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();
}
}
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
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() );
}
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
// <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";
}
