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
/** * @name derivativeMatrix * @brief This is the main working function of the file. Every work of the file is done in this function. * @param[in] vector<double> Points * This would denote the inteprolating points for which the Lagrange polynomials have to be written. * * Example usage * @code * double integral = lobattoIntegration(unsigned n);//Storing the coefficient of the nth degree Legendre roots. * @endcode */ vector< vector<double> > derivativeMatrix(vector<double> Points) { unsigned n = Points.size(); sort(Points.begin(),Points.end()); double start = Points[0];///The first element. double end = Points[n-1];///The last element. vector< vector<double> > DerivativeMatrix; DerivativeMatrix=zeros(n,n); vector< vector<double> > LagrangePolynomials = lagrangePolynomials(Points); unsigned i,j;///Counters for the loop. function<double(double)> eval; for(i=0;i<n;i++) { for(j=0;j<n;j++) { eval = [&LagrangePolynomials,&i,&j](double x){ return ((polyEval(LagrangePolynomials[i],x)*polyEval(polyDeriv(LagrangePolynomials[j]),x)));}; DerivativeMatrix[i][j] = lobattoIntegration(start,end,n,eval); } } return DerivativeMatrix; }