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

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 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 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;
  }

  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;
  }

  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

//.........这里部分代码省略.........

  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 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);
//.........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 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]);
//.........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.........

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