void HeatTransferStabilizationHelper::compute_res_energy_steady_and_derivs ( AssemblyContext& context, unsigned int qp, const libMesh::Real rho, const libMesh::Real Cp, const libMesh::Real k, libMesh::Real &res, libMesh::Real &d_res_dT, libMesh::Gradient &d_res_dgradT, libMesh::Tensor &d_res_dhessT, libMesh::Gradient &d_res_dU ) const { libMesh::Gradient grad_T = context.fixed_interior_gradient(this->_temp_vars.T(), qp); libMesh::Tensor hess_T = context.fixed_interior_hessian(this->_temp_vars.T(), qp); libMesh::RealGradient rhocpU( rho*Cp*context.fixed_interior_value(this->_flow_vars.u(), qp), rho*Cp*context.fixed_interior_value(this->_flow_vars.v(), qp) ); if(this->_flow_vars.dim() == 3) rhocpU(2) = rho*Cp*context.fixed_interior_value(this->_flow_vars.w(), qp); res = rhocpU*grad_T - k*(hess_T(0,0) + hess_T(1,1) + hess_T(2,2)); d_res_dT = 0; d_res_dgradT = rhocpU; d_res_dhessT = 0; d_res_dhessT(0,0) = -k; d_res_dhessT(1,1) = -k; d_res_dhessT(2,2) = -k; d_res_dU = rho * Cp * grad_T; }
libMesh::Real SpalartAllmarasStabilizationHelper::compute_res_spalart_steady( AssemblyContext& context, unsigned int qp, const libMesh::Real rho, const libMesh::Real mu, const libMesh::Real distance_qp, const bool infinite_distance) const { // The flow velocity libMesh::Number u,v; u = context.interior_value(this->_flow_vars.u(), qp); v = context.interior_value(this->_flow_vars.v(), qp); libMesh::NumberVectorValue U(u,v); if ( this->_flow_vars.dim() == 3 ) U(2) = context.interior_value(this->_flow_vars.w(), qp); libMesh::RealGradient grad_u = context.fixed_interior_gradient(this->_flow_vars.u(), qp); libMesh::RealGradient grad_v = context.fixed_interior_gradient(this->_flow_vars.v(), qp); libMesh::Number nu_value = context.interior_value(this->_turbulence_vars.nu(), qp); libMesh::RealGradient grad_nu = context.fixed_interior_gradient(this->_turbulence_vars.nu(), qp); libMesh::RealTensor hess_nu = context.fixed_interior_hessian(this->_turbulence_vars.nu(), qp); // The convection term libMesh::Number rhoUdotGradnu = rho*(U*grad_nu); // The diffusion term libMesh::Number inv_sigmadivnuplusnuphysicalGradnu = (1./this->_sa_params.get_sigma())*(grad_nu*grad_nu + ((nu_value + mu)*(hess_nu(0,0) + hess_nu(1,1) + (this->_flow_vars.dim() == 3)?hess_nu(2,2):0)) + this->_sa_params.get_cb2()*grad_nu*grad_nu); // The source term libMesh::Real vorticity_value_qp = this->_spalart_allmaras_helper.vorticity(context, qp); libMesh::Real S_tilde = this->_sa_params.source_fn(nu_value, mu, distance_qp, vorticity_value_qp, infinite_distance); libMesh::Real source_term = this->_sa_params.get_cb1()*S_tilde*nu_value; libMesh::Real kappa2 = (this->_sa_params.get_kappa())*(this->_sa_params.get_kappa()); libMesh::Real cw1 = this->_sa_params.get_cb1()/kappa2 + (1.0 + this->_sa_params.get_cb2())/this->_sa_params.get_sigma(); // The destruction term libMesh::Real fw = this->_sa_params.destruction_fn(nu_value, distance_qp, S_tilde, infinite_distance); libMesh::Real destruction_term = 0.0; if(infinite_distance) { destruction_term = 0.0; } else { destruction_term = cw1*fw*pow(nu_value/distance_qp, 2.); } return rhoUdotGradnu + source_term + inv_sigmadivnuplusnuphysicalGradnu - destruction_term; }
libMesh::Real HeatTransferStabilizationHelper::compute_res_energy_steady( AssemblyContext& context, unsigned int qp, const libMesh::Real rho, const libMesh::Real Cp, const libMesh::Real k ) const { libMesh::Gradient grad_T = context.fixed_interior_gradient(this->_temp_vars.T(), qp); libMesh::Tensor hess_T = context.fixed_interior_hessian(this->_temp_vars.T(), qp); libMesh::RealGradient rhocpU( rho*Cp*context.fixed_interior_value(this->_flow_vars.u(), qp), rho*Cp*context.fixed_interior_value(this->_flow_vars.v(), qp) ); if(this->_flow_vars.dim() == 3) rhocpU(2) = rho*Cp*context.fixed_interior_value(this->_flow_vars.w(), qp); return rhocpU*grad_T - k*(hess_T(0,0) + hess_T(1,1) + hess_T(2,2)); }