void LowMachNavierStokesSPGSMStabilization<Mu,SH,TC>::assemble_energy_time_deriv( bool /*compute_jacobian*/,
AssemblyContext& context )
{
// The number of local degrees of freedom in each variable.
const unsigned int n_T_dofs = context.get_dof_indices(this->_temp_vars.T()).size();
// Element Jacobian * quadrature weights for interior integration.
const std::vector<libMesh::Real> &JxW =
context.get_element_fe(this->_temp_vars.T())->get_JxW();
// The temperature shape functions gradients at interior quadrature points.
const std::vector<std::vector<libMesh::RealGradient> >& T_gradphi =
context.get_element_fe(this->_temp_vars.T())->get_dphi();
libMesh::DenseSubVector<libMesh::Number> &FT = context.get_elem_residual(this->_temp_vars.T()); // R_{T}
unsigned int n_qpoints = context.get_element_qrule().n_points();
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
libMesh::Number u, v;
u = context.interior_value(this->_flow_vars.u(), qp);
v = context.interior_value(this->_flow_vars.v(), qp);
libMesh::Gradient grad_T = context.interior_gradient(this->_temp_vars.T(), qp);
libMesh::NumberVectorValue U(u,v);
if (this->mesh_dim(context) == 3)
U(2) = context.interior_value(this->_flow_vars.w(), qp); // w
libMesh::Real T = context.interior_value( this->_temp_vars.T(), qp );
libMesh::Real rho = this->rho( T, this->get_p0_steady( context, qp ) );
libMesh::Real k = this->_k(T);
libMesh::Real cp = this->_cp(T);
libMesh::Number rho_cp = rho*this->_cp(T);
libMesh::FEBase* fe = context.get_element_fe(this->_flow_vars.u());
libMesh::RealGradient g = this->_stab_helper.compute_g( fe, context, qp );
libMesh::RealTensor G = this->_stab_helper.compute_G( fe, context, qp );
libMesh::Real tau_E = this->_stab_helper.compute_tau_energy( context, qp, g, G, rho, U, k, cp, this->_is_steady );
libMesh::Real RE_s = this->compute_res_energy_steady( context, qp );
for (unsigned int i=0; i != n_T_dofs; i++)
{
FT(i) -= rho_cp*tau_E*RE_s*U*T_gradphi[i][qp]*JxW[qp];
}
}
return;
}
void ReactingLowMachNavierStokesStabilizationBase<Mixture,Evaluator>::compute_res_transient( AssemblyContext& context,
unsigned int qp,
libMesh::Real& RP_t,
libMesh::RealGradient& RM_t,
libMesh::Real& RE_t,
std::vector<libMesh::Real>& Rs_t )
{
libMesh::Real T = context.interior_value( this->_temp_vars.T(), qp );
std::vector<libMesh::Real> 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);
}
Evaluator gas_evaluator( this->_gas_mixture );
const libMesh::Real R_mix = gas_evaluator.R_mix(ws);
const libMesh::Real p0 = this->get_p0_transient(context,qp);
const libMesh::Real rho = this->rho(T, p0, R_mix);
const libMesh::Real cp = gas_evaluator.cp(T,p0,ws);
const libMesh::Real M = gas_evaluator.M_mix( ws );
// M_dot = -M^2 \sum_s w_dot[s]/Ms
libMesh::Real M_dot = 0.0;
std::vector<libMesh::Real> ws_dot(this->n_species());
for(unsigned int s=0; s < this->n_species(); s++)
{
context.interior_rate(this->_species_vars.species(s), qp, ws_dot[s]);
// Start accumulating M_dot
M_dot += ws_dot[s]/this->_gas_mixture.M(s);
}
libMesh::Real M_dot_over_M = M_dot*(-M);
libMesh::RealGradient u_dot;
context.interior_rate(this->_flow_vars.u(), qp, u_dot(0));
context.interior_rate(this->_flow_vars.v(), qp, u_dot(1));
if(this->mesh_dim(context) == 3)
context.interior_rate(this->_flow_vars.w(), qp, u_dot(2));
libMesh::Real T_dot;
context.interior_rate(this->_temp_vars.T(), qp, T_dot);
RP_t = -T_dot/T + M_dot_over_M;
RM_t = rho*u_dot;
RE_t = rho*cp*T_dot;
for(unsigned int s=0; s < this->n_species(); s++)
{
Rs_t[s] = rho*ws_dot[s];
}
return;
}
void LowMachNavierStokesSPGSMStabilization<Mu,SH,TC>::assemble_continuity_time_deriv( bool /*compute_jacobian*/,
AssemblyContext& context )
{
// 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();
// Element Jacobian * quadrature weights for interior integration.
const std::vector<libMesh::Real> &JxW =
context.get_element_fe(this->_flow_vars.u())->get_JxW();
// The pressure shape functions at interior quadrature points.
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}
unsigned int n_qpoints = context.get_element_qrule().n_points();
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
libMesh::FEBase* fe = context.get_element_fe(this->_flow_vars.u());
libMesh::RealGradient g = this->_stab_helper.compute_g( fe, context, qp );
libMesh::RealTensor G = this->_stab_helper.compute_G( fe, context, qp );
libMesh::Real T = context.interior_value( this->_temp_vars.T(), qp );
libMesh::Real mu = this->_mu(T);
libMesh::Real rho = this->rho( T, this->get_p0_steady( 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 );
libMesh::Real tau_M = this->_stab_helper.compute_tau_momentum( context, qp, g, G, rho, U, mu, this->_is_steady );
libMesh::RealGradient RM_s = this->compute_res_momentum_steady( context, qp );
// 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) += tau_M*RM_s*p_dphi[i][qp]*JxW[qp];
}
}
return;
}
void HeatTransferSPGSMStabilization<K>::element_time_derivative
( bool compute_jacobian, AssemblyContext & context )
{
// The number of local degrees of freedom in each variable.
const unsigned int n_T_dofs = context.get_dof_indices(this->_temp_vars.T()).size();
// Element Jacobian * quadrature weights for interior integration.
const std::vector<libMesh::Real> &JxW =
context.get_element_fe(this->_temp_vars.T())->get_JxW();
const std::vector<std::vector<libMesh::RealGradient> >& T_gradphi =
context.get_element_fe(this->_temp_vars.T())->get_dphi();
libMesh::DenseSubVector<libMesh::Number> &FT = context.get_elem_residual(this->_temp_vars.T()); // R_{T}
libMesh::FEBase* fe = context.get_element_fe(this->_temp_vars.T());
unsigned int n_qpoints = context.get_element_qrule().n_points();
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->_flow_vars.dim() == 3 )
{
U(2) = context.interior_value( this->_flow_vars.w(), qp );
}
// Compute Conductivity at this qp
libMesh::Real _k_qp = this->_k(context, qp);
libMesh::Real tau_E = this->_stab_helper.compute_tau_energy( context, G, this->_rho, this->_Cp, _k_qp, U, this->_is_steady );
libMesh::Real RE_s = this->_stab_helper.compute_res_energy_steady( context, qp, this->_rho, this->_Cp, _k_qp );
for (unsigned int i=0; i != n_T_dofs; i++)
{
FT(i) += -tau_E*RE_s*this->_rho*this->_Cp*U*T_gradphi[i][qp]*JxW[qp];
}
if( compute_jacobian )
{
libmesh_not_implemented();
}
}
}
libMesh::Real SpalartAllmarasStabilizationHelper::compute_res_spalart_steady( AssemblyContext& context,
unsigned int qp, const libMesh::Real rho, const libMesh::Real mu, const libMesh::Real distance_qp, const bool infinite_distance) const
{
// The flow velocity
libMesh::Number u,v;
u = context.interior_value(this->_flow_vars.u(), qp);
v = context.interior_value(this->_flow_vars.v(), qp);
libMesh::NumberVectorValue U(u,v);
if ( this->_flow_vars.dim() == 3 )
U(2) = context.interior_value(this->_flow_vars.w(), qp);
libMesh::RealGradient grad_u = context.fixed_interior_gradient(this->_flow_vars.u(), qp);
libMesh::RealGradient grad_v = context.fixed_interior_gradient(this->_flow_vars.v(), qp);
libMesh::Number nu_value = context.interior_value(this->_turbulence_vars.nu(), qp);
libMesh::RealGradient grad_nu = context.fixed_interior_gradient(this->_turbulence_vars.nu(), qp);
libMesh::RealTensor hess_nu = context.fixed_interior_hessian(this->_turbulence_vars.nu(), qp);
// The convection term
libMesh::Number rhoUdotGradnu = rho*(U*grad_nu);
// The diffusion term
libMesh::Number inv_sigmadivnuplusnuphysicalGradnu = (1./this->_sa_params.get_sigma())*(grad_nu*grad_nu + ((nu_value + mu)*(hess_nu(0,0) + hess_nu(1,1) + (this->_flow_vars.dim() == 3)?hess_nu(2,2):0)) + this->_sa_params.get_cb2()*grad_nu*grad_nu);
// The source term
libMesh::Real vorticity_value_qp = this->_spalart_allmaras_helper.vorticity(context, qp);
libMesh::Real S_tilde = this->_sa_params.source_fn(nu_value, mu, distance_qp, vorticity_value_qp, infinite_distance);
libMesh::Real source_term = this->_sa_params.get_cb1()*S_tilde*nu_value;
libMesh::Real kappa2 = (this->_sa_params.get_kappa())*(this->_sa_params.get_kappa());
libMesh::Real cw1 = this->_sa_params.get_cb1()/kappa2 + (1.0 + this->_sa_params.get_cb2())/this->_sa_params.get_sigma();
// The destruction term
libMesh::Real fw = this->_sa_params.destruction_fn(nu_value, distance_qp, S_tilde, infinite_distance);
libMesh::Real destruction_term = 0.0;
if(infinite_distance)
{
destruction_term = 0.0;
}
else
{
destruction_term = cw1*fw*pow(nu_value/distance_qp, 2.);
}
return rhoUdotGradnu + source_term + inv_sigmadivnuplusnuphysicalGradnu - destruction_term;
}
void LowMachNavierStokes<Mu,SH,TC>::assemble_thermo_press_mass_residual( bool /*compute_jacobian*/,
AssemblyContext& context )
{
// The number of local degrees of freedom in each variable.
const unsigned int n_p0_dofs = context.get_dof_indices(this->_p0_var).size();
const unsigned int n_T_dofs = context.get_dof_indices(this->_T_var).size();
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->_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(this->_T_var)->get_phi();
// The temperature shape functions at interior quadrature points.
const std::vector<std::vector<libMesh::Real> >& p_phi =
context.get_element_fe(this->_p_var)->get_phi();
// The subvectors and submatrices we need to fill:
libMesh::DenseSubVector<libMesh::Real> &F_p0 = context.get_elem_residual(this->_p0_var);
libMesh::DenseSubVector<libMesh::Real> &F_T = context.get_elem_residual(this->_T_var);
libMesh::DenseSubVector<libMesh::Real> &F_p = context.get_elem_residual(this->_p_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.fixed_interior_value(this->_T_var, qp);
libMesh::Number cp = this->_cp(T);
libMesh::Number cv = cp + this->_R;
libMesh::Number gamma = cp/cv;
libMesh::Number one_over_gamma = 1.0/(gamma-1.0);
libMesh::Number p0_dot = context.interior_value(this->_p0_var, qp );
libMesh::Number p0 = context.fixed_interior_value(this->_p0_var, qp );
for (unsigned int i=0; i != n_p0_dofs; i++)
{
F_p0(i) += p0_dot*one_over_gamma*JxW[qp];
}
for (unsigned int i=0; i != n_T_dofs; i++)
{
F_T(i) -= p0_dot*T_phi[i][qp]*JxW[qp];
}
for (unsigned int i=0; i != n_p_dofs; i++)
{
F_p(i) -= p0_dot/p0*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;
}
libMesh::Real HeatTransferStabilizationHelper::compute_res_energy_transient( AssemblyContext& context,
unsigned int qp,
const libMesh::Real rho,
const libMesh::Real Cp ) const
{
libMesh::Real T_dot = context.interior_value(this->_temp_vars.T_var(), qp);
return rho*Cp*T_dot;
}
void HeatTransferStabilizationHelper::compute_res_energy_transient_and_derivs
( AssemblyContext& context,
unsigned int qp,
const libMesh::Real rho,
const libMesh::Real Cp,
libMesh::Real &res,
libMesh::Real &d_res_dTdot
) const
{
libMesh::Real T_dot = context.interior_value(this->_temp_vars.T_var(), qp);
res = rho*Cp*T_dot;
d_res_dTdot = rho*Cp;
}
void LowMachNavierStokes<Mu,SH,TC>::assemble_energy_mass_residual( 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 shape functions at interior quadrature points.
const std::vector<std::vector<libMesh::Real> >& T_phi =
context.get_element_fe(this->_T_var)->get_phi();
// The number of local degrees of freedom in each variable
const unsigned int n_T_dofs = context.get_dof_indices(this->_T_var).size();
// The subvectors and submatrices we need to fill:
libMesh::DenseSubVector<libMesh::Real> &F_T = context.get_elem_residual(this->_T_var);
unsigned int n_qpoints = context.get_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(this->_T_var, qp);
libMesh::Real T = context.fixed_interior_value(this->_T_var, qp);
libMesh::Real cp = this->_cp(T);
libMesh::Number rho = this->rho(T, this->get_p0_transient(context, qp));
for (unsigned int i = 0; i != n_T_dofs; ++i)
{
F_T(i) += rho*cp*T_dot*T_phi[i][qp]*JxW[qp];
} // End DoF loop i
} // End quadrature loop qp
return;
}
libMesh::Real SpalartAllmarasStabilizationHelper::compute_res_spalart_transient( AssemblyContext& context, unsigned int qp, const libMesh::Real rho ) const
{
libMesh::Number nu_dot = context.interior_value(this->_turbulence_vars.nu_var(), qp);
return rho*nu_dot;
}
void HeatTransfer::element_time_derivative( bool compute_jacobian,
AssemblyContext& 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.get_dof_indices(_temp_vars.T_var()).size();
const unsigned int n_u_dofs = context.get_dof_indices(_flow_vars.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.get_element_fe(_temp_vars.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(_temp_vars.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(_flow_vars.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.get_element_fe(_temp_vars.T_var())->get_dphi();
const std::vector<libMesh::Point>& u_qpoint =
context.get_element_fe(this->_flow_vars.u_var())->get_xyz();
libMesh::DenseSubMatrix<libMesh::Number> &KTT = context.get_elem_jacobian(_temp_vars.T_var(), _temp_vars.T_var()); // R_{T},{T}
libMesh::DenseSubMatrix<libMesh::Number> &KTu = context.get_elem_jacobian(_temp_vars.T_var(), _flow_vars.u_var()); // R_{T},{u}
libMesh::DenseSubMatrix<libMesh::Number> &KTv = context.get_elem_jacobian(_temp_vars.T_var(), _flow_vars.v_var()); // R_{T},{v}
libMesh::DenseSubMatrix<libMesh::Number>* KTw = NULL;
libMesh::DenseSubVector<libMesh::Number> &FT = context.get_elem_residual(_temp_vars.T_var()); // R_{T}
if( this->_dim == 3 )
{
KTw = &context.get_elem_jacobian(_temp_vars.T_var(), _flow_vars.w_var()); // R_{T},{w}
}
// 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 u, v;
u = context.interior_value(_flow_vars.u_var(), qp);
v = context.interior_value(_flow_vars.v_var(), qp);
libMesh::Gradient grad_T;
grad_T = context.interior_gradient(_temp_vars.T_var(), qp);
libMesh::NumberVectorValue U (u,v);
if (_dim == 3)
U(2) = context.interior_value(_flow_vars.w_var(), qp);
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.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("HeatTransfer::element_time_derivative");
#endif
return;
}
void AveragedTurbine<Mu>::element_time_derivative( bool compute_jacobian,
AssemblyContext& context,
CachedValues& /* cache */ )
{
#ifdef GRINS_USE_GRVY_TIMERS
this->_timer->BeginTimer("AveragedTurbine::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())->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())->get_phi();
const std::vector<libMesh::Point>& u_qpoint =
context.get_element_fe(this->_flow_vars.u())->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()).size();
// The subvectors and submatrices we need to fill:
libMesh::DenseSubMatrix<libMesh::Number> &Kuu = context.get_elem_jacobian(this->_flow_vars.u(), this->_flow_vars.u()); // R_{u},{u}
libMesh::DenseSubMatrix<libMesh::Number> &Kuv = context.get_elem_jacobian(this->_flow_vars.u(), this->_flow_vars.v()); // R_{u},{v}
libMesh::DenseSubMatrix<libMesh::Number> &Kvu = context.get_elem_jacobian(this->_flow_vars.v(), this->_flow_vars.u()); // R_{v},{u}
libMesh::DenseSubMatrix<libMesh::Number> &Kvv = context.get_elem_jacobian(this->_flow_vars.v(), this->_flow_vars.v()); // R_{v},{v}
libMesh::DenseSubMatrix<libMesh::Number> &Kus =
context.get_elem_jacobian(this->_flow_vars.u(),
this->fan_speed_var()); // R_{u},{s}
libMesh::DenseSubMatrix<libMesh::Number> &Ksu =
context.get_elem_jacobian(this->fan_speed_var(),
this->_flow_vars.u()); // R_{s},{u}
libMesh::DenseSubMatrix<libMesh::Number> &Kvs =
context.get_elem_jacobian(this->_flow_vars.v(),
this->fan_speed_var()); // R_{v},{s}
libMesh::DenseSubMatrix<libMesh::Number> &Ksv =
context.get_elem_jacobian(this->fan_speed_var(),
this->_flow_vars.v()); // R_{s},{v}
libMesh::DenseSubMatrix<libMesh::Number> &Kss =
context.get_elem_jacobian(this->fan_speed_var(),
this->fan_speed_var()); // R_{s},{s}
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::DenseSubMatrix<libMesh::Number>* Ksw = NULL;
libMesh::DenseSubMatrix<libMesh::Number>* Kws = NULL;
libMesh::DenseSubVector<libMesh::Number> &Fu = context.get_elem_residual(this->_flow_vars.u()); // R_{u}
libMesh::DenseSubVector<libMesh::Number> &Fv = context.get_elem_residual(this->_flow_vars.v()); // R_{v}
libMesh::DenseSubVector<libMesh::Number>* Fw = NULL;
libMesh::DenseSubVector<libMesh::Number> &Fs = context.get_elem_residual(this->fan_speed_var()); // R_{s}
if( this->mesh_dim(context) == 3 )
{
Kuw = &context.get_elem_jacobian(this->_flow_vars.u(), this->_flow_vars.w()); // R_{u},{w}
Kvw = &context.get_elem_jacobian(this->_flow_vars.v(), this->_flow_vars.w()); // R_{v},{w}
Kwu = &context.get_elem_jacobian(this->_flow_vars.w(), this->_flow_vars.u()); // R_{w},{u}
Kwv = &context.get_elem_jacobian(this->_flow_vars.w(), this->_flow_vars.v()); // R_{w},{v}
Kww = &context.get_elem_jacobian(this->_flow_vars.w(), this->_flow_vars.w()); // R_{w},{w}
Fw = &context.get_elem_residual(this->_flow_vars.w()); // R_{w}
Ksw = &context.get_elem_jacobian(this->fan_speed_var(), this->_flow_vars.w()); // R_{s},{w}
Kws = &context.get_elem_jacobian(this->_flow_vars.w(), this->fan_speed_var()); // R_{w},{s}
Fw = &context.get_elem_residual(this->_flow_vars.w()); // 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, s;
u = context.interior_value(this->_flow_vars.u(), qp);
v = context.interior_value(this->_flow_vars.v(), qp);
s = context.interior_value(this->fan_speed_var(), qp);
libMesh::NumberVectorValue U(u,v);
if (this->mesh_dim(context) == 3)
U(2) = context.interior_value(this->_flow_vars.w(), qp); // w
libMesh::NumberVectorValue U_B_1;
libMesh::NumberVectorValue F;
libMesh::NumberTensorValue dFdU;
libMesh::NumberTensorValue* dFdU_ptr =
compute_jacobian ? &dFdU : NULL;
libMesh::NumberVectorValue dFds;
libMesh::NumberVectorValue* dFds_ptr =
compute_jacobian ? &dFds : NULL;
if (!this->compute_force(u_qpoint[qp], context.time, U, s,
U_B_1, F, dFdU_ptr, dFds_ptr))
continue;
libMesh::Real jac = JxW[qp];
// Using this dot product to derive torque *depends* on s=1
// and U_B_1 corresponding to 1 rad/sec base velocity; this
// means that the length of U_B_1 is equal to radius.
// F is the force on the air, so *negative* F is the force on
// the turbine.
Fs(0) -= U_B_1 * F * jac;
if (compute_jacobian)
{
Kss(0,0) -= U_B_1 * dFds * jac;
for (unsigned int j=0; j != n_u_dofs; j++)
{
libMesh::Real jac_j = JxW[qp] * u_phi[j][qp];
for (unsigned int d=0; d != 3; ++d)
{
Ksu(0,j) -= jac_j * U_B_1(d) * dFdU(d,0);
Ksv(0,j) -= jac_j * U_B_1(d) * dFdU(d,1);
}
if (this->mesh_dim(context) == 3)
{
for (unsigned int d=0; d != 3; ++d)
(*Ksw)(0,j) -= jac_j * U_B_1(d) * dFdU(d,2);
}
} // End j dof loop
}
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->mesh_dim(context) == 3 )
(*Fw)(i) += F(2)*jac_i;
if( compute_jacobian )
{
Kus(i,0) += dFds(0) * jac_i;
Kvs(i,0) += dFds(1) * jac_i;
if( this->mesh_dim(context) == 3 )
(*Kws)(i,0) += dFds(2) * jac_i;
for (unsigned int j=0; j != n_u_dofs; j++)
{
const libMesh::Number jac_ij = 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->mesh_dim(context) == 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("AveragedTurbine::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 PracticeCDRinv::element_time_derivative( bool compute_jacobian,
AssemblyContext& context,
CachedValues& /*cache*/ ){
// The number of local degrees of freedom in each variable.
const unsigned int n_c_dofs = context.get_dof_indices(_c_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(_c_var)->get_JxW();
// The temperature shape function gradients (in global coords.)
// at interior quadrature points.
const std::vector<std::vector<libMesh::RealGradient> >& dphi =
context.get_element_fe(_c_var)->get_dphi();
const std::vector<std::vector<libMesh::Real> >& phi = context.get_element_fe(_c_var)->get_phi();
const std::vector<libMesh::Point>& q_points =
context.get_element_fe(_c_var)->get_xyz();
libMesh::DenseSubMatrix<libMesh::Number> &J_c_zc = context.get_elem_jacobian(_c_var, _zc_var);
libMesh::DenseSubMatrix<libMesh::Number> &J_c_c = context.get_elem_jacobian(_c_var, _c_var);
libMesh::DenseSubMatrix<libMesh::Number> &J_zc_c = context.get_elem_jacobian(_zc_var, _c_var);
libMesh::DenseSubMatrix<libMesh::Number> &J_zc_fc = context.get_elem_jacobian(_zc_var, _fc_var);
libMesh::DenseSubMatrix<libMesh::Number> &J_fc_zc = context.get_elem_jacobian(_fc_var, _zc_var);
libMesh::DenseSubMatrix<libMesh::Number> &J_fc_fc = context.get_elem_jacobian(_fc_var, _fc_var);
libMesh::DenseSubVector<libMesh::Number> &Rc = context.get_elem_residual( _c_var );;
libMesh::DenseSubVector<libMesh::Number> &Rzc = context.get_elem_residual( _zc_var );
libMesh::DenseSubVector<libMesh::Number> &Rfc = context.get_elem_residual( _fc_var );
// 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++){
libMesh::Number
c = context.interior_value(_c_var, qp),
zc = context.interior_value(_zc_var, qp),
fc = context.interior_value(_fc_var, qp);
libMesh::Gradient
grad_c = context.interior_gradient(_c_var, qp),
grad_zc = context.interior_gradient(_zc_var, qp),
grad_fc = context.interior_gradient(_fc_var, qp);
//location of quadrature point
const libMesh::Real ptx = q_points[qp](0);
const libMesh::Real pty = q_points[qp](1);
int xind, yind;
libMesh::Real xdist = 1.e10; libMesh::Real ydist = 1.e10;
for(int ii=0; ii<x_pts.size(); ii++){
libMesh::Real tmp = std::abs(ptx - x_pts[ii]);
if(xdist > tmp){
xdist = tmp;
xind = ii;
}
else
break;
}
for(int jj=0; jj<y_pts[xind].size(); jj++){
libMesh::Real tmp = std::abs(pty - y_pts[xind][jj]);
if(ydist > tmp){
ydist = tmp;
yind = jj;
}
else
break;
}
libMesh::Real u = vel_field[xind][yind](0);
libMesh::Real v = vel_field[xind][yind](1);
libMesh::NumberVectorValue U (u, v);
// First, an i-loop over the degrees of freedom.
for (unsigned int i=0; i != n_c_dofs; i++){
Rc(i) += JxW[qp]*(-_k*grad_zc*dphi[i][qp] + U*grad_zc*phi[i][qp] + 2*_R*zc*c*phi[i][qp]);
Rzc(i) += JxW[qp]*(-_k*grad_c*dphi[i][qp] - U*grad_c*phi[i][qp] + _R*c*c*phi[i][qp] + fc*phi[i][qp]);
Rfc(i) += JxW[qp]*(_beta*grad_fc*dphi[i][qp] + zc*phi[i][qp]);
if (compute_jacobian){
for (unsigned int j=0; j != n_c_dofs; j++){
J_c_zc(i,j) += JxW[qp]*(-_k*dphi[j][qp]*dphi[i][qp] + U*dphi[j][qp]*phi[i][qp]
+ 2*_R*phi[j][qp]*c*phi[i][qp]);
J_c_c(i,j) += JxW[qp]*(2*_R*zc*phi[j][qp]*phi[i][qp]);
J_zc_c(i,j) += JxW[qp]*(-_k*dphi[j][qp]*dphi[i][qp] - U*dphi[j][qp]*phi[i][qp]
+ 2*_R*c*phi[j][qp]*phi[i][qp]);
J_zc_fc(i,j) += JxW[qp]*(phi[j][qp]*phi[i][qp]);
J_fc_zc(i,j) += JxW[qp]*(phi[j][qp]*phi[i][qp]);
J_fc_fc(i,j) += JxW[qp]*(_beta*dphi[j][qp]*dphi[i][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
for(unsigned int dnum=0; dnum<datavals.size(); dnum++){
libMesh::Point data_point = datapts[dnum];
if(context.get_elem().contains_point(data_point)){
libMesh::Number cpred = context.point_value(_c_var, data_point);
libMesh::Number cstar = datavals[dnum];
unsigned int dim = context.get_system().get_mesh().mesh_dimension();
libMesh::FEType fe_type = context.get_element_fe(_c_var)->get_fe_type();
//go between physical and reference element
libMesh::Point c_master = libMesh::FEInterface::inverse_map(dim, fe_type, &context.get_elem(), data_point);
std::vector<libMesh::Real> point_phi(n_c_dofs);
for (unsigned int i=0; i != n_c_dofs; i++){
//get value of basis function at mapped point in reference (master) element
point_phi[i] = libMesh::FEInterface::shape(dim, fe_type, &context.get_elem(), i, c_master);
}
for (unsigned int i=0; i != n_c_dofs; i++){
Rc(i) += (cpred - cstar)*point_phi[i];
if (compute_jacobian){
for (unsigned int j=0; j != n_c_dofs; j++)
J_c_c(i,j) += point_phi[j]*point_phi[i] ;
}
}
}
}
return;
}
void LowMachNavierStokesSPGSMStabilization<Mu,SH,TC>::assemble_momentum_time_deriv( 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(this->_flow_vars.u()).size();
// Check number of dofs is same for _flow_vars.u(), v_var and w_var.
libmesh_assert (n_u_dofs == context.get_dof_indices(this->_flow_vars.v()).size());
if (this->mesh_dim(context) == 3)
libmesh_assert (n_u_dofs == context.get_dof_indices(this->_flow_vars.w()).size());
// Element Jacobian * quadrature weights for interior integration.
const std::vector<libMesh::Real> &JxW =
context.get_element_fe(this->_flow_vars.u())->get_JxW();
// The velocity shape function gradients at interior quadrature points.
const std::vector<std::vector<libMesh::RealGradient> >& u_gradphi =
context.get_element_fe(this->_flow_vars.u())->get_dphi();
libMesh::DenseSubVector<libMesh::Number> &Fu = context.get_elem_residual(this->_flow_vars.u()); // R_{u}
libMesh::DenseSubVector<libMesh::Number> &Fv = context.get_elem_residual(this->_flow_vars.v()); // R_{v}
libMesh::DenseSubVector<libMesh::Real>* Fw = NULL;
if( this->mesh_dim(context) == 3 )
{
Fw = &context.get_elem_residual(this->_flow_vars.w()); // R_{w}
}
unsigned int n_qpoints = context.get_element_qrule().n_points();
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
libMesh::Real T = context.interior_value( this->_temp_vars.T(), qp );
libMesh::Real rho = this->rho( T, this->get_p0_steady( context, qp ) );
libMesh::RealGradient U( context.interior_value(this->_flow_vars.u(), qp),
context.interior_value(this->_flow_vars.v(), 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 grad_w;
if( this->mesh_dim(context) == 3 )
{
U(2) = context.interior_value(this->_flow_vars.w(), qp);
grad_w = context.interior_gradient(this->_flow_vars.w(), qp);
}
libMesh::FEBase* fe = context.get_element_fe(this->_flow_vars.u());
libMesh::RealGradient g = this->_stab_helper.compute_g( fe, context, qp );
libMesh::RealTensor G = this->_stab_helper.compute_G( fe, context, qp );
libMesh::Real mu = this->_mu(T);
libMesh::Real tau_M = this->_stab_helper.compute_tau_momentum( context, qp, g, G, rho, U, mu, this->_is_steady );
libMesh::Real tau_C = this->_stab_helper.compute_tau_continuity( tau_M, g );
libMesh::Real RC_s = this->compute_res_continuity_steady( context, qp );
libMesh::RealGradient RM_s = this->compute_res_momentum_steady( context, qp );
for (unsigned int i=0; i != n_u_dofs; i++)
{
Fu(i) += ( - tau_C*RC_s*u_gradphi[i][qp](0)
- tau_M*RM_s(0)*rho*U*u_gradphi[i][qp] )*JxW[qp];
Fv(i) += ( - tau_C*RC_s*u_gradphi[i][qp](1)
- tau_M*RM_s(1)*rho*U*u_gradphi[i][qp] )*JxW[qp];
if( this->mesh_dim(context) == 3 )
{
(*Fw)(i) += ( - tau_C*RC_s*u_gradphi[i][qp](2)
- tau_M*RM_s(2)*rho*U*u_gradphi[i][qp] )*JxW[qp];
}
}
}
return;
}
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 LowMachNavierStokes<Mu,SH,TC>::assemble_momentum_mass_residual( bool /*compute_jacobian*/,
AssemblyContext& context )
{
// Element Jacobian * quadrature weights for interior integration
const std::vector<libMesh::Real> &JxW =
context.get_element_fe(this->_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->_u_var)->get_phi();
// The number of local degrees of freedom in each variable
const unsigned int n_u_dofs = context.get_dof_indices(this->_u_var).size();
// for convenience
if (this->_dim != 3)
this->_w_var = this->_u_var;
// The subvectors and submatrices we need to fill:
libMesh::DenseSubVector<libMesh::Real> &F_u = context.get_elem_residual(this->_u_var);
libMesh::DenseSubVector<libMesh::Real> &F_v = context.get_elem_residual(this->_v_var);
libMesh::DenseSubVector<libMesh::Real> &F_w = context.get_elem_residual(this->_w_var);
unsigned int n_qpoints = context.get_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 u_dot = context.interior_value(this->_u_var, qp);
libMesh::Real v_dot = context.interior_value(this->_v_var, qp);
libMesh::Real w_dot = 0.0;
if( this->_dim == 3 )
w_dot = context.interior_value(this->_w_var, qp);
libMesh::Real T = context.fixed_interior_value(this->_T_var, qp);
libMesh::Number rho = this->rho(T, this->get_p0_transient(context, qp));
for (unsigned int i = 0; i != n_u_dofs; ++i)
{
F_u(i) += rho*u_dot*u_phi[i][qp]*JxW[qp];
F_v(i) += rho*v_dot*u_phi[i][qp]*JxW[qp];
if( this->_dim == 3 )
F_w(i) += rho*w_dot*u_phi[i][qp]*JxW[qp];
/*
if( compute_jacobian )
{
for (unsigned int j=0; j != n_u_dofs; j++)
{
// Assuming rho is constant w.r.t. u, v, w
// and T (if Boussinesq added).
libMesh::Real value = JxW[qp]*_rho*u_phi[i][qp]*u_phi[j][qp];
M_uu(i,j) += value;
M_vv(i,j) += value;
if( _dim == 3)
{
M_ww(i,j) += value;
}
} // End DoF loop j
} // End Jacobian check
*/
} // End DoF loop i
} // End quadrature loop qp
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 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 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;
}
void LowMachNavierStokes<Mu,SH,TC>::compute_element_time_derivative_cache( const AssemblyContext& context,
CachedValues& cache )
{
const unsigned int n_qpoints = context.get_element_qrule().n_points();
std::vector<libMesh::Real> u, v, w, T, p, p0;
u.resize(n_qpoints);
v.resize(n_qpoints);
if( this->_dim > 2 )
w.resize(n_qpoints);
T.resize(n_qpoints);
p.resize(n_qpoints);
p0.resize(n_qpoints);
std::vector<libMesh::Gradient> grad_u, grad_v, grad_w, grad_T;
grad_u.resize(n_qpoints);
grad_v.resize(n_qpoints);
if( this->_dim > 2 )
grad_w.resize(n_qpoints);
grad_T.resize(n_qpoints);
for (unsigned int qp = 0; qp != n_qpoints; ++qp)
{
u[qp] = context.interior_value(this->_u_var, qp);
v[qp] = context.interior_value(this->_v_var, qp);
grad_u[qp] = context.interior_gradient(this->_u_var, qp);
grad_v[qp] = context.interior_gradient(this->_v_var, qp);
if( this->_dim > 2 )
{
w[qp] = context.interior_value(this->_w_var, qp);
grad_w[qp] = context.interior_gradient(this->_w_var, qp);
}
T[qp] = context.interior_value(this->_T_var, qp);
grad_T[qp] = context.interior_gradient(this->_T_var, qp);
p[qp] = context.interior_value(this->_p_var, qp);
p0[qp] = this->get_p0_steady(context, qp);
}
cache.set_values(Cache::X_VELOCITY, u);
cache.set_values(Cache::Y_VELOCITY, v);
cache.set_gradient_values(Cache::X_VELOCITY_GRAD, grad_u);
cache.set_gradient_values(Cache::Y_VELOCITY_GRAD, grad_v);
if(this->_dim > 2)
{
cache.set_values(Cache::Z_VELOCITY, w);
cache.set_gradient_values(Cache::Z_VELOCITY_GRAD, grad_w);
}
cache.set_values(Cache::TEMPERATURE, T);
cache.set_gradient_values(Cache::TEMPERATURE_GRAD, grad_T);
cache.set_values(Cache::PRESSURE, p);
cache.set_values(Cache::THERMO_PRESSURE, p0);
return;
}
void SpalartAllmarasSPGSMStabilization<Mu>::element_time_derivative
( bool compute_jacobian,
AssemblyContext & context )
{
// Get a pointer to the current element, we need this for computing the distance to wall for the
// quadrature points
libMesh::Elem &elem_pointer = context.get_elem();
// The number of local degrees of freedom in each variable.
const unsigned int n_nu_dofs = context.get_dof_indices(this->_turbulence_vars.nu()).size();
// Element Jacobian * quadrature weights for interior integration.
const std::vector<libMesh::Real> &JxW =
context.get_element_fe(this->_turbulence_vars.nu())->get_JxW();
// The viscosity shape function gradients (in global coords.)
// at interior quadrature points.
const std::vector<std::vector<libMesh::RealGradient> >& nu_gradphi =
context.get_element_fe(this->_turbulence_vars.nu())->get_dphi();
// Quadrature point locations
//const std::vector<libMesh::Point>& nu_qpoint =
//context.get_element_fe(this->_turbulence_vars.nu())->get_xyz();
//libMesh::DenseSubMatrix<libMesh::Number> &Knunu = context.get_elem_jacobian(this->_turbulence_vars.nu(), this->_turbulence_vars.nu()); // R_{nu},{nu}
libMesh::DenseSubVector<libMesh::Number> &Fnu = context.get_elem_residual(this->_turbulence_vars.nu()); // R_{nu}
libMesh::FEBase* fe = context.get_element_fe(this->_turbulence_vars.nu());
unsigned int n_qpoints = context.get_element_qrule().n_points();
// Auto pointer to distance fcn evaluated at quad points
std::unique_ptr< libMesh::DenseVector<libMesh::Real> > distance_qp;
// Fill the vector of distances to quadrature points
distance_qp = this->distance_function->interpolate(&elem_pointer, context.get_element_qrule().get_points());
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
libMesh::Gradient grad_nu;
grad_nu = context.interior_gradient(this->_turbulence_vars.nu(), qp);
libMesh::Real jac = JxW[qp];
// The physical viscosity
libMesh::Real _mu_qp = this->_mu(context, qp);
// To be fixed
// For the channel flow we will just set the distance function analytically
//(*distance_qp)(qp) = std::min(fabs(y),fabs(1 - y));
// The flow velocity
libMesh::Number u,v;
u = context.interior_value(this->_flow_vars.u(), qp);
v = context.interior_value(this->_flow_vars.v(), qp);
libMesh::NumberVectorValue U(u,v);
if (this->_flow_vars.dim() == 3)
U(2) = context.interior_value(this->_flow_vars.w(), qp);
// Stabilization terms
libMesh::RealGradient g = this->_stab_helper.compute_g( fe, context, qp );
libMesh::RealTensor G = this->_stab_helper.compute_G( fe, context, qp );
libMesh::Real tau_spalart = this->_stab_helper.compute_tau_spalart( context, qp, g, G, this->_rho, U, _mu_qp, this->_is_steady );
libMesh::Number RM_spalart = this->_stab_helper.compute_res_spalart_steady( context, qp, this->_rho, _mu_qp, (*distance_qp)(qp), this->_infinite_distance );
for (unsigned int i=0; i != n_nu_dofs; i++)
{
Fnu(i) += jac*( -tau_spalart*RM_spalart*this->_rho*(U*nu_gradphi[i][qp]) );
}
if( compute_jacobian )
{
libmesh_not_implemented();
}
}
}
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 HeatTransfer::mass_residual( bool compute_jacobian,
AssemblyContext& 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.get_element_fe(_temp_vars.T_var())->get_JxW();
// The shape functions at interior quadrature points.
const std::vector<std::vector<libMesh::Real> >& phi =
context.get_element_fe(_temp_vars.T_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_T_dofs = context.get_dof_indices(_temp_vars.T_var()).size();
// The subvectors and submatrices we need to fill:
libMesh::DenseSubVector<libMesh::Real> &F = context.get_elem_residual(_temp_vars.T_var());
libMesh::DenseSubMatrix<libMesh::Real> &M = context.get_elem_jacobian(_temp_vars.T_var(), _temp_vars.T_var());
unsigned int n_qpoints = context.get_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(_temp_vars.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;
}
