void Vorticity::element_qoi( libMesh::DiffContext& context, const libMesh::QoISet& ) { libMesh::FEMContext &c = libmesh_cast_ref<libMesh::FEMContext&>(context); if( _subdomain_ids.find( (c.elem)->subdomain_id() ) != _subdomain_ids.end() ) { libMesh::FEBase* element_fe; c.get_element_fe<libMesh::Real>(this->_u_var, element_fe); const std::vector<libMesh::Real> &JxW = element_fe->get_JxW(); unsigned int n_qpoints = (c.get_element_qrule())->n_points(); /*! \todo Need to generalize this to the multiple QoI case */ libMesh::Number& qoi = c.elem_qoi[0]; for( unsigned int qp = 0; qp != n_qpoints; qp++ ) { libMesh::Gradient grad_u = 0.; libMesh::Gradient grad_v = 0.; c.interior_gradient( this->_u_var, qp, grad_u ); c.interior_gradient( this->_v_var, qp, grad_v ); qoi += (grad_v(0) - grad_u(1)) * JxW[qp]; } } return; }
void LowMachNavierStokes<Mu,SH,TC>::assemble_mass_time_deriv( bool /*compute_jacobian*/, AssemblyContext& context, CachedValues& cache ) { // The number of local degrees of freedom in each variable. const unsigned int n_p_dofs = context.get_dof_indices(this->_p_var).size(); // Element Jacobian * quadrature weights for interior integration. const std::vector<libMesh::Real> &JxW = context.get_element_fe(this->_u_var)->get_JxW(); // The pressure shape functions at interior quadrature points. const std::vector<std::vector<libMesh::Real> >& p_phi = context.get_element_fe(this->_p_var)->get_phi(); libMesh::DenseSubVector<libMesh::Number> &Fp = context.get_elem_residual(this->_p_var); // R_{p} unsigned int n_qpoints = context.get_element_qrule().n_points(); for (unsigned int qp=0; qp != n_qpoints; qp++) { libMesh::Number u, v, T; u = cache.get_cached_values(Cache::X_VELOCITY)[qp]; v = cache.get_cached_values(Cache::Y_VELOCITY)[qp]; T = cache.get_cached_values(Cache::TEMPERATURE)[qp]; libMesh::Gradient grad_u = cache.get_cached_gradient_values(Cache::X_VELOCITY_GRAD)[qp]; libMesh::Gradient grad_v = cache.get_cached_gradient_values(Cache::Y_VELOCITY_GRAD)[qp]; libMesh::Gradient grad_T = cache.get_cached_gradient_values(Cache::TEMPERATURE_GRAD)[qp]; libMesh::NumberVectorValue U(u,v); if (this->_dim == 3) U(2) = cache.get_cached_values(Cache::Z_VELOCITY)[qp]; // w libMesh::Number divU = grad_u(0) + grad_v(1); if (this->_dim == 3) { libMesh::Gradient grad_w = cache.get_cached_gradient_values(Cache::Z_VELOCITY_GRAD)[qp]; divU += grad_w(2); } // Now a loop over the pressure degrees of freedom. This // computes the contributions of the continuity equation. for (unsigned int i=0; i != n_p_dofs; i++) { Fp(i) += (-U*grad_T/T + divU)*p_phi[i][qp]*JxW[qp]; } } return; }
void LowMachNavierStokes<Mu,SH,TC>::assemble_thermo_press_elem_time_deriv( bool /*compute_jacobian*/, AssemblyContext& context ) { // Element Jacobian * quadrature weights for interior integration const std::vector<libMesh::Real> &JxW = context.get_element_fe(this->_T_var)->get_JxW(); // The number of local degrees of freedom in each variable const unsigned int n_p0_dofs = context.get_dof_indices(this->_p0_var).size(); // The subvectors and submatrices we need to fill: libMesh::DenseSubVector<libMesh::Real> &F_p0 = context.get_elem_residual(this->_p0_var); unsigned int n_qpoints = context.get_element_qrule().n_points(); for (unsigned int qp = 0; qp != n_qpoints; ++qp) { libMesh::Number T; T = context.interior_value(this->_T_var, qp); libMesh::Gradient grad_u, grad_v, grad_w; grad_u = context.interior_gradient(this->_u_var, qp); grad_v = context.interior_gradient(this->_v_var, qp); if (this->_dim == 3) grad_w = context.interior_gradient(this->_w_var, qp); libMesh::Number divU = grad_u(0) + grad_v(1); if(this->_dim==3) divU += grad_w(2); //libMesh::Number cp = this->_cp(T); //libMesh::Number cv = cp + this->_R; //libMesh::Number gamma = cp/cv; //libMesh::Number gamma_ratio = gamma/(gamma-1.0); libMesh::Number p0 = context.interior_value( this->_p0_var, qp ); for (unsigned int i = 0; i != n_p0_dofs; ++i) { F_p0(i) += (p0/T - this->_p0/this->_T0)*JxW[qp]; //F_p0(i) -= p0*gamma_ratio*divU*JxW[qp]; } // End DoF loop i } return; }
vec3 MapGradient::compute_gradient( Map::Halfedge* h1, Map::Halfedge* h2, Map::Halfedge* h3, const vec2& W ) { double TU[3] ; double TV[3] ; compute_gradient(h1,h2,h3,TU,TV) ; const vec3& p1 = h1->vertex()->point() ; const vec3& p2 = h2->vertex()->point() ; const vec3& p3 = h3->vertex()->point() ; vec3 grad_u( real(TU[0] * p1.x + TU[1] * p2.x + TU[2] * p3.x), real(TU[0] * p1.y + TU[1] * p2.y + TU[2] * p3.y), real(TU[0] * p1.z + TU[1] * p2.z + TU[2] * p3.z) ) ; vec3 grad_v( real(TV[0] * p1.x + TV[1] * p2.x + TV[2] * p3.x), real(TV[0] * p1.y + TV[1] * p2.y + TV[2] * p3.y), real(TV[0] * p1.z + TV[1] * p2.z + TV[2] * p3.z) ) ; return W.x * grad_u + W.y * grad_v ; }
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 LowMachNavierStokes<Mu,SH,TC>::assemble_momentum_time_deriv( bool /*compute_jacobian*/, AssemblyContext& context, CachedValues& cache ) { // The number of local degrees of freedom in each variable. const unsigned int n_u_dofs = context.get_dof_indices(this->_u_var).size(); // Check number of dofs is same for _u_var, v_var and w_var. libmesh_assert (n_u_dofs == context.get_dof_indices(this->_v_var).size()); if (this->_dim == 3) libmesh_assert (n_u_dofs == context.get_dof_indices(this->_w_var).size()); // Element Jacobian * quadrature weights for interior integration. const std::vector<libMesh::Real> &JxW = context.get_element_fe(this->_u_var)->get_JxW(); // The pressure shape functions at interior quadrature points. const std::vector<std::vector<libMesh::Real> >& u_phi = context.get_element_fe(this->_u_var)->get_phi(); // The velocity shape function gradients at interior quadrature points. const std::vector<std::vector<libMesh::RealGradient> >& u_gradphi = context.get_element_fe(this->_u_var)->get_dphi(); libMesh::DenseSubVector<libMesh::Number> &Fu = context.get_elem_residual(this->_u_var); // R_{u} libMesh::DenseSubVector<libMesh::Number> &Fv = context.get_elem_residual(this->_v_var); // R_{v} libMesh::DenseSubVector<libMesh::Number> &Fw = context.get_elem_residual(this->_w_var); // R_{w} unsigned int n_qpoints = context.get_element_qrule().n_points(); for (unsigned int qp=0; qp != n_qpoints; qp++) { libMesh::Number u, v, p, p0, T; u = cache.get_cached_values(Cache::X_VELOCITY)[qp]; v = cache.get_cached_values(Cache::Y_VELOCITY)[qp]; T = cache.get_cached_values(Cache::TEMPERATURE)[qp]; p = cache.get_cached_values(Cache::PRESSURE)[qp]; p0 = cache.get_cached_values(Cache::THERMO_PRESSURE)[qp]; libMesh::Gradient grad_u = cache.get_cached_gradient_values(Cache::X_VELOCITY_GRAD)[qp]; libMesh::Gradient grad_v = cache.get_cached_gradient_values(Cache::Y_VELOCITY_GRAD)[qp]; libMesh::Gradient grad_w; if (this->_dim == 3) grad_w = cache.get_cached_gradient_values(Cache::Z_VELOCITY_GRAD)[qp]; libMesh::NumberVectorValue grad_uT( grad_u(0), grad_v(0) ); libMesh::NumberVectorValue grad_vT( grad_u(1), grad_v(1) ); libMesh::NumberVectorValue grad_wT; if( this->_dim == 3 ) { grad_uT(2) = grad_w(0); grad_vT(2) = grad_w(1); grad_wT = libMesh::NumberVectorValue( grad_u(2), grad_v(2), grad_w(2) ); } libMesh::NumberVectorValue U(u,v); if (this->_dim == 3) U(2) = cache.get_cached_values(Cache::Z_VELOCITY)[qp]; // w libMesh::Number divU = grad_u(0) + grad_v(1); if (this->_dim == 3) divU += grad_w(2); libMesh::Number rho = this->rho( T, p0 ); // Now a loop over the pressure degrees of freedom. This // computes the contributions of the continuity equation. for (unsigned int i=0; i != n_u_dofs; i++) { Fu(i) += ( -rho*U*grad_u*u_phi[i][qp] // convection term + p*u_gradphi[i][qp](0) // pressure term - this->_mu(T)*(u_gradphi[i][qp]*grad_u + u_gradphi[i][qp]*grad_uT - 2.0/3.0*divU*u_gradphi[i][qp](0) ) // diffusion term + rho*this->_g(0)*u_phi[i][qp] // hydrostatic term )*JxW[qp]; Fv(i) += ( -rho*U*grad_v*u_phi[i][qp] // convection term + p*u_gradphi[i][qp](1) // pressure term - this->_mu(T)*(u_gradphi[i][qp]*grad_v + u_gradphi[i][qp]*grad_vT - 2.0/3.0*divU*u_gradphi[i][qp](1) ) // diffusion term + rho*this->_g(1)*u_phi[i][qp] // hydrostatic term )*JxW[qp]; if (this->_dim == 3) { Fw(i) += ( -rho*U*grad_w*u_phi[i][qp] // convection term + p*u_gradphi[i][qp](2) // pressure term - this->_mu(T)*(u_gradphi[i][qp]*grad_w + u_gradphi[i][qp]*grad_wT - 2.0/3.0*divU*u_gradphi[i][qp](2) ) // diffusion term + rho*this->_g(2)*u_phi[i][qp] // hydrostatic term )*JxW[qp]; } /* if (compute_jacobian && context.get_elem_solution_derivative()) { libmesh_assert (context.get_elem_solution_derivative() == 1.0); for (unsigned int j=0; j != n_u_dofs; j++) { // TODO: precompute some terms like: // (Uvec*vel_gblgradphivec[j][qp]), // vel_phi[i][qp]*vel_phi[j][qp], // (vel_gblgradphivec[i][qp]*vel_gblgradphivec[j][qp]) Kuu(i,j) += JxW[qp] * (-_rho*vel_phi[i][qp]*(Uvec*vel_gblgradphivec[j][qp]) // convection term -_rho*vel_phi[i][qp]*graduvec_x*vel_phi[j][qp] // convection term -_mu*(vel_gblgradphivec[i][qp]*vel_gblgradphivec[j][qp])); // diffusion term Kuv(i,j) += JxW[qp] * (-_rho*vel_phi[i][qp]*graduvec_y*vel_phi[j][qp]); // convection term Kvv(i,j) += JxW[qp] * (-_rho*vel_phi[i][qp]*(Uvec*vel_gblgradphivec[j][qp]) // convection term -_rho*vel_phi[i][qp]*gradvvec_y*vel_phi[j][qp] // convection term -_mu*(vel_gblgradphivec[i][qp]*vel_gblgradphivec[j][qp])); // diffusion term Kvu(i,j) += JxW[qp] * (-_rho*vel_phi[i][qp]*gradvvec_x*vel_phi[j][qp]); // convection term if (_dim == 3) { Kuw(i,j) += JxW[qp] * (-_rho*vel_phi[i][qp]*graduvec_z*vel_phi[j][qp]); // convection term Kvw(i,j) += JxW[qp] * (-_rho*vel_phi[i][qp]*gradvvec_z*vel_phi[j][qp]); // convection term Kww(i,j) += JxW[qp] * (-_rho*vel_phi[i][qp]*(Uvec*vel_gblgradphivec[j][qp]) // convection term -_rho*vel_phi[i][qp]*gradwvec_z*vel_phi[j][qp] // convection term -_mu*(vel_gblgradphivec[i][qp]*vel_gblgradphivec[j][qp])); // diffusion term Kwu(i,j) += JxW[qp] * (-_rho*vel_phi[i][qp]*gradwvec_x*vel_phi[j][qp]); // convection term Kwv(i,j) += JxW[qp] * (-_rho*vel_phi[i][qp]*gradwvec_y*vel_phi[j][qp]); // convection term } } // end of the inner dof (j) loop // Matrix contributions for the up, vp and wp couplings for (unsigned int j=0; j != n_p_dofs; j++) { Kup(i,j) += JxW[qp]*vel_gblgradphivec[i][qp](0)*p_phi[j][qp]; Kvp(i,j) += JxW[qp]*vel_gblgradphivec[i][qp](1)*p_phi[j][qp]; if (_dim == 3) Kwp(i,j) += JxW[qp]*vel_gblgradphivec[i][qp](2)*p_phi[j][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 */ } // End of DoF loop i } // End quadrature loop qp return; }
bool FEMPhysics::eulerian_residual (bool request_jacobian, DiffContext &/*c*/) { // Only calculate a mesh movement residual if it's necessary if (!_mesh_sys) return request_jacobian; libmesh_not_implemented(); #if 0 FEMContext &context = libmesh_cast_ref<FEMContext&>(c); // This function only supports fully coupled mesh motion for now libmesh_assert_equal_to (_mesh_sys, this); unsigned int n_qpoints = (context.get_element_qrule())->n_points(); const unsigned int n_x_dofs = (_mesh_x_var == libMesh::invalid_uint) ? 0 : context.dof_indices_var[_mesh_x_var].size(); const unsigned int n_y_dofs = (_mesh_y_var == libMesh::invalid_uint) ? 0 : context.dof_indices_var[_mesh_y_var].size(); const unsigned int n_z_dofs = (_mesh_z_var == libMesh::invalid_uint) ? 0 : context.dof_indices_var[_mesh_z_var].size(); const unsigned int mesh_xyz_var = n_x_dofs ? _mesh_x_var : (n_y_dofs ? _mesh_y_var : (n_z_dofs ? _mesh_z_var : libMesh::invalid_uint)); // If we're our own _mesh_sys, we'd better be in charge of // at least one coordinate, and we'd better have the same // FE type for all coordinates we are in charge of libmesh_assert_not_equal_to (mesh_xyz_var, libMesh::invalid_uint); libmesh_assert(!n_x_dofs || context.element_fe_var[_mesh_x_var] == context.element_fe_var[mesh_xyz_var]); libmesh_assert(!n_y_dofs || context.element_fe_var[_mesh_y_var] == context.element_fe_var[mesh_xyz_var]); libmesh_assert(!n_z_dofs || context.element_fe_var[_mesh_z_var] == context.element_fe_var[mesh_xyz_var]); const std::vector<std::vector<Real> > &psi = context.element_fe_var[mesh_xyz_var]->get_phi(); for (unsigned int var = 0; var != context.n_vars(); ++var) { // Mesh motion only affects time-evolving variables if (this->is_time_evolving(var)) continue; // The mesh coordinate variables themselves are Lagrangian, // not Eulerian, and no convective term is desired. if (/*_mesh_sys == this && */ (var == _mesh_x_var || var == _mesh_y_var || var == _mesh_z_var)) continue; // Some of this code currently relies on the assumption that // we can pull mesh coordinate data from our own system if (_mesh_sys != this) libmesh_not_implemented(); // This residual should only be called by unsteady solvers: // if the mesh is steady, there's no mesh convection term! UnsteadySolver *unsteady; if (this->time_solver->is_steady()) return request_jacobian; else unsteady = libmesh_cast_ptr<UnsteadySolver*>(this->time_solver.get()); const std::vector<Real> &JxW = context.element_fe_var[var]->get_JxW(); const std::vector<std::vector<Real> > &phi = context.element_fe_var[var]->get_phi(); const std::vector<std::vector<RealGradient> > &dphi = context.element_fe_var[var]->get_dphi(); const unsigned int n_u_dofs = context.dof_indices_var[var].size(); DenseSubVector<Number> &Fu = *context.elem_subresiduals[var]; DenseSubMatrix<Number> &Kuu = *context.elem_subjacobians[var][var]; DenseSubMatrix<Number> *Kux = n_x_dofs ? context.elem_subjacobians[var][_mesh_x_var] : NULL; DenseSubMatrix<Number> *Kuy = n_y_dofs ? context.elem_subjacobians[var][_mesh_y_var] : NULL; DenseSubMatrix<Number> *Kuz = n_z_dofs ? context.elem_subjacobians[var][_mesh_z_var] : NULL; std::vector<Real> delta_x(n_x_dofs, 0.); std::vector<Real> delta_y(n_y_dofs, 0.); std::vector<Real> delta_z(n_z_dofs, 0.); for (unsigned int i = 0; i != n_x_dofs; ++i) { unsigned int j = context.dof_indices_var[_mesh_x_var][i]; delta_x[i] = libmesh_real(this->current_solution(j)) - libmesh_real(unsteady->old_nonlinear_solution(j)); } for (unsigned int i = 0; i != n_y_dofs; ++i) { unsigned int j = context.dof_indices_var[_mesh_y_var][i]; delta_y[i] = libmesh_real(this->current_solution(j)) - libmesh_real(unsteady->old_nonlinear_solution(j)); } for (unsigned int i = 0; i != n_z_dofs; ++i) { unsigned int j = context.dof_indices_var[_mesh_z_var][i]; delta_z[i] = libmesh_real(this->current_solution(j)) - libmesh_real(unsteady->old_nonlinear_solution(j)); } for (unsigned int qp = 0; qp != n_qpoints; ++qp) { Gradient grad_u = context.interior_gradient(var, qp); RealGradient convection(0.); for (unsigned int i = 0; i != n_x_dofs; ++i) convection(0) += delta_x[i] * psi[i][qp]; for (unsigned int i = 0; i != n_y_dofs; ++i) convection(1) += delta_y[i] * psi[i][qp]; for (unsigned int i = 0; i != n_z_dofs; ++i) convection(2) += delta_z[i] * psi[i][qp]; for (unsigned int i = 0; i != n_u_dofs; ++i) { Number JxWxPhiI = JxW[qp] * phi[i][qp]; Fu(i) += (convection * grad_u) * JxWxPhiI; if (request_jacobian) { Number JxWxPhiI = JxW[qp] * phi[i][qp]; for (unsigned int j = 0; j != n_u_dofs; ++j) Kuu(i,j) += JxWxPhiI * (convection * dphi[j][qp]); Number JxWxPhiIoverDT = JxWxPhiI/this->deltat; Number JxWxPhiIxDUDXoverDT = JxWxPhiIoverDT * grad_u(0); for (unsigned int j = 0; j != n_x_dofs; ++j) (*Kux)(i,j) += JxWxPhiIxDUDXoverDT * psi[j][qp]; Number JxWxPhiIxDUDYoverDT = JxWxPhiIoverDT * grad_u(1); for (unsigned int j = 0; j != n_y_dofs; ++j) (*Kuy)(i,j) += JxWxPhiIxDUDYoverDT * psi[j][qp]; Number JxWxPhiIxDUDZoverDT = JxWxPhiIoverDT * grad_u(2); for (unsigned int j = 0; j != n_z_dofs; ++j) (*Kuz)(i,j) += JxWxPhiIxDUDZoverDT * psi[j][qp]; } } } } #endif // 0 return request_jacobian; }
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 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; }
double AbstractFunctionalCalculator<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>::CalculateOnElement(Element<ELEMENT_DIM, SPACE_DIM>& rElement) { double result_on_element = 0; // Third order quadrature. Note that the functional may be non-polynomial (see documentation of class). GaussianQuadratureRule<ELEMENT_DIM> quad_rule(3); /// NOTE: This assumes that the Jacobian is constant on an element, ie /// no curvilinear bases were used for position double jacobian_determinant; c_matrix<double, SPACE_DIM, ELEMENT_DIM> jacobian; c_matrix<double, ELEMENT_DIM, SPACE_DIM> inverse_jacobian; rElement.CalculateInverseJacobian(jacobian, jacobian_determinant, inverse_jacobian); const unsigned num_nodes = rElement.GetNumNodes(); // Loop over Gauss points for (unsigned quad_index=0; quad_index < quad_rule.GetNumQuadPoints(); quad_index++) { const ChastePoint<ELEMENT_DIM>& quad_point = quad_rule.rGetQuadPoint(quad_index); c_vector<double, ELEMENT_DIM+1> phi; LinearBasisFunction<ELEMENT_DIM>::ComputeBasisFunctions(quad_point, phi); c_matrix<double, ELEMENT_DIM, ELEMENT_DIM+1> grad_phi; LinearBasisFunction<ELEMENT_DIM>::ComputeTransformedBasisFunctionDerivatives(quad_point, inverse_jacobian, grad_phi); // Location of the Gauss point in the original element will be stored in x ChastePoint<SPACE_DIM> x(0,0,0); c_vector<double,PROBLEM_DIM> u = zero_vector<double>(PROBLEM_DIM); c_matrix<double,PROBLEM_DIM,SPACE_DIM> grad_u = zero_matrix<double>(PROBLEM_DIM,SPACE_DIM); for (unsigned i=0; i<num_nodes; i++) { const c_vector<double, SPACE_DIM>& r_node_loc = rElement.GetNode(i)->rGetLocation(); // Interpolate x x.rGetLocation() += phi(i)*r_node_loc; // Interpolate u and grad u unsigned node_global_index = rElement.GetNodeGlobalIndex(i); for (unsigned index_of_unknown=0; index_of_unknown<PROBLEM_DIM; index_of_unknown++) { // NOTE - following assumes that, if say there are two unknowns u and v, they // are stored in the current solution vector as // [U1 V1 U2 V2 ... U_n V_n] unsigned index_into_vec = PROBLEM_DIM*node_global_index + index_of_unknown; double u_at_node = mSolutionReplicated[index_into_vec]; u(index_of_unknown) += phi(i)*u_at_node; for (unsigned j=0; j<SPACE_DIM; j++) { grad_u(index_of_unknown,j) += grad_phi(j,i)*u_at_node; } } } double wJ = jacobian_determinant * quad_rule.GetWeight(quad_index); result_on_element += GetIntegrand(x, u, grad_u) * wJ; } return result_on_element; }
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; }