void HeatTransfer::element_time_derivative( bool compute_jacobian,
libMesh::FEMContext& context,
CachedValues& /*cache*/ )
{
#ifdef GRINS_USE_GRVY_TIMERS
this->_timer->BeginTimer("HeatTransfer::element_time_derivative");
#endif
// The number of local degrees of freedom in each variable.
const unsigned int n_T_dofs = context.dof_indices_var[_T_var].size();
const unsigned int n_u_dofs = context.dof_indices_var[_u_var].size();
//TODO: check n_T_dofs is same as n_u_dofs, n_v_dofs, n_w_dofs
// We get some references to cell-specific data that
// will be used to assemble the linear system.
// Element Jacobian * quadrature weights for interior integration.
const std::vector<libMesh::Real> &JxW =
context.element_fe_var[_T_var]->get_JxW();
// The temperature shape functions at interior quadrature points.
const std::vector<std::vector<libMesh::Real> >& T_phi =
context.element_fe_var[_T_var]->get_phi();
// The velocity shape functions at interior quadrature points.
const std::vector<std::vector<libMesh::Real> >& vel_phi =
context.element_fe_var[_u_var]->get_phi();
// The temperature shape function gradients (in global coords.)
// at interior quadrature points.
const std::vector<std::vector<libMesh::RealGradient> >& T_gradphi =
context.element_fe_var[_T_var]->get_dphi();
const std::vector<libMesh::Point>& u_qpoint =
context.element_fe_var[this->_u_var]->get_xyz();
// We do this in the incompressible Navier-Stokes class and need to do it here too
// since _w_var won't have been defined in the global map.
if (_dim != 3)
_w_var = _u_var; // for convenience
libMesh::DenseSubMatrix<libMesh::Number> &KTT = *context.elem_subjacobians[_T_var][_T_var]; // R_{T},{T}
libMesh::DenseSubMatrix<libMesh::Number> &KTu = *context.elem_subjacobians[_T_var][_u_var]; // R_{T},{u}
libMesh::DenseSubMatrix<libMesh::Number> &KTv = *context.elem_subjacobians[_T_var][_v_var]; // R_{T},{v}
libMesh::DenseSubMatrix<libMesh::Number> &KTw = *context.elem_subjacobians[_T_var][_w_var]; // R_{T},{w}
libMesh::DenseSubVector<libMesh::Number> &FT = *context.elem_subresiduals[_T_var]; // R_{T}
// Now we will build the element Jacobian and residual.
// Constructing the residual requires the solution and its
// gradient from the previous timestep. This must be
// calculated at each quadrature point by summing the
// solution degree-of-freedom values by the appropriate
// weight functions.
unsigned int n_qpoints = context.element_qrule->n_points();
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
// Compute the solution & its gradient at the old Newton iterate.
libMesh::Number u, v, w;
u = context.interior_value(_u_var, qp);
v = context.interior_value(_v_var, qp);
if (_dim == 3)
w = context.interior_value(_w_var, qp);
libMesh::Gradient grad_T;
grad_T = context.interior_gradient(_T_var, qp);
libMesh::NumberVectorValue U (u,v);
if (_dim == 3)
U(2) = w;
const libMesh::Number r = u_qpoint[qp](0);
libMesh::Real jac = JxW[qp];
if( _is_axisymmetric )
{
jac *= r;
}
// First, an i-loop over the degrees of freedom.
for (unsigned int i=0; i != n_T_dofs; i++)
{
FT(i) += jac *
(-_rho*_Cp*T_phi[i][qp]*(U*grad_T) // convection term
-_k*(T_gradphi[i][qp]*grad_T) ); // diffusion term
if (compute_jacobian)
{
for (unsigned int j=0; j != n_T_dofs; j++)
{
// TODO: precompute some terms like:
// _rho*_Cp*T_phi[i][qp]*(vel_phi[j][qp]*T_grad_phi[j][qp])
KTT(i,j) += jac *
(-_rho*_Cp*T_phi[i][qp]*(U*T_gradphi[j][qp]) // convection term
-_k*(T_gradphi[i][qp]*T_gradphi[j][qp])); // diffusion term
} // end of the inner dof (j) loop
// Matrix contributions for the Tu, Tv and Tw couplings (n_T_dofs same as n_u_dofs, n_v_dofs and n_w_dofs)
for (unsigned int j=0; j != n_u_dofs; j++)
{
KTu(i,j) += jac*(-_rho*_Cp*T_phi[i][qp]*(vel_phi[j][qp]*grad_T(0)));
KTv(i,j) += jac*(-_rho*_Cp*T_phi[i][qp]*(vel_phi[j][qp]*grad_T(1)));
if (_dim == 3)
KTw(i,j) += jac*(-_rho*_Cp*T_phi[i][qp]*(vel_phi[j][qp]*grad_T(2)));
} // end of the inner dof (j) loop
} // end - if (compute_jacobian && context.elem_solution_derivative)
} // end of the outer dof (i) loop
} // end of the quadrature point (qp) loop
#ifdef GRINS_USE_GRVY_TIMERS
this->_timer->EndTimer("HeatTransfer::element_time_derivative");
#endif
return;
}
void HeatTransfer::mass_residual( bool compute_jacobian,
libMesh::FEMContext& context,
CachedValues& /*cache*/ )
{
#ifdef GRINS_USE_GRVY_TIMERS
this->_timer->BeginTimer("HeatTransfer::mass_residual");
#endif
// First we get some references to cell-specific data that
// will be used to assemble the linear system.
// Element Jacobian * quadrature weights for interior integration
const std::vector<libMesh::Real> &JxW =
context.element_fe_var[_T_var]->get_JxW();
// The shape functions at interior quadrature points.
const std::vector<std::vector<libMesh::Real> >& phi =
context.element_fe_var[_T_var]->get_phi();
const std::vector<libMesh::Point>& u_qpoint =
context.element_fe_var[this->_u_var]->get_xyz();
// The number of local degrees of freedom in each variable
const unsigned int n_T_dofs = context.dof_indices_var[_T_var].size();
// The subvectors and submatrices we need to fill:
libMesh::DenseSubVector<libMesh::Real> &F = *context.elem_subresiduals[_T_var];
libMesh::DenseSubMatrix<libMesh::Real> &M = *context.elem_subjacobians[_T_var][_T_var];
unsigned int n_qpoints = context.element_qrule->n_points();
for (unsigned int qp = 0; qp != n_qpoints; ++qp)
{
// For the mass residual, we need to be a little careful.
// The time integrator is handling the time-discretization
// for us so we need to supply M(u_fixed)*u for the residual.
// u_fixed will be given by the fixed_interior_* functions
// while u will be given by the interior_* functions.
libMesh::Real T_dot = context.interior_value(_T_var, qp);
const libMesh::Number r = u_qpoint[qp](0);
libMesh::Real jac = JxW[qp];
if( _is_axisymmetric )
{
jac *= r;
}
for (unsigned int i = 0; i != n_T_dofs; ++i)
{
F(i) += _rho*_Cp*T_dot*phi[i][qp]*jac;
if( compute_jacobian )
{
for (unsigned int j=0; j != n_T_dofs; j++)
{
// We're assuming rho, cp are constant w.r.t. T here.
M(i,j) += _rho*_Cp*phi[j][qp]*phi[i][qp]*jac;
}
}// End of check on Jacobian
} // End of element dof loop
} // End of the quadrature point loop
#ifdef GRINS_USE_GRVY_TIMERS
this->_timer->EndTimer("HeatTransfer::mass_residual");
#endif
return;
}