void AveragedTurbine<Mu>::nonlocal_time_derivative(bool compute_jacobian, AssemblyContext& context, CachedValues& /* cache */ ) { libMesh::DenseSubMatrix<libMesh::Number> &Kss = context.get_elem_jacobian(this->fan_speed_var(), this->fan_speed_var()); // R_{s},{s} libMesh::DenseSubVector<libMesh::Number> &Fs = context.get_elem_residual(this->fan_speed_var()); // R_{s} const std::vector<libMesh::dof_id_type>& dof_indices = context.get_dof_indices(this->fan_speed_var()); const libMesh::Number fan_speed = context.get_system().current_solution(dof_indices[0]); const libMesh::Number output_torque = this->torque_function(libMesh::Point(0), fan_speed); Fs(0) += output_torque; if (compute_jacobian) { // FIXME: we should replace this FEM with a hook to the AD fparser stuff const libMesh::Number epsilon = 1e-6; const libMesh::Number output_torque_deriv = (this->torque_function(libMesh::Point(0), fan_speed+epsilon) - this->torque_function(libMesh::Point(0), fan_speed-epsilon)) / (2*epsilon); Kss(0,0) += output_torque_deriv * context.get_elem_solution_derivative(); } return; }
void HeatConduction<K>::mass_residual( bool compute_jacobian, AssemblyContext& context, CachedValues& /*cache*/ ) { // First we get some references to cell-specific data that // will be used to assemble the linear system. // Element Jacobian * quadrature weights for interior integration const std::vector<libMesh::Real> &JxW = context.get_element_fe(_temp_vars.T_var())->get_JxW(); // The shape functions at interior quadrature points. const std::vector<std::vector<libMesh::Real> >& phi = context.get_element_fe(_temp_vars.T_var())->get_phi(); // The number of local degrees of freedom in each variable const unsigned int n_T_dofs = context.get_dof_indices(_temp_vars.T_var()).size(); // The subvectors and submatrices we need to fill: libMesh::DenseSubVector<libMesh::Real> &F = context.get_elem_residual(_temp_vars.T_var()); libMesh::DenseSubMatrix<libMesh::Real> &M = context.get_elem_jacobian(_temp_vars.T_var(), _temp_vars.T_var()); unsigned int n_qpoints = context.get_element_qrule().n_points(); for (unsigned int qp = 0; qp != n_qpoints; ++qp) { // For the mass residual, we need to be a little careful. // The time integrator is handling the time-discretization // for us so we need to supply M(u_fixed)*u' for the residual. // u_fixed will be given by the fixed_interior_value function // while u' will be given by the interior_rate function. libMesh::Real T_dot; context.interior_rate(_temp_vars.T_var(), qp, T_dot); for (unsigned int i = 0; i != n_T_dofs; ++i) { F(i) -= JxW[qp]*(_rho*_Cp*T_dot*phi[i][qp] ); if( compute_jacobian ) { for (unsigned int j=0; j != n_T_dofs; j++) { // We're assuming rho, cp are constant w.r.t. T here. M(i,j) -= context.get_elem_solution_rate_derivative() * JxW[qp]*_rho*_Cp*phi[j][qp]*phi[i][qp] ; } }// End of check on Jacobian } // End of element dof loop } // End of the quadrature point loop return; }
void BoundaryConditions::pin_value( AssemblyContext& context, const CachedValues& /*cache*/, const bool request_jacobian, const VariableIndex var, const double pin_value, const libMesh::Point& pin_location, const double penalty ) { if (context.get_elem().contains_point(pin_location)) { libMesh::FEGenericBase<libMesh::Real>* elem_fe = NULL; context.get_element_fe( var, elem_fe ); libMesh::DenseSubVector<libMesh::Number> &F_var = context.get_elem_residual(var); // residual libMesh::DenseSubMatrix<libMesh::Number> &K_var = context.get_elem_jacobian(var,var); // jacobian // The number of local degrees of freedom in p variable. const unsigned int n_var_dofs = context.get_dof_indices(var).size(); libMesh::Number var_value = context.point_value(var, pin_location); libMesh::FEType fe_type = elem_fe->get_fe_type(); libMesh::Point point_loc_in_masterelem = libMesh::FEInterface::inverse_map(context.get_dim(), fe_type, &context.get_elem(), pin_location); std::vector<libMesh::Real> phi(n_var_dofs); for (unsigned int i=0; i != n_var_dofs; i++) { phi[i] = libMesh::FEInterface::shape( context.get_dim(), fe_type, &context.get_elem(), i, point_loc_in_masterelem ); } for (unsigned int i=0; i != n_var_dofs; i++) { F_var(i) += penalty*(var_value - pin_value)*phi[i]; /** \todo What the hell is the context.get_elem_solution_derivative() all about? */ if (request_jacobian && context.get_elem_solution_derivative()) { libmesh_assert (context.get_elem_solution_derivative() == 1.0); for (unsigned int j=0; j != n_var_dofs; j++) K_var(i,j) += penalty*phi[i]*phi[j]; } // End if request_jacobian } // End i loop } // End if pin_location return; }
void ScalarODE::nonlocal_constraint(bool compute_jacobian, AssemblyContext& context, CachedValues& /* cache */ ) { libMesh::DenseSubMatrix<libMesh::Number> &Kss = context.get_elem_jacobian(_scalar_ode_var, _scalar_ode_var); // R_{s},{s} libMesh::DenseSubVector<libMesh::Number> &Fs = context.get_elem_residual(_scalar_ode_var); // R_{s} const libMesh::Number constraint = (*constraint_function)(context, libMesh::Point(0), context.get_time()); Fs(0) += constraint; if (compute_jacobian) { // FIXME: we should replace this hacky FDM with a hook to the // AD fparser stuff libMesh::DenseSubVector<libMesh::Number> &Us = const_cast<libMesh::DenseSubVector<libMesh::Number>&> (context.get_elem_solution(_scalar_ode_var)); // U_{s} const libMesh::Number s = Us(0); Us(0) = s + this->_epsilon; libMesh::Number constraint_jacobian = (*constraint_function)(context, libMesh::Point(0), context.get_time()); Us(0) = s - this->_epsilon; constraint_jacobian -= (*constraint_function)(context, libMesh::Point(0), context.get_time()); Us(0) = s; constraint_jacobian /= (2*this->_epsilon); Kss(0,0) += constraint_jacobian * context.get_elem_solution_derivative(); } return; }
void AveragedTurbine<Mu>::nonlocal_mass_residual( bool compute_jacobian, AssemblyContext& context, CachedValues& /* cache */ ) { libMesh::DenseSubMatrix<libMesh::Number> &Kss = context.get_elem_jacobian(this->fan_speed_var(), this->fan_speed_var()); // R_{s},{s} libMesh::DenseSubVector<libMesh::Number> &Fs = context.get_elem_residual(this->fan_speed_var()); // R_{s} const libMesh::DenseSubVector<libMesh::Number> &Us = context.get_elem_solution_rate(this->fan_speed_var()); const libMesh::Number& fan_speed = Us(0); Fs(0) -= this->moment_of_inertia * fan_speed; if (compute_jacobian) { Kss(0,0) -= this->moment_of_inertia * context.get_elem_solution_rate_derivative(); } return; }
void ElasticMembranePressure<PressureType>::element_time_derivative ( bool compute_jacobian, AssemblyContext & context ) { unsigned int u_var = this->_disp_vars.u(); unsigned int v_var = this->_disp_vars.v(); unsigned int w_var = this->_disp_vars.w(); const unsigned int n_u_dofs = context.get_dof_indices(u_var).size(); const std::vector<libMesh::Real> &JxW = this->get_fe(context)->get_JxW(); const std::vector<std::vector<libMesh::Real> >& u_phi = this->get_fe(context)->get_phi(); const MultiphysicsSystem & system = context.get_multiphysics_system(); unsigned int u_dot_var = system.get_second_order_dot_var(u_var); unsigned int v_dot_var = system.get_second_order_dot_var(v_var); unsigned int w_dot_var = system.get_second_order_dot_var(w_var); libMesh::DenseSubVector<libMesh::Number> &Fu = context.get_elem_residual(u_dot_var); libMesh::DenseSubVector<libMesh::Number> &Fv = context.get_elem_residual(v_dot_var); libMesh::DenseSubVector<libMesh::Number> &Fw = context.get_elem_residual(w_dot_var); libMesh::DenseSubMatrix<libMesh::Number>& Kuv = context.get_elem_jacobian(u_dot_var,v_var); libMesh::DenseSubMatrix<libMesh::Number>& Kuw = context.get_elem_jacobian(u_dot_var,w_var); libMesh::DenseSubMatrix<libMesh::Number>& Kvu = context.get_elem_jacobian(v_dot_var,u_var); libMesh::DenseSubMatrix<libMesh::Number>& Kvw = context.get_elem_jacobian(v_dot_var,w_var); libMesh::DenseSubMatrix<libMesh::Number>& Kwu = context.get_elem_jacobian(w_dot_var,u_var); libMesh::DenseSubMatrix<libMesh::Number>& Kwv = context.get_elem_jacobian(w_dot_var,v_var); unsigned int n_qpoints = context.get_element_qrule().n_points(); // All shape function gradients are w.r.t. master element coordinates const std::vector<std::vector<libMesh::Real> >& dphi_dxi = this->get_fe(context)->get_dphidxi(); const std::vector<std::vector<libMesh::Real> >& dphi_deta = this->get_fe(context)->get_dphideta(); const libMesh::DenseSubVector<libMesh::Number>& u_coeffs = context.get_elem_solution( u_var ); const libMesh::DenseSubVector<libMesh::Number>& v_coeffs = context.get_elem_solution( v_var ); const libMesh::DenseSubVector<libMesh::Number>& w_coeffs = context.get_elem_solution( w_var ); const std::vector<libMesh::RealGradient>& dxdxi = this->get_fe(context)->get_dxyzdxi(); const std::vector<libMesh::RealGradient>& dxdeta = this->get_fe(context)->get_dxyzdeta(); for (unsigned int qp=0; qp != n_qpoints; qp++) { // sqrt(det(a_cov)), a_cov being the covariant metric tensor of undeformed body libMesh::Real sqrt_a = sqrt( dxdxi[qp]*dxdxi[qp]*dxdeta[qp]*dxdeta[qp] - dxdxi[qp]*dxdeta[qp]*dxdeta[qp]*dxdxi[qp] ); // Gradients are w.r.t. master element coordinates libMesh::Gradient grad_u, grad_v, grad_w; for( unsigned int d = 0; d < n_u_dofs; d++ ) { libMesh::RealGradient u_gradphi( dphi_dxi[d][qp], dphi_deta[d][qp] ); grad_u += u_coeffs(d)*u_gradphi; grad_v += v_coeffs(d)*u_gradphi; grad_w += w_coeffs(d)*u_gradphi; } libMesh::RealGradient dudxi( grad_u(0), grad_v(0), grad_w(0) ); libMesh::RealGradient dudeta( grad_u(1), grad_v(1), grad_w(1) ); libMesh::RealGradient A_1 = dxdxi[qp] + dudxi; libMesh::RealGradient A_2 = dxdeta[qp] + dudeta; libMesh::RealGradient A_3 = A_1.cross(A_2); // Compute pressure at this quadrature point libMesh::Real press = (*_pressure)(context,qp); // Small optimization libMesh::Real p_over_sa = press/sqrt_a; /* The formula here is actually P*\sqrt{\frac{A}{a}}*A_3, where A_3 is a unit vector But, |A_3| = \sqrt{A} so the normalizing part kills the \sqrt{A} in the numerator, so we can leave it out and *not* normalize A_3. */ libMesh::RealGradient traction = p_over_sa*A_3; for (unsigned int i=0; i != n_u_dofs; i++) { // Small optimization libMesh::Real phi_times_jac = u_phi[i][qp]*JxW[qp]; Fu(i) -= traction(0)*phi_times_jac; Fv(i) -= traction(1)*phi_times_jac; Fw(i) -= traction(2)*phi_times_jac; if( compute_jacobian ) { for (unsigned int j=0; j != n_u_dofs; j++) { libMesh::RealGradient u_gradphi( dphi_dxi[j][qp], dphi_deta[j][qp] ); const libMesh::Real dt0_dv = p_over_sa*(u_gradphi(0)*A_2(2) - A_1(2)*u_gradphi(1)); const libMesh::Real dt0_dw = p_over_sa*(A_1(1)*u_gradphi(1) - u_gradphi(0)*A_2(1)); const libMesh::Real dt1_du = p_over_sa*(A_1(2)*u_gradphi(1) - u_gradphi(0)*A_2(2)); const libMesh::Real dt1_dw = p_over_sa*(u_gradphi(0)*A_2(0) - A_1(0)*u_gradphi(1)); const libMesh::Real dt2_du = p_over_sa*(u_gradphi(0)*A_2(1) - A_1(1)*u_gradphi(1)); const libMesh::Real dt2_dv = p_over_sa*(A_1(0)*u_gradphi(1) - u_gradphi(0)*A_2(0)); Kuv(i,j) -= dt0_dv*phi_times_jac; Kuw(i,j) -= dt0_dw*phi_times_jac; Kvu(i,j) -= dt1_du*phi_times_jac; Kvw(i,j) -= dt1_dw*phi_times_jac; Kwu(i,j) -= dt2_du*phi_times_jac; Kwv(i,j) -= dt2_dv*phi_times_jac; } } } } }
void AxisymmetricBoussinesqBuoyancy::element_time_derivative( bool compute_jacobian, AssemblyContext& context, CachedValues& /*cache*/ ) { #ifdef GRINS_USE_GRVY_TIMERS this->_timer->BeginTimer("AxisymmetricBoussinesqBuoyancy::element_time_derivative"); #endif // The number of local degrees of freedom in each variable. const unsigned int n_u_dofs = context.get_dof_indices(_flow_vars.u_var()).size(); const unsigned int n_T_dofs = context.get_dof_indices(_temp_vars.T_var()).size(); // Element Jacobian * quadrature weights for interior integration. const std::vector<libMesh::Real> &JxW = context.get_element_fe(_flow_vars.u_var())->get_JxW(); // The velocity shape functions at interior quadrature points. const std::vector<std::vector<libMesh::Real> >& vel_phi = context.get_element_fe(_flow_vars.u_var())->get_phi(); // The temperature shape functions at interior quadrature points. const std::vector<std::vector<libMesh::Real> >& T_phi = context.get_element_fe(_temp_vars.T_var())->get_phi(); // Physical location of the quadrature points const std::vector<libMesh::Point>& u_qpoint = context.get_element_fe(_flow_vars.u_var())->get_xyz(); // Get residuals libMesh::DenseSubVector<libMesh::Number> &Fr = context.get_elem_residual(_flow_vars.u_var()); // R_{r} libMesh::DenseSubVector<libMesh::Number> &Fz = context.get_elem_residual(_flow_vars.v_var()); // R_{z} // Get Jacobians libMesh::DenseSubMatrix<libMesh::Number> &KrT = context.get_elem_jacobian(_flow_vars.u_var(), _temp_vars.T_var()); // R_{r},{T} libMesh::DenseSubMatrix<libMesh::Number> &KzT = context.get_elem_jacobian(_flow_vars.v_var(), _temp_vars.T_var()); // R_{z},{T} // Now we will build the element Jacobian and residual. // Constructing the residual requires the solution and its // gradient from the previous timestep. This must be // calculated at each quadrature point by summing the // solution degree-of-freedom values by the appropriate // weight functions. unsigned int n_qpoints = context.get_element_qrule().n_points(); for (unsigned int qp=0; qp != n_qpoints; qp++) { const libMesh::Number r = u_qpoint[qp](0); // Compute the solution & its gradient at the old Newton iterate. libMesh::Number T; T = context.interior_value(_temp_vars.T_var(), qp); // First, an i-loop over the velocity degrees of freedom. // We know that n_u_dofs == n_v_dofs so we can compute contributions // for both at the same time. for (unsigned int i=0; i != n_u_dofs; i++) { Fr(i) += -_rho*_beta_T*(T - _T_ref)*_g(0)*vel_phi[i][qp]*r*JxW[qp]; Fz(i) += -_rho*_beta_T*(T - _T_ref)*_g(1)*vel_phi[i][qp]*r*JxW[qp]; if (compute_jacobian && context.get_elem_solution_derivative()) { for (unsigned int j=0; j != n_T_dofs; j++) { const libMesh::Number val = -_rho*_beta_T*vel_phi[i][qp]*T_phi[j][qp]*r*JxW[qp] * context.get_elem_solution_derivative(); KrT(i,j) += val*_g(0); KzT(i,j) += val*_g(1); } // End j dof loop } // End compute_jacobian check } // End i dof loop } // End quadrature loop #ifdef GRINS_USE_GRVY_TIMERS this->_timer->EndTimer("AxisymmetricBoussinesqBuoyancy::element_time_derivative"); #endif return; }
void VelocityPenalty<Mu>::element_time_derivative( bool compute_jacobian, AssemblyContext& context, CachedValues& /* cache */ ) { #ifdef GRINS_USE_GRVY_TIMERS this->_timer->BeginTimer("VelocityPenalty::element_time_derivative"); #endif // Element Jacobian * quadrature weights for interior integration const std::vector<libMesh::Real> &JxW = context.get_element_fe(this->_flow_vars.u_var())->get_JxW(); // The shape functions at interior quadrature points. const std::vector<std::vector<libMesh::Real> >& u_phi = context.get_element_fe(this->_flow_vars.u_var())->get_phi(); const std::vector<libMesh::Point>& u_qpoint = context.get_element_fe(this->_flow_vars.u_var())->get_xyz(); // The number of local degrees of freedom in each variable const unsigned int n_u_dofs = context.get_dof_indices(this->_flow_vars.u_var()).size(); // The subvectors and submatrices we need to fill: libMesh::DenseSubMatrix<libMesh::Number> &Kuu = context.get_elem_jacobian(this->_flow_vars.u_var(), this->_flow_vars.u_var()); // R_{u},{u} libMesh::DenseSubMatrix<libMesh::Number> &Kuv = context.get_elem_jacobian(this->_flow_vars.u_var(), this->_flow_vars.v_var()); // R_{u},{v} libMesh::DenseSubMatrix<libMesh::Number> &Kvu = context.get_elem_jacobian(this->_flow_vars.v_var(), this->_flow_vars.u_var()); // R_{v},{u} libMesh::DenseSubMatrix<libMesh::Number> &Kvv = context.get_elem_jacobian(this->_flow_vars.v_var(), this->_flow_vars.v_var()); // R_{v},{v} libMesh::DenseSubMatrix<libMesh::Number>* Kwu = NULL; libMesh::DenseSubMatrix<libMesh::Number>* Kwv = NULL; libMesh::DenseSubMatrix<libMesh::Number>* Kww = NULL; libMesh::DenseSubMatrix<libMesh::Number>* Kuw = NULL; libMesh::DenseSubMatrix<libMesh::Number>* Kvw = NULL; libMesh::DenseSubVector<libMesh::Number> &Fu = context.get_elem_residual(this->_flow_vars.u_var()); // R_{u} libMesh::DenseSubVector<libMesh::Number> &Fv = context.get_elem_residual(this->_flow_vars.v_var()); // R_{v} libMesh::DenseSubVector<libMesh::Number>* Fw = NULL; if( this->_dim == 3 ) { Kuw = &context.get_elem_jacobian(this->_flow_vars.u_var(), this->_flow_vars.w_var()); // R_{u},{w} Kvw = &context.get_elem_jacobian(this->_flow_vars.v_var(), this->_flow_vars.w_var()); // R_{v},{w} Kwu = &context.get_elem_jacobian(this->_flow_vars.w_var(), this->_flow_vars.u_var()); // R_{w},{u} Kwv = &context.get_elem_jacobian(this->_flow_vars.w_var(), this->_flow_vars.v_var()); // R_{w},{v} Kww = &context.get_elem_jacobian(this->_flow_vars.w_var(), this->_flow_vars.w_var()); // R_{w},{w} Fw = &context.get_elem_residual(this->_flow_vars.w_var()); // R_{w} } unsigned int n_qpoints = context.get_element_qrule().n_points(); for (unsigned int qp=0; qp != n_qpoints; qp++) { // Compute the solution at the old Newton iterate. libMesh::Number u, v; u = context.interior_value(this->_flow_vars.u_var(), qp); v = context.interior_value(this->_flow_vars.v_var(), qp); libMesh::NumberVectorValue U(u,v); if (this->_dim == 3) U(2) = context.interior_value(this->_flow_vars.w_var(), qp); // w libMesh::NumberVectorValue F; libMesh::NumberTensorValue dFdU; libMesh::NumberTensorValue* dFdU_ptr = compute_jacobian ? &dFdU : NULL; if (!this->compute_force(u_qpoint[qp], context, U, F, dFdU_ptr)) continue; const libMesh::Real jac = JxW[qp]; for (unsigned int i=0; i != n_u_dofs; i++) { const libMesh::Number jac_i = jac * u_phi[i][qp]; Fu(i) += F(0)*jac_i; Fv(i) += F(1)*jac_i; if( this->_dim == 3 ) { (*Fw)(i) += F(2)*jac_i; } if( compute_jacobian ) { for (unsigned int j=0; j != n_u_dofs; j++) { const libMesh::Number jac_ij = context.get_elem_solution_derivative() * jac_i * u_phi[j][qp]; Kuu(i,j) += jac_ij * dFdU(0,0); Kuv(i,j) += jac_ij * dFdU(0,1); Kvu(i,j) += jac_ij * dFdU(1,0); Kvv(i,j) += jac_ij * dFdU(1,1); if( this->_dim == 3 ) { (*Kuw)(i,j) += jac_ij * dFdU(0,2); (*Kvw)(i,j) += jac_ij * dFdU(1,2); (*Kwu)(i,j) += jac_ij * dFdU(2,0); (*Kwv)(i,j) += jac_ij * dFdU(2,1); (*Kww)(i,j) += jac_ij * dFdU(2,2); } } } } } #ifdef GRINS_USE_GRVY_TIMERS this->_timer->EndTimer("VelocityPenalty::element_time_derivative"); #endif return; }
void ElasticCableRayleighDamping<StressStrainLaw>::damping_residual( bool compute_jacobian, AssemblyContext& context, CachedValues& /*cache*/) { // First, do the "mass" contribution this->mass_residual_impl(compute_jacobian, context, &libMesh::FEMContext::interior_rate, &libMesh::DiffContext::get_elem_solution_rate_derivative, _mu_factor); // Now do the stiffness contribution const unsigned int n_u_dofs = context.get_dof_indices(this->_disp_vars.u()).size(); const std::vector<libMesh::Real> &JxW = this->get_fe(context)->get_JxW(); // Residuals that we're populating libMesh::DenseSubVector<libMesh::Number> &Fu = context.get_elem_residual(this->_disp_vars.u()); libMesh::DenseSubVector<libMesh::Number> &Fv = context.get_elem_residual(this->_disp_vars.v()); libMesh::DenseSubVector<libMesh::Number> &Fw = context.get_elem_residual(this->_disp_vars.w()); //Grab the Jacobian matrix as submatrices //libMesh::DenseMatrix<libMesh::Number> &K = context.get_elem_jacobian(); libMesh::DenseSubMatrix<libMesh::Number> &Kuu = context.get_elem_jacobian(this->_disp_vars.u(),this->_disp_vars.u()); libMesh::DenseSubMatrix<libMesh::Number> &Kuv = context.get_elem_jacobian(this->_disp_vars.u(),this->_disp_vars.v()); libMesh::DenseSubMatrix<libMesh::Number> &Kuw = context.get_elem_jacobian(this->_disp_vars.u(),this->_disp_vars.w()); libMesh::DenseSubMatrix<libMesh::Number> &Kvu = context.get_elem_jacobian(this->_disp_vars.v(),this->_disp_vars.u()); libMesh::DenseSubMatrix<libMesh::Number> &Kvv = context.get_elem_jacobian(this->_disp_vars.v(),this->_disp_vars.v()); libMesh::DenseSubMatrix<libMesh::Number> &Kvw = context.get_elem_jacobian(this->_disp_vars.v(),this->_disp_vars.w()); libMesh::DenseSubMatrix<libMesh::Number> &Kwu = context.get_elem_jacobian(this->_disp_vars.w(),this->_disp_vars.u()); libMesh::DenseSubMatrix<libMesh::Number> &Kwv = context.get_elem_jacobian(this->_disp_vars.w(),this->_disp_vars.v()); libMesh::DenseSubMatrix<libMesh::Number> &Kww = context.get_elem_jacobian(this->_disp_vars.w(),this->_disp_vars.w()); unsigned int n_qpoints = context.get_element_qrule().n_points(); // All shape function gradients are w.r.t. master element coordinates const std::vector<std::vector<libMesh::Real> >& dphi_dxi = this->get_fe(context)->get_dphidxi(); const libMesh::DenseSubVector<libMesh::Number>& u_coeffs = context.get_elem_solution( this->_disp_vars.u() ); const libMesh::DenseSubVector<libMesh::Number>& v_coeffs = context.get_elem_solution( this->_disp_vars.v() ); const libMesh::DenseSubVector<libMesh::Number>& w_coeffs = context.get_elem_solution( this->_disp_vars.w() ); const libMesh::DenseSubVector<libMesh::Number>& dudt_coeffs = context.get_elem_solution_rate( this->_disp_vars.u() ); const libMesh::DenseSubVector<libMesh::Number>& dvdt_coeffs = context.get_elem_solution_rate( this->_disp_vars.v() ); const libMesh::DenseSubVector<libMesh::Number>& dwdt_coeffs = context.get_elem_solution_rate( this->_disp_vars.w() ); // Need these to build up the covariant and contravariant metric tensors const std::vector<libMesh::RealGradient>& dxdxi = this->get_fe(context)->get_dxyzdxi(); const unsigned int dim = 1; // The cable dimension is always 1 for this physics for (unsigned int qp=0; qp != n_qpoints; qp++) { // Gradients are w.r.t. master element coordinates libMesh::Gradient grad_u, grad_v, grad_w; libMesh::Gradient dgradu_dt, dgradv_dt, dgradw_dt; for( unsigned int d = 0; d < n_u_dofs; d++ ) { libMesh::RealGradient u_gradphi( dphi_dxi[d][qp] ); grad_u += u_coeffs(d)*u_gradphi; grad_v += v_coeffs(d)*u_gradphi; grad_w += w_coeffs(d)*u_gradphi; dgradu_dt += dudt_coeffs(d)*u_gradphi; dgradv_dt += dvdt_coeffs(d)*u_gradphi; dgradw_dt += dwdt_coeffs(d)*u_gradphi; } libMesh::RealGradient grad_x( dxdxi[qp](0) ); libMesh::RealGradient grad_y( dxdxi[qp](1) ); libMesh::RealGradient grad_z( dxdxi[qp](2) ); libMesh::TensorValue<libMesh::Real> a_cov, a_contra, A_cov, A_contra; libMesh::Real lambda_sq = 0; this->compute_metric_tensors( qp, *(this->get_fe(context)), context, grad_u, grad_v, grad_w, a_cov, a_contra, A_cov, A_contra, lambda_sq ); // Compute stress tensor libMesh::TensorValue<libMesh::Real> tau; ElasticityTensor C; this->_stress_strain_law.compute_stress_and_elasticity(dim,a_contra,a_cov,A_contra,A_cov,tau,C); libMesh::Real jac = JxW[qp]; for (unsigned int i=0; i != n_u_dofs; i++) { libMesh::RealGradient u_gradphi( dphi_dxi[i][qp] ); libMesh::Real u_diag_factor = _lambda_factor*this->_A*jac*tau(0,0)*dgradu_dt(0)*u_gradphi(0); libMesh::Real v_diag_factor = _lambda_factor*this->_A*jac*tau(0,0)*dgradv_dt(0)*u_gradphi(0); libMesh::Real w_diag_factor = _lambda_factor*this->_A*jac*tau(0,0)*dgradw_dt(0)*u_gradphi(0); const libMesh::Real C1 = _lambda_factor*this->_A*jac*C(0,0,0,0)*u_gradphi(0); const libMesh::Real gamma_u = (grad_x(0)+grad_u(0)); const libMesh::Real gamma_v = (grad_y(0)+grad_v(0)); const libMesh::Real gamma_w = (grad_z(0)+grad_w(0)); const libMesh::Real x_term = C1*gamma_u; const libMesh::Real y_term = C1*gamma_v; const libMesh::Real z_term = C1*gamma_w; const libMesh::Real dt_term = dgradu_dt(0)*gamma_u + dgradv_dt(0)*gamma_v + dgradw_dt(0)*gamma_w; Fu(i) += u_diag_factor + x_term*dt_term; Fv(i) += v_diag_factor + y_term*dt_term; Fw(i) += w_diag_factor + z_term*dt_term; } if( compute_jacobian ) { for(unsigned int i=0; i != n_u_dofs; i++) { libMesh::RealGradient u_gradphi_I( dphi_dxi[i][qp] ); for(unsigned int j=0; j != n_u_dofs; j++) { libMesh::RealGradient u_gradphi_J( dphi_dxi[j][qp] ); libMesh::Real common_factor = _lambda_factor*this->_A*jac*u_gradphi_I(0); const libMesh::Real diag_term_1 = common_factor*tau(0,0)*u_gradphi_J(0)*context.get_elem_solution_rate_derivative(); const libMesh::Real dgamma_du = ( u_gradphi_J(0)*(grad_x(0)+grad_u(0)) ); const libMesh::Real dgamma_dv = ( u_gradphi_J(0)*(grad_y(0)+grad_v(0)) ); const libMesh::Real dgamma_dw = ( u_gradphi_J(0)*(grad_z(0)+grad_w(0)) ); const libMesh::Real diag_term_2_factor = common_factor*C(0,0,0,0)*context.get_elem_solution_derivative(); Kuu(i,j) += diag_term_1 + dgradu_dt(0)*diag_term_2_factor*dgamma_du; Kuv(i,j) += dgradu_dt(0)*diag_term_2_factor*dgamma_dv; Kuw(i,j) += dgradu_dt(0)*diag_term_2_factor*dgamma_dw; Kvu(i,j) += dgradv_dt(0)*diag_term_2_factor*dgamma_du; Kvv(i,j) += diag_term_1 + dgradv_dt(0)*diag_term_2_factor*dgamma_dv; Kvw(i,j) += dgradv_dt(0)*diag_term_2_factor*dgamma_dw; Kwu(i,j) += dgradw_dt(0)*diag_term_2_factor*dgamma_du; Kwv(i,j) += dgradw_dt(0)*diag_term_2_factor*dgamma_dv; Kww(i,j) += diag_term_1 + dgradw_dt(0)*diag_term_2_factor*dgamma_dw; const libMesh::Real C1 = common_factor*C(0,0,0,0); const libMesh::Real gamma_u = (grad_x(0)+grad_u(0)); const libMesh::Real gamma_v = (grad_y(0)+grad_v(0)); const libMesh::Real gamma_w = (grad_z(0)+grad_w(0)); const libMesh::Real x_term = C1*gamma_u; const libMesh::Real y_term = C1*gamma_v; const libMesh::Real z_term = C1*gamma_w; const libMesh::Real ddtterm_du = u_gradphi_J(0)*(gamma_u*context.get_elem_solution_rate_derivative() + dgradu_dt(0)*context.get_elem_solution_derivative()); const libMesh::Real ddtterm_dv = u_gradphi_J(0)*(gamma_v*context.get_elem_solution_rate_derivative() + dgradv_dt(0)*context.get_elem_solution_derivative()); const libMesh::Real ddtterm_dw = u_gradphi_J(0)*(gamma_w*context.get_elem_solution_rate_derivative() + dgradw_dt(0)*context.get_elem_solution_derivative()); Kuu(i,j) += x_term*ddtterm_du; Kuv(i,j) += x_term*ddtterm_dv; Kuw(i,j) += x_term*ddtterm_dw; Kvu(i,j) += y_term*ddtterm_du; Kvv(i,j) += y_term*ddtterm_dv; Kvw(i,j) += y_term*ddtterm_dw; Kwu(i,j) += z_term*ddtterm_du; Kwv(i,j) += z_term*ddtterm_dv; Kww(i,j) += z_term*ddtterm_dw; const libMesh::Real dt_term = dgradu_dt(0)*gamma_u + dgradv_dt(0)*gamma_v + dgradw_dt(0)*gamma_w; // Here, we're missing derivatives of C(0,0,0,0) w.r.t. strain // Nonzero for hyperelasticity models const libMesh::Real dxterm_du = C1*u_gradphi_J(0)*context.get_elem_solution_derivative(); const libMesh::Real dyterm_dv = dxterm_du; const libMesh::Real dzterm_dw = dxterm_du; Kuu(i,j) += dxterm_du*dt_term; Kvv(i,j) += dyterm_dv*dt_term; Kww(i,j) += dzterm_dw*dt_term; } // end j-loop } // end i-loop } // end if(compute_jacobian) } // end qp loop }
void HeatTransfer::mass_residual( bool compute_jacobian, AssemblyContext& context, CachedValues& /*cache*/ ) { #ifdef GRINS_USE_GRVY_TIMERS this->_timer->BeginTimer("HeatTransfer::mass_residual"); #endif // First we get some references to cell-specific data that // will be used to assemble the linear system. // Element Jacobian * quadrature weights for interior integration const std::vector<libMesh::Real> &JxW = context.get_element_fe(_temp_vars.T_var())->get_JxW(); // The shape functions at interior quadrature points. const std::vector<std::vector<libMesh::Real> >& phi = context.get_element_fe(_temp_vars.T_var())->get_phi(); const std::vector<libMesh::Point>& u_qpoint = context.get_element_fe(this->_flow_vars.u_var())->get_xyz(); // The number of local degrees of freedom in each variable const unsigned int n_T_dofs = context.get_dof_indices(_temp_vars.T_var()).size(); // The subvectors and submatrices we need to fill: libMesh::DenseSubVector<libMesh::Real> &F = context.get_elem_residual(_temp_vars.T_var()); libMesh::DenseSubMatrix<libMesh::Real> &M = context.get_elem_jacobian(_temp_vars.T_var(), _temp_vars.T_var()); unsigned int n_qpoints = context.get_element_qrule().n_points(); for (unsigned int qp = 0; qp != n_qpoints; ++qp) { // For the mass residual, we need to be a little careful. // The time integrator is handling the time-discretization // for us so we need to supply M(u_fixed)*u for the residual. // u_fixed will be given by the fixed_interior_* functions // while u will be given by the interior_* functions. libMesh::Real T_dot = context.interior_value(_temp_vars.T_var(), qp); const libMesh::Number r = u_qpoint[qp](0); libMesh::Real jac = JxW[qp]; if( _is_axisymmetric ) { jac *= r; } for (unsigned int i = 0; i != n_T_dofs; ++i) { F(i) += _rho*_Cp*T_dot*phi[i][qp]*jac; if( compute_jacobian ) { for (unsigned int j=0; j != n_T_dofs; j++) { // We're assuming rho, cp are constant w.r.t. T here. M(i,j) += _rho*_Cp*phi[j][qp]*phi[i][qp]*jac; } }// End of check on Jacobian } // End of element dof loop } // End of the quadrature point loop #ifdef GRINS_USE_GRVY_TIMERS this->_timer->EndTimer("HeatTransfer::mass_residual"); #endif return; }
void PracticeCDRinv::element_time_derivative( bool compute_jacobian, AssemblyContext& context, CachedValues& /*cache*/ ){ // The number of local degrees of freedom in each variable. const unsigned int n_c_dofs = context.get_dof_indices(_c_var).size(); // We get some references to cell-specific data that // will be used to assemble the linear system. // Element Jacobian * quadrature weights for interior integration. const std::vector<libMesh::Real> &JxW = context.get_element_fe(_c_var)->get_JxW(); // The temperature shape function gradients (in global coords.) // at interior quadrature points. const std::vector<std::vector<libMesh::RealGradient> >& dphi = context.get_element_fe(_c_var)->get_dphi(); const std::vector<std::vector<libMesh::Real> >& phi = context.get_element_fe(_c_var)->get_phi(); const std::vector<libMesh::Point>& q_points = context.get_element_fe(_c_var)->get_xyz(); libMesh::DenseSubMatrix<libMesh::Number> &J_c_zc = context.get_elem_jacobian(_c_var, _zc_var); libMesh::DenseSubMatrix<libMesh::Number> &J_c_c = context.get_elem_jacobian(_c_var, _c_var); libMesh::DenseSubMatrix<libMesh::Number> &J_zc_c = context.get_elem_jacobian(_zc_var, _c_var); libMesh::DenseSubMatrix<libMesh::Number> &J_zc_fc = context.get_elem_jacobian(_zc_var, _fc_var); libMesh::DenseSubMatrix<libMesh::Number> &J_fc_zc = context.get_elem_jacobian(_fc_var, _zc_var); libMesh::DenseSubMatrix<libMesh::Number> &J_fc_fc = context.get_elem_jacobian(_fc_var, _fc_var); libMesh::DenseSubVector<libMesh::Number> &Rc = context.get_elem_residual( _c_var );; libMesh::DenseSubVector<libMesh::Number> &Rzc = context.get_elem_residual( _zc_var ); libMesh::DenseSubVector<libMesh::Number> &Rfc = context.get_elem_residual( _fc_var ); // Now we will build the element Jacobian and residual. // Constructing the residual requires the solution and its // gradient from the previous timestep. This must be // calculated at each quadrature point by summing the // solution degree-of-freedom values by the appropriate // weight functions. unsigned int n_qpoints = context.get_element_qrule().n_points(); for (unsigned int qp=0; qp != n_qpoints; qp++){ libMesh::Number c = context.interior_value(_c_var, qp), zc = context.interior_value(_zc_var, qp), fc = context.interior_value(_fc_var, qp); libMesh::Gradient grad_c = context.interior_gradient(_c_var, qp), grad_zc = context.interior_gradient(_zc_var, qp), grad_fc = context.interior_gradient(_fc_var, qp); //location of quadrature point const libMesh::Real ptx = q_points[qp](0); const libMesh::Real pty = q_points[qp](1); int xind, yind; libMesh::Real xdist = 1.e10; libMesh::Real ydist = 1.e10; for(int ii=0; ii<x_pts.size(); ii++){ libMesh::Real tmp = std::abs(ptx - x_pts[ii]); if(xdist > tmp){ xdist = tmp; xind = ii; } else break; } for(int jj=0; jj<y_pts[xind].size(); jj++){ libMesh::Real tmp = std::abs(pty - y_pts[xind][jj]); if(ydist > tmp){ ydist = tmp; yind = jj; } else break; } libMesh::Real u = vel_field[xind][yind](0); libMesh::Real v = vel_field[xind][yind](1); libMesh::NumberVectorValue U (u, v); // First, an i-loop over the degrees of freedom. for (unsigned int i=0; i != n_c_dofs; i++){ Rc(i) += JxW[qp]*(-_k*grad_zc*dphi[i][qp] + U*grad_zc*phi[i][qp] + 2*_R*zc*c*phi[i][qp]); Rzc(i) += JxW[qp]*(-_k*grad_c*dphi[i][qp] - U*grad_c*phi[i][qp] + _R*c*c*phi[i][qp] + fc*phi[i][qp]); Rfc(i) += JxW[qp]*(_beta*grad_fc*dphi[i][qp] + zc*phi[i][qp]); if (compute_jacobian){ for (unsigned int j=0; j != n_c_dofs; j++){ J_c_zc(i,j) += JxW[qp]*(-_k*dphi[j][qp]*dphi[i][qp] + U*dphi[j][qp]*phi[i][qp] + 2*_R*phi[j][qp]*c*phi[i][qp]); J_c_c(i,j) += JxW[qp]*(2*_R*zc*phi[j][qp]*phi[i][qp]); J_zc_c(i,j) += JxW[qp]*(-_k*dphi[j][qp]*dphi[i][qp] - U*dphi[j][qp]*phi[i][qp] + 2*_R*c*phi[j][qp]*phi[i][qp]); J_zc_fc(i,j) += JxW[qp]*(phi[j][qp]*phi[i][qp]); J_fc_zc(i,j) += JxW[qp]*(phi[j][qp]*phi[i][qp]); J_fc_fc(i,j) += JxW[qp]*(_beta*dphi[j][qp]*dphi[i][qp]); } // end of the inner dof (j) loop } // end - if (compute_jacobian && context.get_elem_solution_derivative()) } // end of the outer dof (i) loop } // end of the quadrature point (qp) loop for(unsigned int dnum=0; dnum<datavals.size(); dnum++){ libMesh::Point data_point = datapts[dnum]; if(context.get_elem().contains_point(data_point)){ libMesh::Number cpred = context.point_value(_c_var, data_point); libMesh::Number cstar = datavals[dnum]; unsigned int dim = context.get_system().get_mesh().mesh_dimension(); libMesh::FEType fe_type = context.get_element_fe(_c_var)->get_fe_type(); //go between physical and reference element libMesh::Point c_master = libMesh::FEInterface::inverse_map(dim, fe_type, &context.get_elem(), data_point); std::vector<libMesh::Real> point_phi(n_c_dofs); for (unsigned int i=0; i != n_c_dofs; i++){ //get value of basis function at mapped point in reference (master) element point_phi[i] = libMesh::FEInterface::shape(dim, fe_type, &context.get_elem(), i, c_master); } for (unsigned int i=0; i != n_c_dofs; i++){ Rc(i) += (cpred - cstar)*point_phi[i]; if (compute_jacobian){ for (unsigned int j=0; j != n_c_dofs; j++) J_c_c(i,j) += point_phi[j]*point_phi[i] ; } } } } return; }
void VelocityPenaltyAdjointStabilization<Mu>::element_constraint( bool compute_jacobian, AssemblyContext& context, CachedValues& /*cache*/ ) { #ifdef GRINS_USE_GRVY_TIMERS this->_timer->BeginTimer("VelocityPenaltyAdjointStabilization::element_constraint"); #endif // The number of local degrees of freedom in each variable. const unsigned int n_p_dofs = context.get_dof_indices(this->_press_var.p()).size(); const unsigned int n_u_dofs = context.get_dof_indices(this->_flow_vars.u()).size(); // Element Jacobian * quadrature weights for interior integration. const std::vector<libMesh::Real> &JxW = context.get_element_fe(this->_flow_vars.u())->get_JxW(); const std::vector<libMesh::Point>& u_qpoint = context.get_element_fe(this->_flow_vars.u())->get_xyz(); const std::vector<std::vector<libMesh::Real> >& u_phi = context.get_element_fe(this->_flow_vars.u())->get_phi(); const std::vector<std::vector<libMesh::RealGradient> >& p_dphi = context.get_element_fe(this->_press_var.p())->get_dphi(); libMesh::DenseSubVector<libMesh::Number> &Fp = context.get_elem_residual(this->_press_var.p()); // R_{p} libMesh::DenseSubMatrix<libMesh::Number> &Kpu = context.get_elem_jacobian(this->_press_var.p(), this->_flow_vars.u()); // J_{pu} libMesh::DenseSubMatrix<libMesh::Number> &Kpv = context.get_elem_jacobian(this->_press_var.p(), this->_flow_vars.v()); // J_{pv} libMesh::DenseSubMatrix<libMesh::Number> *Kpw = NULL; if(this->mesh_dim(context) == 3) { Kpw = &context.get_elem_jacobian (this->_press_var.p(), this->_flow_vars.w()); // J_{pw} } // Now we will build the element Jacobian and residual. // Constructing the residual requires the solution and its // gradient from the previous timestep. This must be // calculated at each quadrature point by summing the // solution degree-of-freedom values by the appropriate // weight functions. unsigned int n_qpoints = context.get_element_qrule().n_points(); libMesh::FEBase* fe = context.get_element_fe(this->_flow_vars.u()); for (unsigned int qp=0; qp != n_qpoints; qp++) { libMesh::RealGradient g = this->_stab_helper.compute_g( fe, context, qp ); libMesh::RealTensor G = this->_stab_helper.compute_G( fe, context, qp ); libMesh::RealGradient U( context.interior_value( this->_flow_vars.u(), qp ), context.interior_value( this->_flow_vars.v(), qp ) ); if( this->mesh_dim(context) == 3 ) { U(2) = context.interior_value( this->_flow_vars.w(), qp ); } // Compute the viscosity at this qp libMesh::Real mu_qp = this->_mu(context, qp); libMesh::Real tau_M; libMesh::Real d_tau_M_d_rho; libMesh::Gradient d_tau_M_dU; if (compute_jacobian) this->_stab_helper.compute_tau_momentum_and_derivs ( context, qp, g, G, this->_rho, U, mu_qp, tau_M, d_tau_M_d_rho, d_tau_M_dU, this->_is_steady ); else tau_M = this->_stab_helper.compute_tau_momentum ( context, qp, g, G, this->_rho, U, mu_qp, this->_is_steady ); libMesh::NumberVectorValue F; libMesh::NumberTensorValue dFdU; libMesh::NumberTensorValue* dFdU_ptr = compute_jacobian ? &dFdU : NULL; if (!this->compute_force(u_qpoint[qp], context, U, F, dFdU_ptr)) continue; // First, an i-loop over the velocity degrees of freedom. // We know that n_u_dofs == n_v_dofs so we can compute contributions // for both at the same time. for (unsigned int i=0; i != n_p_dofs; i++) { Fp(i) += -tau_M*F*p_dphi[i][qp]*JxW[qp]; if (compute_jacobian) { for (unsigned int j=0; j != n_u_dofs; ++j) { Kpu(i,j) += -d_tau_M_dU(0)*u_phi[j][qp]*F*p_dphi[i][qp]*JxW[qp]*context.get_elem_solution_derivative(); Kpv(i,j) += -d_tau_M_dU(1)*u_phi[j][qp]*F*p_dphi[i][qp]*JxW[qp]*context.get_elem_solution_derivative(); for (unsigned int d=0; d != 3; ++d) { Kpu(i,j) += -tau_M*dFdU(d,0)*u_phi[j][qp]*p_dphi[i][qp](d)*JxW[qp]*context.get_elem_solution_derivative(); Kpv(i,j) += -tau_M*dFdU(d,1)*u_phi[j][qp]*p_dphi[i][qp](d)*JxW[qp]*context.get_elem_solution_derivative(); } } if( this->mesh_dim(context) == 3 ) for (unsigned int j=0; j != n_u_dofs; ++j) { (*Kpw)(i,j) += -d_tau_M_dU(2)*u_phi[j][qp]*F*p_dphi[i][qp]*JxW[qp]*context.get_elem_solution_derivative(); for (unsigned int d=0; d != 3; ++d) { (*Kpw)(i,j) += -tau_M*dFdU(d,2)*u_phi[j][qp]*p_dphi[i][qp](d)*JxW[qp]*context.get_elem_solution_derivative(); } } } } } // End quadrature loop #ifdef GRINS_USE_GRVY_TIMERS this->_timer->EndTimer("VelocityPenaltyAdjointStabilization::element_constraint"); #endif return; }
void ElasticMembraneConstantPressure::element_time_derivative( bool compute_jacobian, AssemblyContext& context, CachedValues& /*cache*/ ) { const unsigned int n_u_dofs = context.get_dof_indices(_disp_vars.u()).size(); const std::vector<libMesh::Real> &JxW = this->get_fe(context)->get_JxW(); const std::vector<std::vector<libMesh::Real> >& u_phi = this->get_fe(context)->get_phi(); libMesh::DenseSubVector<libMesh::Number> &Fu = context.get_elem_residual(_disp_vars.u()); libMesh::DenseSubVector<libMesh::Number> &Fv = context.get_elem_residual(_disp_vars.v()); libMesh::DenseSubVector<libMesh::Number> &Fw = context.get_elem_residual(_disp_vars.w()); libMesh::DenseSubMatrix<libMesh::Number>& Kuv = context.get_elem_jacobian(_disp_vars.u(),_disp_vars.v()); libMesh::DenseSubMatrix<libMesh::Number>& Kuw = context.get_elem_jacobian(_disp_vars.u(),_disp_vars.w()); libMesh::DenseSubMatrix<libMesh::Number>& Kvu = context.get_elem_jacobian(_disp_vars.v(),_disp_vars.u()); libMesh::DenseSubMatrix<libMesh::Number>& Kvw = context.get_elem_jacobian(_disp_vars.v(),_disp_vars.w()); libMesh::DenseSubMatrix<libMesh::Number>& Kwu = context.get_elem_jacobian(_disp_vars.w(),_disp_vars.u()); libMesh::DenseSubMatrix<libMesh::Number>& Kwv = context.get_elem_jacobian(_disp_vars.w(),_disp_vars.v()); unsigned int n_qpoints = context.get_element_qrule().n_points(); // All shape function gradients are w.r.t. master element coordinates const std::vector<std::vector<libMesh::Real> >& dphi_dxi = this->get_fe(context)->get_dphidxi(); const std::vector<std::vector<libMesh::Real> >& dphi_deta = this->get_fe(context)->get_dphideta(); const libMesh::DenseSubVector<libMesh::Number>& u_coeffs = context.get_elem_solution( _disp_vars.u() ); const libMesh::DenseSubVector<libMesh::Number>& v_coeffs = context.get_elem_solution( _disp_vars.v() ); const libMesh::DenseSubVector<libMesh::Number>& w_coeffs = context.get_elem_solution( _disp_vars.w() ); const std::vector<libMesh::RealGradient>& dxdxi = this->get_fe(context)->get_dxyzdxi(); const std::vector<libMesh::RealGradient>& dxdeta = this->get_fe(context)->get_dxyzdeta(); for (unsigned int qp=0; qp != n_qpoints; qp++) { // sqrt(det(a_cov)), a_cov being the covariant metric tensor of undeformed body libMesh::Real sqrt_a = sqrt( dxdxi[qp]*dxdxi[qp]*dxdeta[qp]*dxdeta[qp] - dxdxi[qp]*dxdeta[qp]*dxdeta[qp]*dxdxi[qp] ); // Gradients are w.r.t. master element coordinates libMesh::Gradient grad_u, grad_v, grad_w; for( unsigned int d = 0; d < n_u_dofs; d++ ) { libMesh::RealGradient u_gradphi( dphi_dxi[d][qp], dphi_deta[d][qp] ); grad_u += u_coeffs(d)*u_gradphi; grad_v += v_coeffs(d)*u_gradphi; grad_w += w_coeffs(d)*u_gradphi; } libMesh::RealGradient dudxi( grad_u(0), grad_v(0), grad_w(0) ); libMesh::RealGradient dudeta( grad_u(1), grad_v(1), grad_w(1) ); libMesh::RealGradient A_1 = dxdxi[qp] + dudxi; libMesh::RealGradient A_2 = dxdeta[qp] + dudeta; libMesh::RealGradient A_3 = A_1.cross(A_2); /* The formula here is actually P*\sqrt{\frac{A}{a}}*A_3, where A_3 is a unit vector But, |A_3| = \sqrt{A} so the normalizing part kills the \sqrt{A} in the numerator, so we can leave it out and *not* normalize A_3. */ libMesh::RealGradient traction = _pressure/sqrt_a*A_3; libMesh::Real jac = JxW[qp]; for (unsigned int i=0; i != n_u_dofs; i++) { Fu(i) -= traction(0)*u_phi[i][qp]*jac; Fv(i) -= traction(1)*u_phi[i][qp]*jac; Fw(i) -= traction(2)*u_phi[i][qp]*jac; if( compute_jacobian ) { for (unsigned int j=0; j != n_u_dofs; j++) { libMesh::RealGradient u_gradphi( dphi_dxi[j][qp], dphi_deta[j][qp] ); const libMesh::Real dt0_dv = _pressure/sqrt_a*(u_gradphi(0)*A_2(2) - A_1(2)*u_gradphi(1)); const libMesh::Real dt0_dw = _pressure/sqrt_a*(A_1(1)*u_gradphi(1) - u_gradphi(0)*A_2(1)); const libMesh::Real dt1_du = _pressure/sqrt_a*(A_1(2)*u_gradphi(1) - u_gradphi(0)*A_2(2)); const libMesh::Real dt1_dw = _pressure/sqrt_a*(u_gradphi(0)*A_2(0) - A_1(0)*u_gradphi(1)); const libMesh::Real dt2_du = _pressure/sqrt_a*(u_gradphi(0)*A_2(1) - A_1(1)*u_gradphi(1)); const libMesh::Real dt2_dv = _pressure/sqrt_a*(A_1(0)*u_gradphi(1) - u_gradphi(0)*A_2(0)); Kuv(i,j) -= dt0_dv*u_phi[i][qp]*jac; Kuw(i,j) -= dt0_dw*u_phi[i][qp]*jac; Kvu(i,j) -= dt1_du*u_phi[i][qp]*jac; Kvw(i,j) -= dt1_dw*u_phi[i][qp]*jac; Kwu(i,j) -= dt2_du*u_phi[i][qp]*jac; Kwv(i,j) -= dt2_dv*u_phi[i][qp]*jac; } } } } return; }
void BoundaryConditions::apply_neumann_axisymmetric( AssemblyContext& context, const CachedValues& cache, const bool request_jacobian, const VariableIndex var, const libMesh::Real sign, SharedPtr<NeumannFuncObj> neumann_func ) const { libMesh::FEGenericBase<libMesh::Real>* side_fe = NULL; context.get_side_fe( var, side_fe ); // The number of local degrees of freedom const unsigned int n_var_dofs = context.get_dof_indices(var).size(); // Element Jacobian * quadrature weight for side integration. const std::vector<libMesh::Real> &JxW_side = side_fe->get_JxW(); // The var shape functions at side quadrature points. const std::vector<std::vector<libMesh::Real> >& var_phi_side = side_fe->get_phi(); // Physical location of the quadrature points const std::vector<libMesh::Point>& var_qpoint = side_fe->get_xyz(); const std::vector<libMesh::Point> &normals = side_fe->get_normals(); libMesh::DenseSubVector<libMesh::Number> &F_var = context.get_elem_residual(var); // residual libMesh::DenseSubMatrix<libMesh::Number> &K_var = context.get_elem_jacobian(var,var); // jacobian unsigned int n_qpoints = context.get_side_qrule().n_points(); for (unsigned int qp=0; qp != n_qpoints; qp++) { const libMesh::Point bc_value = neumann_func->value( context, cache, qp ); libMesh::Point jac_value; if (request_jacobian) { jac_value = neumann_func->derivative( context, cache, qp ); } const libMesh::Number r = var_qpoint[qp](0); for (unsigned int i=0; i != n_var_dofs; i++) { F_var(i) += sign*r*JxW_side[qp]*bc_value*normals[qp]*var_phi_side[i][qp]; if (request_jacobian) { for (unsigned int j=0; j != n_var_dofs; j++) { K_var(i,j) += sign*r*JxW_side[qp]*jac_value*normals[qp]* var_phi_side[i][qp]*var_phi_side[j][qp]; } } } } // End quadrature loop // Now must take care of the case that the boundary condition depends on variables // other than var. std::vector<VariableIndex> other_jac_vars = neumann_func->get_other_jac_vars(); if( (other_jac_vars.size() > 0) && request_jacobian ) { for( std::vector<VariableIndex>::const_iterator var2 = other_jac_vars.begin(); var2 != other_jac_vars.end(); var2++ ) { libMesh::FEGenericBase<libMesh::Real>* side_fe2 = NULL; context.get_side_fe( *var2, side_fe2 ); libMesh::DenseSubMatrix<libMesh::Number> &K_var2 = context.get_elem_jacobian(var,*var2); // jacobian const unsigned int n_var2_dofs = context.get_dof_indices(*var2).size(); const std::vector<std::vector<libMesh::Real> >& var2_phi_side = side_fe2->get_phi(); for (unsigned int qp=0; qp != n_qpoints; qp++) { const libMesh::Number r = var_qpoint[qp](0); const libMesh::Point jac_value = neumann_func->derivative( context, cache, qp, *var2 ); for (unsigned int i=0; i != n_var_dofs; i++) { for (unsigned int j=0; j != n_var2_dofs; j++) { K_var2(i,j) += sign*r*JxW_side[qp]*jac_value*normals[qp]* var_phi_side[i][qp]*var2_phi_side[j][qp]; } } } } // End loop over auxillary Jacobian variables } return; }
void AxisymmetricHeatTransfer<Conductivity>::element_time_derivative( bool compute_jacobian, AssemblyContext& context, CachedValues& /*cache*/ ) { #ifdef GRINS_USE_GRVY_TIMERS this->_timer->BeginTimer("AxisymmetricHeatTransfer::element_time_derivative"); #endif // The number of local degrees of freedom in each variable. const unsigned int n_T_dofs = context.get_dof_indices(_T_var).size(); const unsigned int n_u_dofs = context.get_dof_indices(_u_r_var).size(); //TODO: check n_T_dofs is same as n_u_dofs, n_v_dofs, n_w_dofs // We get some references to cell-specific data that // will be used to assemble the linear system. // Element Jacobian * quadrature weights for interior integration. const std::vector<libMesh::Real> &JxW = context.get_element_fe(_T_var)->get_JxW(); // The temperature shape functions at interior quadrature points. const std::vector<std::vector<libMesh::Real> >& T_phi = context.get_element_fe(_T_var)->get_phi(); // The velocity shape functions at interior quadrature points. const std::vector<std::vector<libMesh::Real> >& vel_phi = context.get_element_fe(_u_r_var)->get_phi(); // The temperature shape function gradients (in global coords.) // at interior quadrature points. const std::vector<std::vector<libMesh::RealGradient> >& T_gradphi = context.get_element_fe(_T_var)->get_dphi(); // Physical location of the quadrature points const std::vector<libMesh::Point>& u_qpoint = context.get_element_fe(_u_r_var)->get_xyz(); // The subvectors and submatrices we need to fill: libMesh::DenseSubVector<libMesh::Number> &FT = context.get_elem_residual(_T_var); // R_{T} libMesh::DenseSubMatrix<libMesh::Number> &KTT = context.get_elem_jacobian(_T_var, _T_var); // R_{T},{T} libMesh::DenseSubMatrix<libMesh::Number> &KTr = context.get_elem_jacobian(_T_var, _u_r_var); // R_{T},{r} libMesh::DenseSubMatrix<libMesh::Number> &KTz = context.get_elem_jacobian(_T_var, _u_z_var); // R_{T},{z} // Now we will build the element Jacobian and residual. // Constructing the residual requires the solution and its // gradient from the previous timestep. This must be // calculated at each quadrature point by summing the // solution degree-of-freedom values by the appropriate // weight functions. unsigned int n_qpoints = context.get_element_qrule().n_points(); for (unsigned int qp=0; qp != n_qpoints; qp++) { const libMesh::Number r = u_qpoint[qp](0); // Compute the solution & its gradient at the old Newton iterate. libMesh::Number u_r, u_z; u_r = context.interior_value(_u_r_var, qp); u_z = context.interior_value(_u_z_var, qp); libMesh::Gradient grad_T; grad_T = context.interior_gradient(_T_var, qp); libMesh::NumberVectorValue U (u_r,u_z); libMesh::Number k = this->_k( context, qp ); // FIXME - once we have T-dependent k, we'll need its // derivatives in Jacobians // libMesh::Number dk_dT = this->_k.deriv( T ); // First, an i-loop over the degrees of freedom. for (unsigned int i=0; i != n_T_dofs; i++) { FT(i) += JxW[qp]*r* (-_rho*_Cp*T_phi[i][qp]*(U*grad_T) // convection term -k*(T_gradphi[i][qp]*grad_T) ); // diffusion term if (compute_jacobian) { libmesh_assert (context.get_elem_solution_derivative() == 1.0); for (unsigned int j=0; j != n_T_dofs; j++) { // TODO: precompute some terms like: // _rho*_Cp*T_phi[i][qp]*(vel_phi[j][qp]*T_grad_phi[j][qp]) KTT(i,j) += JxW[qp] * context.get_elem_solution_derivative() *r* (-_rho*_Cp*T_phi[i][qp]*(U*T_gradphi[j][qp]) // convection term -k*(T_gradphi[i][qp]*T_gradphi[j][qp])); // diffusion term } // end of the inner dof (j) loop #if 0 if( dk_dT != 0.0 ) { for (unsigned int j=0; j != n_T_dofs; j++) { // TODO: precompute some terms like: KTT(i,j) -= JxW[qp] * context.get_elem_solution_derivative() *r*( dk_dT*T_phi[j][qp]*T_gradphi[i][qp]*grad_T ); } } #endif // Matrix contributions for the Tu, Tv and Tw couplings (n_T_dofs same as n_u_dofs, n_v_dofs and n_w_dofs) for (unsigned int j=0; j != n_u_dofs; j++) { KTr(i,j) += JxW[qp] * context.get_elem_solution_derivative() *r*(-_rho*_Cp*T_phi[i][qp]*(vel_phi[j][qp]*grad_T(0))); KTz(i,j) += JxW[qp] * context.get_elem_solution_derivative() *r*(-_rho*_Cp*T_phi[i][qp]*(vel_phi[j][qp]*grad_T(1))); } // end of the inner dof (j) loop } // end - if (compute_jacobian && context.get_elem_solution_derivative()) } // end of the outer dof (i) loop } // end of the quadrature point (qp) loop #ifdef GRINS_USE_GRVY_TIMERS this->_timer->EndTimer("AxisymmetricHeatTransfer::element_time_derivative"); #endif return; }
void HeatTransfer::element_time_derivative( bool compute_jacobian, AssemblyContext& context, CachedValues& /*cache*/ ) { #ifdef GRINS_USE_GRVY_TIMERS this->_timer->BeginTimer("HeatTransfer::element_time_derivative"); #endif // The number of local degrees of freedom in each variable. const unsigned int n_T_dofs = context.get_dof_indices(_temp_vars.T_var()).size(); const unsigned int n_u_dofs = context.get_dof_indices(_flow_vars.u_var()).size(); //TODO: check n_T_dofs is same as n_u_dofs, n_v_dofs, n_w_dofs // We get some references to cell-specific data that // will be used to assemble the linear system. // Element Jacobian * quadrature weights for interior integration. const std::vector<libMesh::Real> &JxW = context.get_element_fe(_temp_vars.T_var())->get_JxW(); // The temperature shape functions at interior quadrature points. const std::vector<std::vector<libMesh::Real> >& T_phi = context.get_element_fe(_temp_vars.T_var())->get_phi(); // The velocity shape functions at interior quadrature points. const std::vector<std::vector<libMesh::Real> >& vel_phi = context.get_element_fe(_flow_vars.u_var())->get_phi(); // The temperature shape function gradients (in global coords.) // at interior quadrature points. const std::vector<std::vector<libMesh::RealGradient> >& T_gradphi = context.get_element_fe(_temp_vars.T_var())->get_dphi(); const std::vector<libMesh::Point>& u_qpoint = context.get_element_fe(this->_flow_vars.u_var())->get_xyz(); libMesh::DenseSubMatrix<libMesh::Number> &KTT = context.get_elem_jacobian(_temp_vars.T_var(), _temp_vars.T_var()); // R_{T},{T} libMesh::DenseSubMatrix<libMesh::Number> &KTu = context.get_elem_jacobian(_temp_vars.T_var(), _flow_vars.u_var()); // R_{T},{u} libMesh::DenseSubMatrix<libMesh::Number> &KTv = context.get_elem_jacobian(_temp_vars.T_var(), _flow_vars.v_var()); // R_{T},{v} libMesh::DenseSubMatrix<libMesh::Number>* KTw = NULL; libMesh::DenseSubVector<libMesh::Number> &FT = context.get_elem_residual(_temp_vars.T_var()); // R_{T} if( this->_dim == 3 ) { KTw = &context.get_elem_jacobian(_temp_vars.T_var(), _flow_vars.w_var()); // R_{T},{w} } // Now we will build the element Jacobian and residual. // Constructing the residual requires the solution and its // gradient from the previous timestep. This must be // calculated at each quadrature point by summing the // solution degree-of-freedom values by the appropriate // weight functions. unsigned int n_qpoints = context.get_element_qrule().n_points(); for (unsigned int qp=0; qp != n_qpoints; qp++) { // Compute the solution & its gradient at the old Newton iterate. libMesh::Number u, v; u = context.interior_value(_flow_vars.u_var(), qp); v = context.interior_value(_flow_vars.v_var(), qp); libMesh::Gradient grad_T; grad_T = context.interior_gradient(_temp_vars.T_var(), qp); libMesh::NumberVectorValue U (u,v); if (_dim == 3) U(2) = context.interior_value(_flow_vars.w_var(), qp); const libMesh::Number r = u_qpoint[qp](0); libMesh::Real jac = JxW[qp]; if( _is_axisymmetric ) { jac *= r; } // First, an i-loop over the degrees of freedom. for (unsigned int i=0; i != n_T_dofs; i++) { FT(i) += jac * (-_rho*_Cp*T_phi[i][qp]*(U*grad_T) // convection term -_k*(T_gradphi[i][qp]*grad_T) ); // diffusion term if (compute_jacobian) { for (unsigned int j=0; j != n_T_dofs; j++) { // TODO: precompute some terms like: // _rho*_Cp*T_phi[i][qp]*(vel_phi[j][qp]*T_grad_phi[j][qp]) KTT(i,j) += jac * (-_rho*_Cp*T_phi[i][qp]*(U*T_gradphi[j][qp]) // convection term -_k*(T_gradphi[i][qp]*T_gradphi[j][qp])); // diffusion term } // end of the inner dof (j) loop // Matrix contributions for the Tu, Tv and Tw couplings (n_T_dofs same as n_u_dofs, n_v_dofs and n_w_dofs) for (unsigned int j=0; j != n_u_dofs; j++) { KTu(i,j) += jac*(-_rho*_Cp*T_phi[i][qp]*(vel_phi[j][qp]*grad_T(0))); KTv(i,j) += jac*(-_rho*_Cp*T_phi[i][qp]*(vel_phi[j][qp]*grad_T(1))); if (_dim == 3) (*KTw)(i,j) += jac*(-_rho*_Cp*T_phi[i][qp]*(vel_phi[j][qp]*grad_T(2))); } // end of the inner dof (j) loop } // end - if (compute_jacobian && context.get_elem_solution_derivative()) } // end of the outer dof (i) loop } // end of the quadrature point (qp) loop #ifdef GRINS_USE_GRVY_TIMERS this->_timer->EndTimer("HeatTransfer::element_time_derivative"); #endif return; }
void BoussinesqBuoyancyAdjointStabilization<Mu>::element_constraint( bool compute_jacobian, AssemblyContext& context, CachedValues& /*cache*/ ) { #ifdef GRINS_USE_GRVY_TIMERS this->_timer->BeginTimer("BoussinesqBuoyancyAdjointStabilization::element_constraint"); #endif // The number of local degrees of freedom in each variable. const unsigned int n_p_dofs = context.get_dof_indices(_flow_vars.p_var()).size(); const unsigned int n_u_dofs = context.get_dof_indices(_flow_vars.u_var()).size(); const unsigned int n_T_dofs = context.get_dof_indices(_temp_vars.T_var()).size(); // Element Jacobian * quadrature weights for interior integration. const std::vector<libMesh::Real> &JxW = context.get_element_fe(_flow_vars.u_var())->get_JxW(); const std::vector<std::vector<libMesh::Real> >& T_phi = context.get_element_fe(this->_temp_vars.T_var())->get_phi(); const std::vector<std::vector<libMesh::Real> >& u_phi = context.get_element_fe(this->_flow_vars.u_var())->get_phi(); const std::vector<std::vector<libMesh::RealGradient> >& p_dphi = context.get_element_fe(this->_flow_vars.p_var())->get_dphi(); libMesh::DenseSubVector<libMesh::Number> &Fp = context.get_elem_residual(this->_flow_vars.p_var()); // R_{p} libMesh::DenseSubMatrix<libMesh::Number> &KpT = context.get_elem_jacobian(_flow_vars.p_var(), _temp_vars.T_var()); // J_{pT} libMesh::DenseSubMatrix<libMesh::Number> &Kpu = context.get_elem_jacobian(_flow_vars.p_var(), _flow_vars.u_var()); // J_{pu} libMesh::DenseSubMatrix<libMesh::Number> &Kpv = context.get_elem_jacobian(_flow_vars.p_var(), _flow_vars.v_var()); // J_{pv} libMesh::DenseSubMatrix<libMesh::Number> *Kpw = NULL; if(this->_dim == 3) { Kpw = &context.get_elem_jacobian (_flow_vars.p_var(), _flow_vars.w_var()); // J_{pw} } // Now we will build the element Jacobian and residual. // Constructing the residual requires the solution and its // gradient from the previous timestep. This must be // calculated at each quadrature point by summing the // solution degree-of-freedom values by the appropriate // weight functions. unsigned int n_qpoints = context.get_element_qrule().n_points(); libMesh::FEBase* fe = context.get_element_fe(this->_flow_vars.u_var()); for (unsigned int qp=0; qp != n_qpoints; qp++) { libMesh::RealGradient g = this->_stab_helper.compute_g( fe, context, qp ); libMesh::RealTensor G = this->_stab_helper.compute_G( fe, context, qp ); libMesh::RealGradient U( context.interior_value( this->_flow_vars.u_var(), qp ), context.interior_value( this->_flow_vars.v_var(), qp ) ); if( this->_dim == 3 ) { U(2) = context.interior_value( this->_flow_vars.w_var(), qp ); } // Compute the viscosity at this qp libMesh::Real mu_qp = this->_mu(context, qp); libMesh::Real tau_M; libMesh::Real d_tau_M_d_rho; libMesh::Gradient d_tau_M_dU; if (compute_jacobian) this->_stab_helper.compute_tau_momentum_and_derivs ( context, qp, g, G, this->_rho, U, mu_qp, tau_M, d_tau_M_d_rho, d_tau_M_dU, this->_is_steady ); else tau_M = this->_stab_helper.compute_tau_momentum ( context, qp, g, G, this->_rho, U, mu_qp, this->_is_steady ); // Compute the solution & its gradient at the old Newton iterate. libMesh::Number T; T = context.interior_value(_temp_vars.T_var(), qp); libMesh::RealGradient d_residual_dT = _rho_ref*_beta_T*_g; // d_residual_dU = 0 libMesh::RealGradient residual = (T-_T_ref)*d_residual_dT; // First, an i-loop over the velocity degrees of freedom. // We know that n_u_dofs == n_v_dofs so we can compute contributions // for both at the same time. for (unsigned int i=0; i != n_p_dofs; i++) { Fp(i) += tau_M*residual*p_dphi[i][qp]*JxW[qp]; if (compute_jacobian) { for (unsigned int j=0; j != n_T_dofs; ++j) { KpT(i,j) += tau_M*d_residual_dT*T_phi[j][qp]*p_dphi[i][qp]*JxW[qp] * context.get_elem_solution_derivative(); } for (unsigned int j=0; j != n_u_dofs; ++j) { Kpu(i,j) += d_tau_M_dU(0)*u_phi[j][qp]*residual*p_dphi[i][qp]*JxW[qp] * context.get_elem_solution_derivative(); Kpv(i,j) += d_tau_M_dU(1)*u_phi[j][qp]*residual*p_dphi[i][qp]*JxW[qp] * context.get_elem_solution_derivative(); } if( this->_dim == 3 ) for (unsigned int j=0; j != n_u_dofs; ++j) { (*Kpw)(i,j) += d_tau_M_dU(2)*u_phi[j][qp]*residual*p_dphi[i][qp]*JxW[qp] * context.get_elem_solution_derivative(); } } } } // End quadrature loop #ifdef GRINS_USE_GRVY_TIMERS this->_timer->EndTimer("BoussinesqBuoyancyAdjointStabilization::element_constraint"); #endif return; }
void AveragedTurbine<Mu>::element_time_derivative( bool compute_jacobian, AssemblyContext& context, CachedValues& /* cache */ ) { #ifdef GRINS_USE_GRVY_TIMERS this->_timer->BeginTimer("AveragedTurbine::element_time_derivative"); #endif // Element Jacobian * quadrature weights for interior integration const std::vector<libMesh::Real> &JxW = context.get_element_fe(this->_flow_vars.u())->get_JxW(); // The shape functions at interior quadrature points. const std::vector<std::vector<libMesh::Real> >& u_phi = context.get_element_fe(this->_flow_vars.u())->get_phi(); const std::vector<libMesh::Point>& u_qpoint = context.get_element_fe(this->_flow_vars.u())->get_xyz(); // The number of local degrees of freedom in each variable const unsigned int n_u_dofs = context.get_dof_indices(this->_flow_vars.u()).size(); // The subvectors and submatrices we need to fill: libMesh::DenseSubMatrix<libMesh::Number> &Kuu = context.get_elem_jacobian(this->_flow_vars.u(), this->_flow_vars.u()); // R_{u},{u} libMesh::DenseSubMatrix<libMesh::Number> &Kuv = context.get_elem_jacobian(this->_flow_vars.u(), this->_flow_vars.v()); // R_{u},{v} libMesh::DenseSubMatrix<libMesh::Number> &Kvu = context.get_elem_jacobian(this->_flow_vars.v(), this->_flow_vars.u()); // R_{v},{u} libMesh::DenseSubMatrix<libMesh::Number> &Kvv = context.get_elem_jacobian(this->_flow_vars.v(), this->_flow_vars.v()); // R_{v},{v} libMesh::DenseSubMatrix<libMesh::Number> &Kus = context.get_elem_jacobian(this->_flow_vars.u(), this->fan_speed_var()); // R_{u},{s} libMesh::DenseSubMatrix<libMesh::Number> &Ksu = context.get_elem_jacobian(this->fan_speed_var(), this->_flow_vars.u()); // R_{s},{u} libMesh::DenseSubMatrix<libMesh::Number> &Kvs = context.get_elem_jacobian(this->_flow_vars.v(), this->fan_speed_var()); // R_{v},{s} libMesh::DenseSubMatrix<libMesh::Number> &Ksv = context.get_elem_jacobian(this->fan_speed_var(), this->_flow_vars.v()); // R_{s},{v} libMesh::DenseSubMatrix<libMesh::Number> &Kss = context.get_elem_jacobian(this->fan_speed_var(), this->fan_speed_var()); // R_{s},{s} libMesh::DenseSubMatrix<libMesh::Number>* Kwu = NULL; libMesh::DenseSubMatrix<libMesh::Number>* Kwv = NULL; libMesh::DenseSubMatrix<libMesh::Number>* Kww = NULL; libMesh::DenseSubMatrix<libMesh::Number>* Kuw = NULL; libMesh::DenseSubMatrix<libMesh::Number>* Kvw = NULL; libMesh::DenseSubMatrix<libMesh::Number>* Ksw = NULL; libMesh::DenseSubMatrix<libMesh::Number>* Kws = NULL; libMesh::DenseSubVector<libMesh::Number> &Fu = context.get_elem_residual(this->_flow_vars.u()); // R_{u} libMesh::DenseSubVector<libMesh::Number> &Fv = context.get_elem_residual(this->_flow_vars.v()); // R_{v} libMesh::DenseSubVector<libMesh::Number>* Fw = NULL; libMesh::DenseSubVector<libMesh::Number> &Fs = context.get_elem_residual(this->fan_speed_var()); // R_{s} if( this->mesh_dim(context) == 3 ) { Kuw = &context.get_elem_jacobian(this->_flow_vars.u(), this->_flow_vars.w()); // R_{u},{w} Kvw = &context.get_elem_jacobian(this->_flow_vars.v(), this->_flow_vars.w()); // R_{v},{w} Kwu = &context.get_elem_jacobian(this->_flow_vars.w(), this->_flow_vars.u()); // R_{w},{u} Kwv = &context.get_elem_jacobian(this->_flow_vars.w(), this->_flow_vars.v()); // R_{w},{v} Kww = &context.get_elem_jacobian(this->_flow_vars.w(), this->_flow_vars.w()); // R_{w},{w} Fw = &context.get_elem_residual(this->_flow_vars.w()); // R_{w} Ksw = &context.get_elem_jacobian(this->fan_speed_var(), this->_flow_vars.w()); // R_{s},{w} Kws = &context.get_elem_jacobian(this->_flow_vars.w(), this->fan_speed_var()); // R_{w},{s} Fw = &context.get_elem_residual(this->_flow_vars.w()); // R_{w} } unsigned int n_qpoints = context.get_element_qrule().n_points(); for (unsigned int qp=0; qp != n_qpoints; qp++) { // Compute the solution at the old Newton iterate. libMesh::Number u, v, s; u = context.interior_value(this->_flow_vars.u(), qp); v = context.interior_value(this->_flow_vars.v(), qp); s = context.interior_value(this->fan_speed_var(), qp); libMesh::NumberVectorValue U(u,v); if (this->mesh_dim(context) == 3) U(2) = context.interior_value(this->_flow_vars.w(), qp); // w libMesh::NumberVectorValue U_B_1; libMesh::NumberVectorValue F; libMesh::NumberTensorValue dFdU; libMesh::NumberTensorValue* dFdU_ptr = compute_jacobian ? &dFdU : NULL; libMesh::NumberVectorValue dFds; libMesh::NumberVectorValue* dFds_ptr = compute_jacobian ? &dFds : NULL; if (!this->compute_force(u_qpoint[qp], context.time, U, s, U_B_1, F, dFdU_ptr, dFds_ptr)) continue; libMesh::Real jac = JxW[qp]; // Using this dot product to derive torque *depends* on s=1 // and U_B_1 corresponding to 1 rad/sec base velocity; this // means that the length of U_B_1 is equal to radius. // F is the force on the air, so *negative* F is the force on // the turbine. Fs(0) -= U_B_1 * F * jac; if (compute_jacobian) { Kss(0,0) -= U_B_1 * dFds * jac; for (unsigned int j=0; j != n_u_dofs; j++) { libMesh::Real jac_j = JxW[qp] * u_phi[j][qp]; for (unsigned int d=0; d != 3; ++d) { Ksu(0,j) -= jac_j * U_B_1(d) * dFdU(d,0); Ksv(0,j) -= jac_j * U_B_1(d) * dFdU(d,1); } if (this->mesh_dim(context) == 3) { for (unsigned int d=0; d != 3; ++d) (*Ksw)(0,j) -= jac_j * U_B_1(d) * dFdU(d,2); } } // End j dof loop } for (unsigned int i=0; i != n_u_dofs; i++) { const libMesh::Number jac_i = jac * u_phi[i][qp]; Fu(i) += F(0)*jac_i; Fv(i) += F(1)*jac_i; if( this->mesh_dim(context) == 3 ) (*Fw)(i) += F(2)*jac_i; if( compute_jacobian ) { Kus(i,0) += dFds(0) * jac_i; Kvs(i,0) += dFds(1) * jac_i; if( this->mesh_dim(context) == 3 ) (*Kws)(i,0) += dFds(2) * jac_i; for (unsigned int j=0; j != n_u_dofs; j++) { const libMesh::Number jac_ij = jac_i * u_phi[j][qp]; Kuu(i,j) += jac_ij * dFdU(0,0); Kuv(i,j) += jac_ij * dFdU(0,1); Kvu(i,j) += jac_ij * dFdU(1,0); Kvv(i,j) += jac_ij * dFdU(1,1); if( this->mesh_dim(context) == 3 ) { (*Kuw)(i,j) += jac_ij * dFdU(0,2); (*Kvw)(i,j) += jac_ij * dFdU(1,2); (*Kwu)(i,j) += jac_ij * dFdU(2,0); (*Kwv)(i,j) += jac_ij * dFdU(2,1); (*Kww)(i,j) += jac_ij * dFdU(2,2); } } } } } #ifdef GRINS_USE_GRVY_TIMERS this->_timer->EndTimer("AveragedTurbine::element_time_derivative"); #endif return; }
void BoussinesqBuoyancyAdjointStabilization<Mu>::element_time_derivative( bool compute_jacobian, AssemblyContext& context, CachedValues& /*cache*/ ) { #ifdef GRINS_USE_GRVY_TIMERS this->_timer->BeginTimer("BoussinesqBuoyancyAdjointStabilization::element_time_derivative"); #endif // The number of local degrees of freedom in each variable. const unsigned int n_u_dofs = context.get_dof_indices(_flow_vars.u_var()).size(); const unsigned int n_T_dofs = context.get_dof_indices(_temp_vars.T_var()).size(); // Element Jacobian * quadrature weights for interior integration. const std::vector<libMesh::Real> &JxW = context.get_element_fe(_flow_vars.u_var())->get_JxW(); const std::vector<std::vector<libMesh::Real> >& T_phi = context.get_element_fe(this->_temp_vars.T_var())->get_phi(); const std::vector<std::vector<libMesh::Real> >& u_phi = context.get_element_fe(this->_flow_vars.u_var())->get_phi(); const std::vector<std::vector<libMesh::RealGradient> >& u_gradphi = context.get_element_fe(this->_flow_vars.u_var())->get_dphi(); const std::vector<std::vector<libMesh::RealTensor> >& u_hessphi = context.get_element_fe(this->_flow_vars.u_var())->get_d2phi(); // Get residuals and jacobians libMesh::DenseSubVector<libMesh::Number> &Fu = context.get_elem_residual(_flow_vars.u_var()); // R_{u} libMesh::DenseSubVector<libMesh::Number> &Fv = context.get_elem_residual(_flow_vars.v_var()); // R_{v} libMesh::DenseSubVector<libMesh::Number> *Fw = NULL; libMesh::DenseSubMatrix<libMesh::Number> &KuT = context.get_elem_jacobian(_flow_vars.u_var(), _temp_vars.T_var()); // J_{uT} libMesh::DenseSubMatrix<libMesh::Number> &KvT = context.get_elem_jacobian(_flow_vars.v_var(), _temp_vars.T_var()); // J_{vT} libMesh::DenseSubMatrix<libMesh::Number> &Kuu = context.get_elem_jacobian(_flow_vars.u_var(), _flow_vars.u_var()); // J_{uu} libMesh::DenseSubMatrix<libMesh::Number> &Kuv = context.get_elem_jacobian(_flow_vars.u_var(), _flow_vars.v_var()); // J_{uv} libMesh::DenseSubMatrix<libMesh::Number> &Kvu = context.get_elem_jacobian(_flow_vars.v_var(), _flow_vars.u_var()); // J_{vu} libMesh::DenseSubMatrix<libMesh::Number> &Kvv = context.get_elem_jacobian(_flow_vars.v_var(), _flow_vars.v_var()); // J_{vv} libMesh::DenseSubMatrix<libMesh::Number> *KwT = NULL; libMesh::DenseSubMatrix<libMesh::Number> *Kuw = NULL; libMesh::DenseSubMatrix<libMesh::Number> *Kvw = NULL; libMesh::DenseSubMatrix<libMesh::Number> *Kwu = NULL; libMesh::DenseSubMatrix<libMesh::Number> *Kwv = NULL; libMesh::DenseSubMatrix<libMesh::Number> *Kww = NULL; if(this->_dim == 3) { Fw = &context.get_elem_residual(this->_flow_vars.w_var()); // R_{w} KwT = &context.get_elem_jacobian (_flow_vars.w_var(), _temp_vars.T_var()); // J_{wT} Kuw = &context.get_elem_jacobian (_flow_vars.u_var(), _flow_vars.w_var()); // J_{uw} Kvw = &context.get_elem_jacobian (_flow_vars.v_var(), _flow_vars.w_var()); // J_{vw} Kwu = &context.get_elem_jacobian (_flow_vars.w_var(), _flow_vars.u_var()); // J_{wu} Kwv = &context.get_elem_jacobian (_flow_vars.w_var(), _flow_vars.v_var()); // J_{wv} Kww = &context.get_elem_jacobian (_flow_vars.w_var(), _flow_vars.w_var()); // J_{ww} } // Now we will build the element Jacobian and residual. // Constructing the residual requires the solution and its // gradient from the previous timestep. This must be // calculated at each quadrature point by summing the // solution degree-of-freedom values by the appropriate // weight functions. unsigned int n_qpoints = context.get_element_qrule().n_points(); libMesh::FEBase* fe = context.get_element_fe(this->_flow_vars.u_var()); for (unsigned int qp=0; qp != n_qpoints; qp++) { libMesh::RealGradient g = this->_stab_helper.compute_g( fe, context, qp ); libMesh::RealTensor G = this->_stab_helper.compute_G( fe, context, qp ); libMesh::RealGradient U( context.interior_value( this->_flow_vars.u_var(), qp ), context.interior_value( this->_flow_vars.v_var(), qp ) ); if( this->_dim == 3 ) { U(2) = context.interior_value( this->_flow_vars.w_var(), qp ); } // Compute the viscosity at this qp libMesh::Real mu_qp = this->_mu(context, qp); libMesh::Real tau_M; libMesh::Real d_tau_M_d_rho; libMesh::Gradient d_tau_M_dU; if (compute_jacobian) this->_stab_helper.compute_tau_momentum_and_derivs ( context, qp, g, G, this->_rho, U, mu_qp, tau_M, d_tau_M_d_rho, d_tau_M_dU, this->_is_steady ); else tau_M = this->_stab_helper.compute_tau_momentum ( context, qp, g, G, this->_rho, U, mu_qp, this->_is_steady ); // Compute the solution & its gradient at the old Newton iterate. libMesh::Number T; T = context.interior_value(_temp_vars.T_var(), qp); libMesh::RealGradient d_residual_dT = _rho_ref*_beta_T*_g; // d_residual_dU = 0 libMesh::RealGradient residual = (T-_T_ref)*d_residual_dT; for (unsigned int i=0; i != n_u_dofs; i++) { libMesh::Real test_func = this->_rho*U*u_gradphi[i][qp] + mu_qp*( u_hessphi[i][qp](0,0) + u_hessphi[i][qp](1,1) + u_hessphi[i][qp](2,2) ); Fu(i) += -tau_M*residual(0)*test_func*JxW[qp]; Fv(i) += -tau_M*residual(1)*test_func*JxW[qp]; if (_dim == 3) { (*Fw)(i) += -tau_M*residual(2)*test_func*JxW[qp]; } if (compute_jacobian) { libMesh::Gradient d_test_func_dU = this->_rho*u_gradphi[i][qp]; // d_test_func_dT = 0 for (unsigned int j=0; j != n_u_dofs; ++j) { Kuu(i,j) += -tau_M*residual(0)*d_test_func_dU(0)*u_phi[j][qp]*JxW[qp] * context.get_elem_solution_derivative(); Kuu(i,j) += -d_tau_M_dU(0)*u_phi[j][qp]*residual(0)*test_func*JxW[qp] * context.get_elem_solution_derivative(); Kuv(i,j) += -tau_M*residual(0)*d_test_func_dU(1)*u_phi[j][qp]*JxW[qp] * context.get_elem_solution_derivative(); Kuv(i,j) += -d_tau_M_dU(1)*u_phi[j][qp]*residual(0)*test_func*JxW[qp] * context.get_elem_solution_derivative(); Kvu(i,j) += -tau_M*residual(1)*d_test_func_dU(0)*u_phi[j][qp]*JxW[qp] * context.get_elem_solution_derivative(); Kvu(i,j) += -d_tau_M_dU(0)*u_phi[j][qp]*residual(1)*test_func*JxW[qp] * context.get_elem_solution_derivative(); Kvv(i,j) += -tau_M*residual(1)*d_test_func_dU(1)*u_phi[j][qp]*JxW[qp] * context.get_elem_solution_derivative(); Kvv(i,j) += -d_tau_M_dU(1)*u_phi[j][qp]*residual(1)*test_func*JxW[qp] * context.get_elem_solution_derivative(); } for (unsigned int j=0; j != n_T_dofs; ++j) { // KuT(i,j) += -tau_M*residual(0)*dtest_func_dT[j]*JxW[qp] * context.get_elem_solution_derivative(); KuT(i,j) += -tau_M*d_residual_dT(0)*T_phi[j][qp]*test_func*JxW[qp] * context.get_elem_solution_derivative(); // KvT(i,j) += -tau_M*residual(1)*dtest_func_dT[j]*JxW[qp] * context.get_elem_solution_derivative(); KvT(i,j) += -tau_M*d_residual_dT(1)*T_phi[j][qp]*test_func*JxW[qp] * context.get_elem_solution_derivative(); } if (_dim == 3) { for (unsigned int j=0; j != n_T_dofs; ++j) { // KwT(i,j) += -tau_M*residual(2)*dtest_func_dT[j]*JxW[qp] * context.get_elem_solution_derivative(); (*KwT)(i,j) += -tau_M*d_residual_dT(2)*T_phi[j][qp]*test_func*JxW[qp] * context.get_elem_solution_derivative(); } for (unsigned int j=0; j != n_u_dofs; ++j) { (*Kuw)(i,j) += -tau_M*residual(0)*d_test_func_dU(2)*u_phi[j][qp]*JxW[qp] * context.get_elem_solution_derivative(); (*Kuw)(i,j) += -d_tau_M_dU(2)*u_phi[j][qp]*residual(0)*test_func*JxW[qp] * context.get_elem_solution_derivative(); (*Kvw)(i,j) += -tau_M*residual(1)*d_test_func_dU(2)*u_phi[j][qp]*JxW[qp] * context.get_elem_solution_derivative(); (*Kvw)(i,j) += -d_tau_M_dU(2)*u_phi[j][qp]*residual(1)*test_func*JxW[qp] * context.get_elem_solution_derivative(); (*Kwu)(i,j) += -tau_M*residual(2)*d_test_func_dU(0)*u_phi[j][qp]*JxW[qp] * context.get_elem_solution_derivative(); (*Kwu)(i,j) += -d_tau_M_dU(0)*u_phi[j][qp]*residual(2)*test_func*JxW[qp] * context.get_elem_solution_derivative(); (*Kwv)(i,j) += -tau_M*residual(2)*d_test_func_dU(1)*u_phi[j][qp]*JxW[qp] * context.get_elem_solution_derivative(); (*Kwv)(i,j) += -d_tau_M_dU(1)*u_phi[j][qp]*residual(2)*test_func*JxW[qp] * context.get_elem_solution_derivative(); (*Kww)(i,j) += -tau_M*residual(2)*d_test_func_dU(2)*u_phi[j][qp]*JxW[qp] * context.get_elem_solution_derivative(); (*Kww)(i,j) += -d_tau_M_dU(2)*u_phi[j][qp]*residual(2)*test_func*JxW[qp] * context.get_elem_solution_derivative(); } } } // End compute_jacobian check } // End i dof loop } // End quadrature loop #ifdef GRINS_USE_GRVY_TIMERS this->_timer->EndTimer("BoussinesqBuoyancyAdjointStabilization::element_time_derivative"); #endif return; }
void BoussinesqBuoyancy::element_time_derivative ( bool compute_jacobian, AssemblyContext & context ) { // The number of local degrees of freedom in each variable. const unsigned int n_u_dofs = context.get_dof_indices(_flow_vars.u()).size(); const unsigned int n_T_dofs = context.get_dof_indices(_temp_vars.T()).size(); // Element Jacobian * quadrature weights for interior integration. const std::vector<libMesh::Real> &JxW = context.get_element_fe(_flow_vars.u())->get_JxW(); // The velocity shape functions at interior quadrature points. const std::vector<std::vector<libMesh::Real> >& vel_phi = context.get_element_fe(_flow_vars.u())->get_phi(); // The temperature shape functions at interior quadrature points. const std::vector<std::vector<libMesh::Real> >& T_phi = context.get_element_fe(_temp_vars.T())->get_phi(); // Get residuals libMesh::DenseSubVector<libMesh::Number> &Fu = context.get_elem_residual(_flow_vars.u()); // R_{u} libMesh::DenseSubVector<libMesh::Number> &Fv = context.get_elem_residual(_flow_vars.v()); // R_{v} libMesh::DenseSubVector<libMesh::Number>* Fw = NULL; // Get Jacobians libMesh::DenseSubMatrix<libMesh::Number> &KuT = context.get_elem_jacobian(_flow_vars.u(), _temp_vars.T()); // R_{u},{T} libMesh::DenseSubMatrix<libMesh::Number> &KvT = context.get_elem_jacobian(_flow_vars.v(), _temp_vars.T()); // R_{v},{T} libMesh::DenseSubMatrix<libMesh::Number>* KwT = NULL; if( this->_flow_vars.dim() == 3 ) { Fw = &context.get_elem_residual(_flow_vars.w()); // R_{w} KwT = &context.get_elem_jacobian(_flow_vars.w(), _temp_vars.T()); // R_{w},{T} } // Now we will build the element Jacobian and residual. // Constructing the residual requires the solution and its // gradient from the previous timestep. This must be // calculated at each quadrature point by summing the // solution degree-of-freedom values by the appropriate // weight functions. unsigned int n_qpoints = context.get_element_qrule().n_points(); for (unsigned int qp=0; qp != n_qpoints; qp++) { // Compute the solution & its gradient at the old Newton iterate. libMesh::Number T; T = context.interior_value(_temp_vars.T(), qp); // First, an i-loop over the velocity degrees of freedom. // We know that n_u_dofs == n_v_dofs so we can compute contributions // for both at the same time. for (unsigned int i=0; i != n_u_dofs; i++) { Fu(i) += -_rho*_beta_T*(T - _T_ref)*_g(0)*vel_phi[i][qp]*JxW[qp]; Fv(i) += -_rho*_beta_T*(T - _T_ref)*_g(1)*vel_phi[i][qp]*JxW[qp]; if (this->_flow_vars.dim() == 3) (*Fw)(i) += -_rho*_beta_T*(T - _T_ref)*_g(2)*vel_phi[i][qp]*JxW[qp]; if (compute_jacobian) { for (unsigned int j=0; j != n_T_dofs; j++) { KuT(i,j) += context.get_elem_solution_derivative() * -_rho*_beta_T*_g(0)*vel_phi[i][qp]*T_phi[j][qp]*JxW[qp]; KvT(i,j) += context.get_elem_solution_derivative() * -_rho*_beta_T*_g(1)*vel_phi[i][qp]*T_phi[j][qp]*JxW[qp]; if (this->_flow_vars.dim() == 3) (*KwT)(i,j) += context.get_elem_solution_derivative() * -_rho*_beta_T*_g(2)*vel_phi[i][qp]*T_phi[j][qp]*JxW[qp]; } // End j dof loop } // End compute_jacobian check } // End i dof loop } // End quadrature loop }
void HeatConduction<K>::element_time_derivative( bool compute_jacobian, AssemblyContext& context, CachedValues& /*cache*/ ) { // The number of local degrees of freedom in each variable. const unsigned int n_T_dofs = context.get_dof_indices(_temp_vars.T_var()).size(); // We get some references to cell-specific data that // will be used to assemble the linear system. // Element Jacobian * quadrature weights for interior integration. const std::vector<libMesh::Real> &JxW = context.get_element_fe(_temp_vars.T_var())->get_JxW(); // The temperature shape function gradients (in global coords.) // at interior quadrature points. const std::vector<std::vector<libMesh::RealGradient> >& T_gradphi = context.get_element_fe(_temp_vars.T_var())->get_dphi(); // The subvectors and submatrices we need to fill: // // K_{\alpha \beta} = R_{\alpha},{\beta} = \partial{ R_{\alpha} } / \partial{ {\beta} } (where R denotes residual) // e.g., for \alpha = T and \beta = v we get: K_{Tu} = R_{T},{u} // libMesh::DenseSubMatrix<libMesh::Number> &KTT = context.get_elem_jacobian(_temp_vars.T_var(), _temp_vars.T_var()); // R_{T},{T} libMesh::DenseSubVector<libMesh::Number> &FT = context.get_elem_residual(_temp_vars.T_var()); // R_{T} // Now we will build the element Jacobian and residual. // Constructing the residual requires the solution and its // gradient from the previous timestep. This must be // calculated at each quadrature point by summing the // solution degree-of-freedom values by the appropriate // weight functions. unsigned int n_qpoints = context.get_element_qrule().n_points(); for (unsigned int qp=0; qp != n_qpoints; qp++) { // Compute the solution & its gradient at the old Newton iterate. libMesh::Gradient grad_T; grad_T = context.interior_gradient(_temp_vars.T_var(), qp); // Compute the conductivity at this qp libMesh::Real _k_qp = this->_k(context, qp); // First, an i-loop over the degrees of freedom. for (unsigned int i=0; i != n_T_dofs; i++) { FT(i) += JxW[qp]*(-_k_qp*(T_gradphi[i][qp]*grad_T)); if (compute_jacobian) { for (unsigned int j=0; j != n_T_dofs; j++) { // TODO: precompute some terms like: // _rho*_Cp*T_phi[i][qp]*(vel_phi[j][qp]*T_grad_phi[j][qp]) KTT(i,j) += JxW[qp] * context.get_elem_solution_derivative() * ( -_k_qp*(T_gradphi[i][qp]*T_gradphi[j][qp]) ); // diffusion term } // end of the inner dof (j) loop } // end - if (compute_jacobian && context.get_elem_solution_derivative()) } // end of the outer dof (i) loop } // end of the quadrature point (qp) loop return; }