void TPZArtDiff::ContributeImplDiff(int dim, TPZFMatrix<REAL> &jacinv, TPZVec<FADREAL> &sol, TPZVec<FADREAL> &dsol, TPZFMatrix<STATE> &ek, TPZFMatrix<STATE> &ef, REAL weight, REAL timeStep, REAL deltaX)
{
TPZVec<STATE> solReal(sol.NElements());
int i;
for(i = 0; i < sol.NElements(); i++)
solReal[i] = sol[i].val();
REAL delta = Delta(deltaX, solReal);
REAL constant = /*-*/ delta * weight * timeStep;
TPZVec<TPZVec<FADREAL> > TauDiv;
PrepareFastDiff(dim, jacinv, sol, dsol, TauDiv);
TPZVec<FADREAL> Diff;
TPZVec<REAL> gradv(dim);
int j, k, l;
int nstate = dim + 2;
int neq = sol[0].size();
int nshape = neq/nstate;
for(l=0;l<nshape;l++)
{
for(k=0;k<dim;k++)
gradv[k] = dsol[k].dx/*fastAccessDx*/(/*k+*/l*nstate);// always retrieving this information from the first state variable...
ODotOperator(gradv, TauDiv, Diff);
for(i=0;i<nstate;i++)
{
ef(i+l*nstate,0) += constant * Diff[i].val();
for(j=0;j<neq;j++)
ek(i+l*nstate, j) -= constant * Diff[i].dx/*fastAccessDx*/(j);
}
}
}
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() );
}
double H1_error(const space_ptrtype & Xh, const element_type & T, const double & values) const
{
// replace params by specified values
ex solution = getSolution(values);
auto gradg = expr<1,Dim,2>(grad(solution,vars), vars );
auto mesh = Xh->mesh();
double L2error = L2_error(Xh, T, values);
double H1seminorm = math::sqrt( integrate( elements(mesh), Px()*(gradv(T) - gradg)*trans(gradv(T) - gradg) ).evaluate()(0,0) );
return math::sqrt( L2error*L2error + H1seminorm*H1seminorm);
}
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
cv<Dim,Order>::run()
{
auto mesh = loadMesh(_mesh = new mesh_type ,_update = MESH_CHECK|MESH_UPDATE_FACES|MESH_UPDATE_EDGES|MESH_RENUMBER );
auto Xh = space_type::New( mesh );
auto Xhm1 = space_pm1_type::New( mesh );
auto Xhm1vec = space_pm1vec_type::New( mesh );
auto phi = Xh->element();
auto gphi = Xhm1vec->element();
auto gphi0 = Xhm1->element();
phi = vf::project(Xh,elements(mesh), Px()*Px() + Py()*Py() );
// P0 vector
gphi = vf::project(Xhm1vec, elements(mesh), trans( gradv(phi) ) );
// P0 scalar
auto gphi_compx = gphi.comp( ( ComponentType )0 );
gphi0 = vf::project(Xhm1, elements(mesh), idv(gphi_compx) );
auto e = exporter(_mesh = mesh, _name = "myExporter");
e->add( "phi", phi );
e->add( "grad_phi", gphi );
e->add( "grad_phi0", gphi0 );
e->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
element_type grad_error_project(const space_ptrtype & Xh, const element_type & T, const double & val)
{
auto gproj = grad_exact_project(Xh, val);
return (gproj - gradv(T));
}
