%4%/" )
                            % this->about().appName()
                            % entity_type::name()
                            % nOrder
                            % meshSize );
    /*
     * First we create the mesh
     */
    mesh_ptrtype mesh = createGMSHMesh( _mesh=new mesh_type,
                                        _update=MESH_UPDATE_EDGES|MESH_UPDATE_FACES|MESH_CHECK,
                                        _desc=domain( _name=( boost::format( "beam-%1%" ) % nDim ).str() ,

                                                      _shape="hypercube",
                                                      _xmin=0., _xmax=0.351,
                                                      _ymin=0., _ymax=0.02,
                                                      _zmin=0., _zmax=0.02,
                                                      _h=meshSize ) );
    // add marker clamped to the mesh
    mesh->addMarkerName( "clamped",( nDim==2 )?1:19, (nDim==2)?1:2);
    mesh->addMarkerName( "tip",( nDim==2)?3:27, (nDim==2)?1:2);
    /*
     * The function space and some associate elements are then defined
     */
    timers["init"].first.restart();
    space_ptrtype Xh = space_type::New( mesh );
    Xh->printInfo();

    element_type u( Xh, "u" );
    element_type v( Xh, "v" );
    timers["init"].second = timers["init"].first.elapsed();

    /*
     * Data associated with the simulation
     */
    auto E = doption(_name="E")*pascal;
    const double nu = doption(_name="nu");

    auto mu = E/( 2*( 1+nu ) );
    auto lambda = E*nu/( ( 1+nu )*( 1-2*nu ) );
    auto density = 1e3;
    auto gravity = -2*newton/pow<Dim>(meter);//-density*0.05;
    LOG(INFO) << "lambda = " << lambda << "\n"
          << "mu     = " << mu << "\n"
          << "gravity= " << gravity << "\n";

    /*
     * Construction of the right hand side
     *
     * \f$ f = \int_\Omega g * v \f$ where \f$ g \f$ is a vector
     * directed in the \f$ y \f$ direction.
     */
    auto F = backend()->newVector( Xh );
    F->zero();
    timers["assembly"].first.restart();

    if ( Dim == 3 )
        form1( _test=Xh, _vector=F ) = integrate( elements( mesh ), trans( gravity.value()*oneZ() )*id( v ) );
    else
        form1( _test=Xh, _vector=F ) = integrate( elements( mesh ), trans( gravity.value()*oneY() )*id( v ) );

    timers["assembly"].second = timers["assembly"].first.elapsed();

    /*
     * Construction of the left hand side
     */
    auto D = backend()->newMatrix( Xh, Xh );
    timers["assembly"].first.restart();
    auto deft = sym(gradt(u));
    auto def = sym(grad(u));
    auto a = form2( _test=Xh, _trial=Xh, _matrix=D );
    a = integrate( elements( mesh ),
                   lambda.value()*divt( u )*div( v )  +
                   2.*mu.value()*trace( trans( deft )*def ) );

    if ( M_bctype == 1 ) // weak Dirichlet bc
    {
        auto Id = eye<nDim>();
        a += integrate( markedfaces( mesh, "clamped" ),
                        - trans( ( 2.*mu.value()*deft+lambda.value()*trace( deft )*Id )*N() )*id( v )
                        - trans( ( 2.*mu.value()*def+lambda.value()*trace( def )*Id )*N() )*idt( u )
                        + bcCoeff*std::max(2.*mu.value(),lambda.value())*trans( idt( u ) )*id( v )/hFace() );
    }

    if ( M_bctype == 0 )
        a += on( markedfaces( mesh, "clamped" ), u, F, zero<nDim,1>() );

    timers["assembly"].second += timers["assembly"].first.elapsed();

    backend(_rebuild=true)->solve( _matrix=D, _solution=u, _rhs=F );

    v = vf::project( Xh, elements( Xh->mesh() ), P() );
    this->exportResults( 0, u, v );

    auto i1 = mean( _range=markedfaces( mesh, "tip"  ), _expr=idv( u ) );
    LOG(INFO) << "deflection: " << i1 << "\n";

} // Beam::run
示例#6
0
// <int Order_s, int Order_p, int Order_t>
void Convection ::initLinearOperator2( sparse_matrix_ptrtype& L )
{
    boost::timer ti;
    LOG(INFO) << "[initLinearOperator2] start\n";

    mesh_ptrtype mesh = Xh->mesh();
    element_type U( Xh, "u" );
    element_type Un( Xh, "un" );
    element_type V( Xh, "v" );
    element_0_type u = U. element<0>(); // fonction vitesse
    element_0_type un = Un. element<0>(); // fonction vitesse
    element_0_type v = V. element<0>(); // fonction test vitesse
    element_1_type p = U. element<1>(); // fonction pression
    element_1_type pn = Un. element<1>(); // fonction pression
    element_1_type q = V. element<1>(); // fonction test pression
    element_2_type t = U. element<2>(); // fonction temperature
    element_2_type tn = Un. element<2>(); // fonction temperature
    element_2_type s = V. element<2>(); // fonction test temperature
#if defined( FEELPP_USE_LM )
    element_3_type xi = U. element<3>(); // fonction multipliers
    element_3_type eta = V. element<3>(); // fonction test multipliers
#endif

    double gr= M_current_Grashofs;
    double sqgr( 1/math::sqrt( gr ) );
    double pr = M_current_Prandtl;
    double sqgrpr( 1/( pr*math::sqrt( gr ) ) );
    double gamma( this->vm()["penalbc"]. as<double>() );

    double k=this->vm()["k"]. as<double>();
    double nu=this->vm()["nu"]. as<double>();
    double rho=this->vm()["rho"]. as<double>();
    //double dt=this->vm()["dt"]. as<double>();
    int adim=this->vm()["adim"]. as<int>();
    int weakdir=this->vm()["weakdir"]. as<int>();
    //choix de la valeur des paramètres dimensionnés ou adimensionnés
    double a=0.0,b=0.0,c=0.0;
    double pC=1;

    if ( adim == 0 ) pC = this->vm()["pC"]. as<double>();

    if ( adim==1 )
    {
        a=1;
        b=sqgr;
        c=sqgrpr;
    }

    else
    {
        a=rho;
        b=nu;
        c=k;
    }

    double expansion = 1;

    if ( adim == 0 ) expansion=3.7e-3;

    auto bf = form2( _test=Xh, _trial=Xh, _matrix=L );
    // Temperature
#if CONVECTION_DIM==2
    // buyoancy forces c(theta,v)
    bf +=integrate( _range=elements( mesh ),
                    _expr=-expansion*idt( t )*( trans( vec( constant( 0. ),constant( 1.0 ) ) )*id( v ) ) );
#else
    bf +=integrate( _range=elements( mesh ),
                    _expr=-expansion*idt( t )*( trans( vec( cst(0.), constant( 0. ),constant( 1.0 ) ) )*id( v ) ) );
#endif

    LOG(INFO) << "[initLinearOperator] temperature Force terms done\n";
    // heat conduction/diffusion: e(beta1,theta,chi)+f(theta,chi)
    bf  += integrate( _range=elements( mesh ),
                      _expr=cst( c )*gradt( t )*trans( grad( s ) ) );
    LOG(INFO) << "[initLinearOperator] Temperature Diffusion terms done\n";

    if ( weakdir == 1 )
    {
        // weak Dirichlet on temperature (T=0|left wall)
        bf  += integrate ( markedfaces( mesh, "Tfixed"  ),
                           - gradt( t )*N()*id( s )*cst_ref( sqgrpr ) );
        bf  += integrate ( markedfaces( mesh, "Tfixed"  ),
                           - grad( s )*N()*idt( t )*cst_ref( sqgrpr ) );
        bf  += integrate ( markedfaces( mesh, "Tfixed"  ),
                           gamma*idt( t )*id( s )/hFace() );
    }

    LOG(INFO) << "[initLinearOperator2] done in " << ti.elapsed() << "s\n";
}