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 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 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 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 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 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 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 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 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 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 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;
}