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 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;
}