C++ AssemblyContext::get_elem_residual方法代码示例

  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 BoundaryConditions::apply_neumann_normal( AssemblyContext& context,
                                                 const VariableIndex var,
                                                 const libMesh::Real sign,
                                                 const FEShape& value ) const
  {
    libMesh::FEGenericBase<FEShape>* side_fe = NULL; 
    context.get_side_fe( var, side_fe );

    // The number of local degrees of freedom in each variable.
    const unsigned int n_var_dofs = context.get_dof_indices(var).size();

    // Element Jacobian * quadrature weight for side integration.
    const std::vector<libMesh::Real> &JxW_side = side_fe->get_JxW();

    // The var shape functions at side quadrature points.
    const std::vector<std::vector<FEShape> >& var_phi_side = side_fe->get_phi();

    libMesh::DenseSubVector<libMesh::Number> &F_var = context.get_elem_residual(var); // residual

    unsigned int n_qpoints = context.get_side_qrule().n_points();
    for (unsigned int qp=0; qp != n_qpoints; qp++)
      {
	for (unsigned int i=0; i != n_var_dofs; i++)
	  {
	    F_var(i) += sign*value*var_phi_side[i][qp]*JxW_side[qp];
	  }
      }

    return;
  }

  void AveragedTurbine<Mu>::nonlocal_time_derivative(bool compute_jacobian,
				                 AssemblyContext& context,
				                 CachedValues& /* cache */ )
  {
    libMesh::DenseSubMatrix<libMesh::Number> &Kss =
            context.get_elem_jacobian(this->fan_speed_var(), this->fan_speed_var()); // R_{s},{s}

    libMesh::DenseSubVector<libMesh::Number> &Fs =
            context.get_elem_residual(this->fan_speed_var()); // R_{s}

    const std::vector<libMesh::dof_id_type>& dof_indices =
      context.get_dof_indices(this->fan_speed_var());

    const libMesh::Number fan_speed =
      context.get_system().current_solution(dof_indices[0]);

    const libMesh::Number output_torque =
      this->torque_function(libMesh::Point(0), fan_speed);

    Fs(0) += output_torque;

    if (compute_jacobian)
      {
        // FIXME: we should replace this FEM with a hook to the AD fparser stuff
        const libMesh::Number epsilon = 1e-6;
        const libMesh::Number output_torque_deriv =
          (this->torque_function(libMesh::Point(0), fan_speed+epsilon) -
           this->torque_function(libMesh::Point(0), fan_speed-epsilon)) / (2*epsilon);

        Kss(0,0) += output_torque_deriv * context.get_elem_solution_derivative();
      }

    return;
  }

  void HeatConduction<K>::mass_residual( bool compute_jacobian,
				      AssemblyContext& context,
				      CachedValues& /*cache*/ )
  {
    // 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();

    // 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_value function
	// while u' will be given by the interior_rate function.
        libMesh::Real T_dot;
        context.interior_rate(_temp_vars.T_var(), qp, T_dot);

	for (unsigned int i = 0; i != n_T_dofs; ++i)
	  {
	    F(i) -= JxW[qp]*(_rho*_Cp*T_dot*phi[i][qp] );

	    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) -=
                      context.get_elem_solution_rate_derivative()
                        * JxW[qp]*_rho*_Cp*phi[j][qp]*phi[i][qp] ;
                  }
              }// End of check on Jacobian

	  } // End of element dof loop

      } // End of the quadrature point loop

    return;
  }

void LowMachNavierStokesSPGSMStabilization<Mu,SH,TC>::assemble_energy_mass_residual( 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.fixed_interior_value(this->_flow_vars.u(), qp);
        v = context.fixed_interior_value(this->_flow_vars.v(), qp);

        libMesh::Gradient grad_T = context.fixed_interior_gradient(this->_temp_vars.T(), qp);

        libMesh::NumberVectorValue U(u,v);
        if (this->mesh_dim(context) == 3)
            U(2) = context.fixed_interior_value(this->_flow_vars.w(), qp); // w

        libMesh::Real T = context.fixed_interior_value( this->_temp_vars.T(), qp );
        libMesh::Real rho = this->rho( T, this->get_p0_transient( 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, false );

        libMesh::Real RE_t = this->compute_res_energy_transient( context, qp );

        for (unsigned int i=0; i != n_T_dofs; i++)
        {
            FT(i) -= rho_cp*tau_E*RE_t*U*T_gradphi[i][qp]*JxW[qp];
        }

    }

    return;
}

  void LowMachNavierStokes<Mu,SH,TC>::assemble_mass_time_deriv( bool /*compute_jacobian*/, 
								AssemblyContext& context,
								CachedValues& cache )
  {
    // The number of local degrees of freedom in each variable.
    const unsigned int n_p_dofs = context.get_dof_indices(this->_p_var).size();

    // Element Jacobian * quadrature weights for interior integration.
    const std::vector<libMesh::Real> &JxW =
      context.get_element_fe(this->_u_var)->get_JxW();

    // The pressure shape functions at interior quadrature points.
    const std::vector<std::vector<libMesh::Real> >& p_phi =
      context.get_element_fe(this->_p_var)->get_phi();

    libMesh::DenseSubVector<libMesh::Number> &Fp = context.get_elem_residual(this->_p_var); // R_{p}

    unsigned int n_qpoints = context.get_element_qrule().n_points();

    for (unsigned int qp=0; qp != n_qpoints; qp++)
      {
	libMesh::Number u, v, T;
	u = cache.get_cached_values(Cache::X_VELOCITY)[qp];
	v = cache.get_cached_values(Cache::Y_VELOCITY)[qp];

	T = cache.get_cached_values(Cache::TEMPERATURE)[qp];

	libMesh::Gradient grad_u = cache.get_cached_gradient_values(Cache::X_VELOCITY_GRAD)[qp];
	libMesh::Gradient grad_v = cache.get_cached_gradient_values(Cache::Y_VELOCITY_GRAD)[qp];

	libMesh::Gradient grad_T = cache.get_cached_gradient_values(Cache::TEMPERATURE_GRAD)[qp];

	libMesh::NumberVectorValue U(u,v);
	if (this->_dim == 3)
	  U(2) = cache.get_cached_values(Cache::Z_VELOCITY)[qp]; // w

	libMesh::Number divU = grad_u(0) + grad_v(1);
	if (this->_dim == 3)
          {
	    libMesh::Gradient grad_w = cache.get_cached_gradient_values(Cache::Z_VELOCITY_GRAD)[qp];
	    divU += grad_w(2);
          }

	// Now a loop over the pressure degrees of freedom.  This
	// computes the contributions of the continuity equation.
	for (unsigned int i=0; i != n_p_dofs; i++)
	  {
	    Fp(i) += (-U*grad_T/T + divU)*p_phi[i][qp]*JxW[qp];
	  }
      }

    return;
  }

  void BoundaryConditions::pin_value( AssemblyContext& context,
                                      const CachedValues& /*cache*/,
                                      const bool request_jacobian,
                                      const VariableIndex var, 
                                      const double pin_value,
                                      const libMesh::Point& pin_location, 
                                      const double penalty )
  {
    if (context.get_elem().contains_point(pin_location))
      {
        libMesh::FEGenericBase<libMesh::Real>* elem_fe = NULL; 
        context.get_element_fe( var, elem_fe );

	libMesh::DenseSubVector<libMesh::Number> &F_var = context.get_elem_residual(var); // residual
	libMesh::DenseSubMatrix<libMesh::Number> &K_var = context.get_elem_jacobian(var,var); // jacobian

	// The number of local degrees of freedom in p variable.
	const unsigned int n_var_dofs = context.get_dof_indices(var).size();

	libMesh::Number var_value = context.point_value(var, pin_location);

	libMesh::FEType fe_type = elem_fe->get_fe_type();
      
	libMesh::Point point_loc_in_masterelem = 
	  libMesh::FEInterface::inverse_map(context.get_dim(), fe_type, &context.get_elem(), pin_location);

	std::vector<libMesh::Real> phi(n_var_dofs);

	for (unsigned int i=0; i != n_var_dofs; i++)
          {
            phi[i] = libMesh::FEInterface::shape( context.get_dim(), fe_type, &context.get_elem(), i, 
                                                  point_loc_in_masterelem );
          }
      
	for (unsigned int i=0; i != n_var_dofs; i++)
	  {
	    F_var(i) += penalty*(var_value - pin_value)*phi[i];
	  
	    /** \todo What the hell is the context.get_elem_solution_derivative() all about? */
	    if (request_jacobian && context.get_elem_solution_derivative())
	      {
		libmesh_assert (context.get_elem_solution_derivative() == 1.0);
	      
		for (unsigned int j=0; j != n_var_dofs; j++)
		  K_var(i,j) += penalty*phi[i]*phi[j];

	      } // End if request_jacobian
	  } // End i loop
      } // End if pin_location

    return;
  }

  void 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();
          }

      }
  }

  void HeatTransferSource<SourceFunction>::element_time_derivative( bool /*compute_jacobian*/,
								    AssemblyContext& context,
								    CachedValues& /*cache*/ )
  {
#ifdef GRINS_USE_GRVY_TIMERS
    this->_timer->BeginTimer("HeatTransferSource::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();

    // 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();

    // Locations of quadrature points
    const std::vector<libMesh::Point>& x_qp = context.get_element_fe(_temp_vars.T_var())->get_xyz();

    // Get residuals
    libMesh::DenseSubVector<libMesh::Number> &FT = context.get_elem_residual(_temp_vars.T_var()); // R_{T}

    // Now we will build the element Jacobian and residual.
    // Constructing the residual requires the solution and its
    // gradient from the previous timestep.  This must be
    // calculated at each quadrature point by summing the
    // solution degree-of-freedom values by the appropriate
    // weight functions.
    unsigned int n_qpoints = context.get_element_qrule().n_points();

    for (unsigned int qp=0; qp != n_qpoints; qp++)
      {
	libMesh::Real q = _source( x_qp[qp] );

	for (unsigned int i=0; i != n_T_dofs; i++)
	  {
	    FT(i) += q*T_phi[i][qp]*JxW[qp];
	  }
      }

#ifdef GRINS_USE_GRVY_TIMERS
    this->_timer->EndTimer("HeatTransferSource::element_time_derivative");
#endif

    return;
  }

  void ScalarODE::nonlocal_constraint(bool compute_jacobian,
				      AssemblyContext& context,
				      CachedValues& /* cache */ )
  {
    libMesh::DenseSubMatrix<libMesh::Number> &Kss =
            context.get_elem_jacobian(_scalar_ode_var, _scalar_ode_var); // R_{s},{s}

    libMesh::DenseSubVector<libMesh::Number> &Fs =
            context.get_elem_residual(_scalar_ode_var); // R_{s}

    const libMesh::Number constraint =
      (*constraint_function)(context, libMesh::Point(0),
                             context.get_time());

    Fs(0) += constraint;

    if (compute_jacobian)
      {
        // FIXME: we should replace this hacky FDM with a hook to the
        // AD fparser stuff
        libMesh::DenseSubVector<libMesh::Number> &Us =
          const_cast<libMesh::DenseSubVector<libMesh::Number>&>
            (context.get_elem_solution(_scalar_ode_var)); // U_{s}

        const libMesh::Number s = Us(0);
        Us(0) = s + this->_epsilon;
        libMesh::Number constraint_jacobian =
          (*constraint_function)(context, libMesh::Point(0),
                                 context.get_time());

        Us(0) = s - this->_epsilon;
        constraint_jacobian -=
          (*constraint_function)(context, libMesh::Point(0),
                                 context.get_time());
           
        Us(0) = s;
        constraint_jacobian /= (2*this->_epsilon);

        Kss(0,0) += constraint_jacobian *
          context.get_elem_solution_derivative();
      }

    return;
  }

  void ConstantSourceTerm::element_time_derivative
  ( bool /*compute_jacobian*/, AssemblyContext & context )
  {
    for( std::vector<VariableIndex>::const_iterator v_it = _vars.begin();
         v_it != _vars.end(); ++v_it )
      {
        VariableIndex var = *v_it;

        // The number of local degrees of freedom in each variable.
        const unsigned int n_dofs = context.get_dof_indices(var).size();

        // Element Jacobian * quadrature weights for interior integration.
        const std::vector<libMesh::Real> &JxW =
          context.get_element_fe(var)->get_JxW();

        // The temperature shape functions at interior quadrature points.
        const std::vector<std::vector<libMesh::Real> >& phi =
          context.get_element_fe(var)->get_phi();

        // Get residuals
        libMesh::DenseSubVector<libMesh::Number> &F_var = context.get_elem_residual(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++)
          {
            for (unsigned int i=0; i != n_dofs; i++)
              {
                F_var(i) += (this->_value)*phi[i][qp]*JxW[qp];
              }
          }

      } // Variable loop

    return;
  }

  void AveragedTurbine<Mu>::nonlocal_mass_residual( bool compute_jacobian,
				                AssemblyContext& context,
				                CachedValues& /* cache */ )
  {
    libMesh::DenseSubMatrix<libMesh::Number> &Kss =
            context.get_elem_jacobian(this->fan_speed_var(), this->fan_speed_var()); // R_{s},{s}

    libMesh::DenseSubVector<libMesh::Number> &Fs =
            context.get_elem_residual(this->fan_speed_var()); // R_{s}

    const libMesh::DenseSubVector<libMesh::Number> &Us =
      context.get_elem_solution_rate(this->fan_speed_var());

    const libMesh::Number& fan_speed = Us(0);

    Fs(0) -= this->moment_of_inertia * fan_speed;

    if (compute_jacobian)
      {
        Kss(0,0) -= this->moment_of_inertia * context.get_elem_solution_rate_derivative();
      }

    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;
//.........这里部分代码省略.........

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)
//.........这里部分代码省略.........

  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();
          }

      }
  }