void HeatTransfer::element_time_derivative( bool compute_jacobian, libMesh::FEMContext& 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.dof_indices_var[_T_var].size(); const unsigned int n_u_dofs = context.dof_indices_var[_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.element_fe_var[_T_var]->get_JxW(); // The temperature shape functions at interior quadrature points. const std::vector<std::vector<libMesh::Real> >& T_phi = context.element_fe_var[_T_var]->get_phi(); // The velocity shape functions at interior quadrature points. const std::vector<std::vector<libMesh::Real> >& vel_phi = context.element_fe_var[_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.element_fe_var[_T_var]->get_dphi(); const std::vector<libMesh::Point>& u_qpoint = context.element_fe_var[this->_u_var]->get_xyz(); // We do this in the incompressible Navier-Stokes class and need to do it here too // since _w_var won't have been defined in the global map. if (_dim != 3) _w_var = _u_var; // for convenience libMesh::DenseSubMatrix<libMesh::Number> &KTT = *context.elem_subjacobians[_T_var][_T_var]; // R_{T},{T} libMesh::DenseSubMatrix<libMesh::Number> &KTu = *context.elem_subjacobians[_T_var][_u_var]; // R_{T},{u} libMesh::DenseSubMatrix<libMesh::Number> &KTv = *context.elem_subjacobians[_T_var][_v_var]; // R_{T},{v} libMesh::DenseSubMatrix<libMesh::Number> &KTw = *context.elem_subjacobians[_T_var][_w_var]; // R_{T},{w} libMesh::DenseSubVector<libMesh::Number> &FT = *context.elem_subresiduals[_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.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, w; u = context.interior_value(_u_var, qp); v = context.interior_value(_v_var, qp); if (_dim == 3) w = context.interior_value(_w_var, qp); libMesh::Gradient grad_T; grad_T = context.interior_gradient(_T_var, qp); libMesh::NumberVectorValue U (u,v); if (_dim == 3) U(2) = w; 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.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 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 ReactingLowMachNavierStokesStabilizationBase<Mixture,Evaluator>::compute_res_steady( AssemblyContext& context, unsigned int qp, libMesh::Real& RP_s, libMesh::RealGradient& RM_s, libMesh::Real& RE_s, std::vector<libMesh::Real>& Rs_s ) { Rs_s.resize(this->n_species(),0.0); // Grab r-coordinate for axisymmetric terms // We're assuming all variables are using the same quadrature rule libMesh::Real r = (context.get_element_fe(this->_flow_vars.u())->get_xyz())[qp](0); libMesh::RealGradient grad_p = context.interior_gradient(this->_press_var.p(), qp); libMesh::RealGradient grad_u = context.interior_gradient(this->_flow_vars.u(), qp); libMesh::RealGradient grad_v = context.interior_gradient(this->_flow_vars.v(), qp); libMesh::RealGradient U( context.interior_value(this->_flow_vars.u(), qp), context.interior_value(this->_flow_vars.v(), qp) ); libMesh::Real divU = grad_u(0) + grad_v(1); if( this->_is_axisymmetric ) divU += U(0)/r; if(this->mesh_dim(context) == 3) { U(2) = context.interior_value(this->_flow_vars.w(), qp); divU += (context.interior_gradient(this->_flow_vars.w(), qp))(2); } // We don't add axisymmetric terms here since we don't directly use hess_{u,v} // axisymmetric terms are built into divGradU, etc. functions below libMesh::RealTensor hess_u = context.interior_hessian(this->_flow_vars.u(), qp); libMesh::RealTensor hess_v = context.interior_hessian(this->_flow_vars.v(), qp); libMesh::Real T = context.interior_value(this->_temp_vars.T(), qp); libMesh::Gradient grad_T = context.interior_gradient(this->_temp_vars.T(), qp); libMesh::Tensor hess_T = context.interior_hessian(this->_temp_vars.T(), qp); libMesh::Real hess_T_term = hess_T(0,0) + hess_T(1,1); #if LIBMESH_DIM > 2 hess_T_term += hess_T(2,2); #endif // Add axisymmetric terms, if needed if( this->_is_axisymmetric ) hess_T_term += grad_T(0)/r; std::vector<libMesh::Real> ws(this->n_species()); std::vector<libMesh::RealGradient> grad_ws(this->n_species()); std::vector<libMesh::RealTensor> hess_ws(this->n_species()); for(unsigned int s=0; s < this->_n_species; s++ ) { ws[s] = context.interior_value(this->_species_vars.species(s), qp); grad_ws[s] = context.interior_gradient(this->_species_vars.species(s), qp); hess_ws[s] = context.interior_hessian(this->_species_vars.species(s), qp); } Evaluator gas_evaluator( this->_gas_mixture ); const libMesh::Real R_mix = gas_evaluator.R_mix(ws); const libMesh::Real p0 = this->get_p0_steady(context,qp); libMesh::Real rho = this->rho(T, p0, R_mix ); libMesh::Real cp = gas_evaluator.cp(T,p0,ws); libMesh::Real M = gas_evaluator.M_mix( ws ); std::vector<libMesh::Real> D( this->n_species() ); libMesh::Real mu, k; gas_evaluator.mu_and_k_and_D( T, rho, cp, ws, mu, k, D ); // grad_rho = drho_dT*gradT + \sum_s drho_dws*grad_ws const libMesh::Real drho_dT = -p0/(R_mix*T*T); libMesh::RealGradient grad_rho = drho_dT*grad_T; for(unsigned int s=0; s < this->_n_species; s++ ) { libMesh::Real Ms = gas_evaluator.M(s); libMesh::Real R_uni = Constants::R_universal/1000.0; /* J/kmol-K --> J/mol-K */ // drho_dws = -p0/(T*R_mix*R_mix)*dR_dws // dR_dws = R_uni*d_dws(1/M) // d_dws(1/M) = d_dws(\sum_s w_s/Ms) = 1/Ms const libMesh::Real drho_dws = -p0/(R_mix*R_mix*T)*R_uni/Ms; grad_rho += drho_dws*grad_ws[s]; } libMesh::RealGradient rhoUdotGradU; libMesh::RealGradient divGradU; libMesh::RealGradient divGradUT; libMesh::RealGradient divdivU; if( this->mesh_dim(context) < 3 ) { rhoUdotGradU = rho*_stab_helper.UdotGradU( U, grad_u, grad_v ); // Call axisymmetric versions if we are doing an axisymmetric run if( this->_is_axisymmetric ) { divGradU = _stab_helper.div_GradU_axi( r, U, grad_u, grad_v, hess_u, hess_v ); divGradUT = _stab_helper.div_GradU_T_axi( r, U, grad_u, hess_u, hess_v ); divdivU = _stab_helper.div_divU_I_axi( r, U, grad_u, hess_u, hess_v ); } else { divGradU = _stab_helper.div_GradU( hess_u, hess_v ); divGradUT = _stab_helper.div_GradU_T( hess_u, hess_v ); divdivU = _stab_helper.div_divU_I( hess_u, hess_v ); } } else { libMesh::RealGradient grad_w = context.interior_gradient(this->_flow_vars.w(), qp); libMesh::RealTensor hess_w = context.interior_hessian(this->_flow_vars.w(), qp); rhoUdotGradU = rho*_stab_helper.UdotGradU( U, grad_u, grad_v, grad_w ); divGradU = _stab_helper.div_GradU( hess_u, hess_v, hess_w ); divGradUT = _stab_helper.div_GradU_T( hess_u, hess_v, hess_w ); divdivU = _stab_helper.div_divU_I( hess_u, hess_v, hess_w ); } // Terms if we have vicosity derivatives w.r.t. temp. /* if( this->_mu.deriv(T) != 0.0 ) { libMesh::Gradient gradTgradu( grad_T*grad_u, grad_T*grad_v ); libMesh::Gradient gradTgraduT( grad_T(0)*grad_u(0) + grad_T(1)*grad_u(1), grad_T(0)*grad_v(0) + grad_T(1)*grad_v(1) ); libMesh::Real divU = grad_u(0) + grad_v(1); libMesh::Gradient gradTdivU( grad_T(0)*divU, grad_T(1)*divU ); if(this->mesh_dim(context) == 3) { libMesh::Gradient grad_w = context.interior_gradient(this->_flow_vars.w(), qp); gradTgradu(2) = grad_T*grad_w; gradTgraduT(0) += grad_T(2)*grad_u(2); gradTgraduT(1) += grad_T(2)*grad_v(2); gradTgraduT(2) = grad_T(0)*grad_w(0) + grad_T(1)*grad_w(1) + grad_T(2)*grad_w(2); divU += grad_w(2); gradTdivU(0) += grad_T(0)*grad_w(2); gradTdivU(1) += grad_T(1)*grad_w(2); gradTdivU(2) += grad_T(2)*divU; } divT += this->_mu.deriv(T)*( gradTgradu + gradTgraduT - 2.0/3.0*gradTdivU ); } */ // Axisymmetric terms already built in libMesh::RealGradient div_stress = mu*(divGradU + divGradUT - 2.0/3.0*divdivU); std::vector<libMesh::Real> omega_dot(this->n_species()); gas_evaluator.omega_dot(T,rho,ws,omega_dot); libMesh::Real chem_term = 0.0; libMesh::Gradient mass_term(0.0,0.0,0.0); for(unsigned int s=0; s < this->_n_species; s++ ) { // Start accumulating chemistry term for energy residual libMesh::Real h_s=gas_evaluator.h_s(T,s); chem_term += h_s*omega_dot[s]; /* Accumulate mass term for continuity residual mass_term = grad_M/M */ mass_term += grad_ws[s]/this->_gas_mixture.M(s); libMesh::Real hess_s_term = hess_ws[s](0,0) + hess_ws[s](1,1); #if LIBMESH_DIM > 2 hess_s_term += hess_ws[s](2,2); #endif // Add axisymmetric terms, if needed if( this->_is_axisymmetric ) hess_s_term += grad_ws[s](0)/r; // Species residual /*! \todo Still missing derivative of species diffusion coefficient. rho*grad_D[s]*grad_ws[s] */ Rs_s[s] = rho*U*grad_ws[s] - rho*D[s]*hess_s_term - grad_rho*D[s]*grad_ws[s] - omega_dot[s]; } mass_term *= M; // Continuity residual RP_s = divU - (U*grad_T)/T - U*mass_term; // Momentum residual RM_s = rhoUdotGradU + grad_p - div_stress - rho*(this->_g); // Energy residual // - this->_k.deriv(T)*(grad_T*grad_T) RE_s = rho*U*cp*grad_T - k*(hess_T_term) + chem_term; return; }