C++ AssemblyContext::get_element_qrule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 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 ParsedInteriorQoI::element_qoi_derivative( AssemblyContext& context,
                                                  const unsigned int qoi_index )
  {
    libMesh::FEBase* element_fe;
    context.get_element_fe<libMesh::Real>(0, element_fe);
    const std::vector<libMesh::Real> &JxW = element_fe->get_JxW();

    const std::vector<libMesh::Point>& x_qp = element_fe->get_xyz();

    // Local DOF count and quadrature point count
    const unsigned int n_u_dofs = context.get_dof_indices().size();

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

    // Local solution vector - non-const version for finite
    // differenting purposes
    libMesh::DenseVector<libMesh::Number>& elem_solution =
      const_cast<libMesh::DenseVector<libMesh::Number>&>
        (context.get_elem_solution());

    /*! \todo Need to generalize this to the multiple QoI case */
    libMesh::DenseVector<libMesh::Number> &Qu =
      context.get_qoi_derivatives()[qoi_index];

    for( unsigned int qp = 0; qp != n_qpoints; qp++ )
      {
        // Central finite differencing to approximate derivatives.
        // FIXME - we should hook the FParserAD stuff into
        // ParsedFEMFunction

        for( unsigned int i = 0; i != n_u_dofs; ++i )
          {
            libMesh::Number &current_solution = elem_solution(i);
            const libMesh::Number original_solution = current_solution;

            current_solution = original_solution + libMesh::TOLERANCE;

            const libMesh::Number plus_val =
              (*qoi_functional)(context, x_qp[qp], context.get_time());

            current_solution = original_solution - libMesh::TOLERANCE;

            const libMesh::Number minus_val =
              (*qoi_functional)(context, x_qp[qp], context.get_time());

            Qu(i) += (plus_val - minus_val) *
                     (0.5 / libMesh::TOLERANCE) * JxW[qp];

            // Don't forget to restore the correct solution...
            current_solution = original_solution;
          }
      }
  }

  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 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 ParsedInteriorQoI::element_qoi( AssemblyContext& context,
                                       const unsigned int qoi_index )
  {
    libMesh::FEBase* element_fe;
    context.get_element_fe<libMesh::Real>(0, element_fe);
    const std::vector<libMesh::Real> &JxW = element_fe->get_JxW();

    const std::vector<libMesh::Point>& x_qp = element_fe->get_xyz();

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

    /*! \todo Need to generalize this to the multiple QoI case */
    libMesh::Number& qoi = context.get_qois()[qoi_index];

    for( unsigned int qp = 0; qp != n_qpoints; qp++ )
      {
        const libMesh::Number func_val =
          (*qoi_functional)(context, x_qp[qp], context.get_time());

        qoi += func_val * JxW[qp];
      }
  }

  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 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

//.........这里部分代码省略.........

  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;
  }

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

    // Check number of dofs is same for _u_var, v_var and w_var.
    libmesh_assert (n_u_dofs == context.get_dof_indices(this->_v_var).size());
    if (this->_dim == 3)
      libmesh_assert (n_u_dofs == context.get_dof_indices(this->_w_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> >& u_phi =
      context.get_element_fe(this->_u_var)->get_phi();

    // The velocity shape function gradients at interior quadrature points.
    const std::vector<std::vector<libMesh::RealGradient> >& u_gradphi =
      context.get_element_fe(this->_u_var)->get_dphi();

    libMesh::DenseSubVector<libMesh::Number> &Fu = context.get_elem_residual(this->_u_var); // R_{u}
    libMesh::DenseSubVector<libMesh::Number> &Fv = context.get_elem_residual(this->_v_var); // R_{v}
    libMesh::DenseSubVector<libMesh::Number> &Fw = context.get_elem_residual(this->_w_var); // R_{w}

    unsigned int n_qpoints = context.get_element_qrule().n_points();
    for (unsigned int qp=0; qp != n_qpoints; qp++)
      {
	libMesh::Number u, v, p, p0, 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];
	p = cache.get_cached_values(Cache::PRESSURE)[qp];
	p0 = cache.get_cached_values(Cache::THERMO_PRESSURE)[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_w;
	if (this->_dim == 3)
	  grad_w = cache.get_cached_gradient_values(Cache::Z_VELOCITY_GRAD)[qp];

	libMesh::NumberVectorValue grad_uT( grad_u(0), grad_v(0) ); 
	libMesh::NumberVectorValue grad_vT( grad_u(1), grad_v(1) );
	libMesh::NumberVectorValue grad_wT;
	if( this->_dim == 3 )
	  {
	    grad_uT(2) = grad_w(0);
	    grad_vT(2) = grad_w(1);
	    grad_wT = libMesh::NumberVectorValue( grad_u(2), grad_v(2), grad_w(2) );
	  }

	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)
	  divU += grad_w(2);

	libMesh::Number rho = this->rho( T, p0 );
      
	// Now a loop over the pressure degrees of freedom.  This
	// computes the contributions of the continuity equation.
	for (unsigned int i=0; i != n_u_dofs; i++)
	  {
	    Fu(i) += ( -rho*U*grad_u*u_phi[i][qp]                 // convection term
		       + p*u_gradphi[i][qp](0)                           // pressure term
		       - this->_mu(T)*(u_gradphi[i][qp]*grad_u + u_gradphi[i][qp]*grad_uT
				       - 2.0/3.0*divU*u_gradphi[i][qp](0) )    // diffusion term
		       + rho*this->_g(0)*u_phi[i][qp]                 // hydrostatic term
		       )*JxW[qp]; 

	    Fv(i) += ( -rho*U*grad_v*u_phi[i][qp]                 // convection term
		       + p*u_gradphi[i][qp](1)                           // pressure term
		       - this->_mu(T)*(u_gradphi[i][qp]*grad_v + u_gradphi[i][qp]*grad_vT
				       - 2.0/3.0*divU*u_gradphi[i][qp](1) )    // diffusion term
		       + rho*this->_g(1)*u_phi[i][qp]                 // hydrostatic term
		       )*JxW[qp];
	    if (this->_dim == 3)
	      {
		Fw(i) += ( -rho*U*grad_w*u_phi[i][qp]                 // convection term
			   + p*u_gradphi[i][qp](2)                           // pressure term
			   - this->_mu(T)*(u_gradphi[i][qp]*grad_w + u_gradphi[i][qp]*grad_wT
					   - 2.0/3.0*divU*u_gradphi[i][qp](2) )    // diffusion term
			   + rho*this->_g(2)*u_phi[i][qp]                 // hydrostatic term
			   )*JxW[qp];
	      }

	    /*
	      if (compute_jacobian && context.get_elem_solution_derivative())
	      {
              libmesh_assert (context.get_elem_solution_derivative() == 1.0);

              for (unsigned int j=0; j != n_u_dofs; j++)
	      {
//.........这里部分代码省略.........

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)
                {
//.........这里部分代码省略.........

  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++)
//.........这里部分代码省略.........