GRINS::HeatTransferAdjointStabilization< Conductivity > Class Template Reference

Adds VMS-based stabilization to LowMachNavierStokes physics class. More...

#include <heat_transfer_adjoint_stab.h>

Inheritance diagram for GRINS::HeatTransferAdjointStabilization< Conductivity >:

Collaboration diagram for GRINS::HeatTransferAdjointStabilization< Conductivity >:

Public Member Functions
	HeatTransferAdjointStabilization (const GRINS::PhysicsName &physics_name, const GetPot &input)
virtual	~HeatTransferAdjointStabilization ()
virtual void	element_time_derivative (bool compute_jacobian, AssemblyContext &context)
	Time dependent part(s) of physics for element interiors. More...
virtual void	mass_residual (bool compute_jacobian, AssemblyContext &context)
	Mass matrix part(s) for element interiors. All boundary terms lie within the time_derivative part. More...
Public Member Functions inherited from GRINS::HeatTransferStabilizationBase< Conductivity >
	HeatTransferStabilizationBase (const GRINS::PhysicsName &physics_name, const GetPot &input)
virtual	~HeatTransferStabilizationBase ()
virtual void	init_context (AssemblyContext &context)
	Initialize context for added physics variables. More...
Public Member Functions inherited from GRINS::HeatTransferBase< Conductivity >
	HeatTransferBase (const std::string &physics_name, const std::string &core_physics_name, const GetPot &input)
	~HeatTransferBase ()
virtual void	set_time_evolving_vars (libMesh::FEMSystem *system)
	Sets velocity variables to be time-evolving. More...
virtual void	register_parameter (const std::string &param_name, libMesh::ParameterMultiAccessor< libMesh::Number > &param_pointer) const
	Each subclass will register its copy of an independent. More...
Public Member Functions inherited from GRINS::Physics
	Physics (const GRINS::PhysicsName &physics_name, const GetPot &input)
virtual	~Physics ()
virtual void	init_variables (libMesh::FEMSystem *)
	Initialize variables for this physics. More...
virtual bool	enabled_on_elem (const libMesh::Elem *elem)
	Find if current physics is active on supplied element. More...
void	set_is_steady (bool is_steady)
	Sets whether this physics is to be solved with a steady solver or not. More...
bool	is_steady () const
	Returns whether or not this physics is being solved with a steady solver. More...
virtual void	auxiliary_init (MultiphysicsSystem &system)
	Any auxillary initialization a Physics class may need. More...
virtual void	register_postprocessing_vars (const GetPot &input, PostProcessedQuantities< libMesh::Real > &postprocessing)
	Register name of postprocessed quantity with PostProcessedQuantities. More...
virtual void	preassembly (MultiphysicsSystem &)
	Perform any necessary setup before element assembly begins. More...
virtual void	reinit (MultiphysicsSystem &)
	Any reinitialization that needs to be done. More...
virtual void	side_time_derivative (bool, AssemblyContext &)
	Time dependent part(s) of physics for boundaries of elements on the domain boundary. More...
virtual void	nonlocal_time_derivative (bool, AssemblyContext &)
	Time dependent part(s) of physics for scalar variables. More...
virtual void	element_constraint (bool, AssemblyContext &)
	Constraint part(s) of physics for element interiors. More...
virtual void	side_constraint (bool, AssemblyContext &)
	Constraint part(s) of physics for boundaries of elements on the domain boundary. More...
virtual void	nonlocal_constraint (bool, AssemblyContext &)
	Constraint part(s) of physics for scalar variables. More...
virtual void	damping_residual (bool, AssemblyContext &)
	Damping matrix part(s) for element interiors. All boundary terms lie within the time_derivative part. More...
virtual void	nonlocal_mass_residual (bool, AssemblyContext &)
	Mass matrix part(s) for scalar variables. More...
void	init_ics (libMesh::FEMSystem *system, libMesh::CompositeFunction< libMesh::Number > &all_ics)
virtual void	compute_element_time_derivative_cache (AssemblyContext &)
virtual void	compute_side_time_derivative_cache (AssemblyContext &)
virtual void	compute_nonlocal_time_derivative_cache (AssemblyContext &)
virtual void	compute_element_constraint_cache (AssemblyContext &)
virtual void	compute_side_constraint_cache (AssemblyContext &)
virtual void	compute_nonlocal_constraint_cache (AssemblyContext &)
virtual void	compute_damping_residual_cache (AssemblyContext &)
virtual void	compute_mass_residual_cache (AssemblyContext &)
virtual void	compute_nonlocal_mass_residual_cache (AssemblyContext &)
virtual void	compute_postprocessed_quantity (unsigned int quantity_index, const AssemblyContext &context, const libMesh::Point &point, libMesh::Real &value)
ICHandlingBase *	get_ic_handler ()
Public Member Functions inherited from GRINS::ParameterUser
	ParameterUser (const std::string &user_name)
virtual	~ParameterUser ()
virtual void	set_parameter (libMesh::Number &param_variable, const GetPot &input, const std::string &param_name, libMesh::Number param_default)
	Each subclass can simultaneously read a parameter value from. More...
virtual void	set_parameter (libMesh::ParsedFunction< libMesh::Number, libMesh::Gradient > &func, const GetPot &input, const std::string &func_param_name, const std::string &param_default)
	Each subclass can simultaneously read a parsed function from. More...
virtual void	set_parameter (libMesh::ParsedFEMFunction< libMesh::Number > &func, const GetPot &input, const std::string &func_param_name, const std::string &param_default)
	Each subclass can simultaneously read a parsed function from. More...
virtual void	move_parameter (const libMesh::Number &old_parameter, libMesh::Number &new_parameter)
	When cloning an object, we need to update parameter pointers. More...
virtual void	move_parameter (const libMesh::ParsedFunction< libMesh::Number, libMesh::Gradient > &old_func, libMesh::ParsedFunction< libMesh::Number, libMesh::Gradient > &new_func)
	When cloning an object, we need to update parameter pointers. More...
virtual void	move_parameter (const libMesh::ParsedFEMFunction< libMesh::Number > &old_func, libMesh::ParsedFEMFunction< libMesh::Number > &new_func)
	When cloning an object, we need to update parameter pointers. More...

Private Member Functions
	HeatTransferAdjointStabilization ()

Additional Inherited Members
Static Public Member Functions inherited from GRINS::Physics
static void	set_is_axisymmetric (bool is_axisymmetric)
	Set whether we should treat the problem as axisymmetric. More...
static bool	is_axisymmetric ()
Static Public Attributes inherited from GRINS::ParameterUser
static std::string	zero_vector_function = std::string("{0}")
	A parseable function string with LIBMESH_DIM components, all 0. More...
Protected Member Functions inherited from GRINS::Physics
libMesh::UniquePtr< libMesh::FEGenericBase< libMesh::Real > >	build_new_fe (const libMesh::Elem *elem, const libMesh::FEGenericBase< libMesh::Real > *fe, const libMesh::Point p)
void	parse_enabled_subdomains (const GetPot &input, const std::string &physics_name)
void	check_var_subdomain_consistency (const FEVariablesBase &var) const
	Check that var is enabled on at least the subdomains this Physics is. More...
Protected Attributes inherited from GRINS::HeatTransferStabilizationBase< Conductivity >
HeatTransferStabilizationHelper	_stab_helper
Protected Attributes inherited from GRINS::HeatTransferBase< Conductivity >
unsigned int	_dim
	Physical dimension of problem. More...
VelocityVariable &	_flow_vars
PressureFEVariable &	_press_var
PrimitiveTempFEVariables &	_temp_vars
libMesh::Number	_rho
	Material parameters, read from input. More...
libMesh::Number	_Cp
Conductivity	_k
	Conductivity. More...
Protected Attributes inherited from GRINS::Physics
const PhysicsName	_physics_name
	Name of the physics object. Used for reading physics specific inputs. More...
GRINS::ICHandlingBase *	_ic_handler
std::set< libMesh::subdomain_id_type >	_enabled_subdomains
	Subdomains on which the current Physics class is enabled. More...
Static Protected Attributes inherited from GRINS::Physics
static bool	_is_steady = false
	Caches whether or not the solver that's being used is steady or not. More...
static bool	_is_axisymmetric = false
	Caches whether we are solving an axisymmetric problem or not. More...

Detailed Description

template<class Conductivity>
class GRINS::HeatTransferAdjointStabilization< Conductivity >

Adds VMS-based stabilization to LowMachNavierStokes physics class.

Definition at line 36 of file heat_transfer_adjoint_stab.h.

Constructor & Destructor Documentation

template<class K >

GRINS::HeatTransferAdjointStabilization< K >::HeatTransferAdjointStabilization	(	const GRINS::PhysicsName &	physics_name,
		const GetPot &	input
	)

Definition at line 38 of file heat_transfer_adjoint_stab.C.

    : HeatTransferStabilizationBase<K>(physics_name,input)
  {
    return;
  }

template<class K >

GRINS::HeatTransferAdjointStabilization< K >::~HeatTransferAdjointStabilization ( )

virtual

Definition at line 46 of file heat_transfer_adjoint_stab.C.

  {
    return;
  }

template<class Conductivity >

GRINS::HeatTransferAdjointStabilization< Conductivity >::HeatTransferAdjointStabilization ( )

private

Member Function Documentation

template<class K >

void GRINS::HeatTransferAdjointStabilization< K >::element_time_derivative ( bool  , AssemblyContext &    )

virtual

Time dependent part(s) of physics for element interiors.

Reimplemented from GRINS::Physics.

Definition at line 53 of file heat_transfer_adjoint_stab.C.

  {
    // 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();
    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->_temp_vars.T())->get_JxW();

    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::Real> >& T_phi =
      context.get_element_fe(this->_temp_vars.T())->get_phi();

    const std::vector<std::vector<libMesh::RealGradient> >& T_gradphi =
      context.get_element_fe(this->_temp_vars.T())->get_dphi();

    const std::vector<std::vector<libMesh::RealTensor> >& T_hessphi =
      context.get_element_fe(this->_temp_vars.T())->get_d2phi();

    /*
      const unsigned int n_u_dofs = context.get_dof_indices(this->_flow_vars.u()).size();

      const std::vector<std::vector<libMesh::Real> >& u_phi =
      context.get_element_fe(this->_flow_vars.u())->get_phi();

      libMesh::DenseSubVector<libMesh::Number> &Fu = context.get_elem_residual(this->_flow_vars.u()); // R_{p}
      libMesh::DenseSubVector<libMesh::Number> &Fv = context.get_elem_residual(this->_flow_vars.v()); // R_{p}
      libMesh::DenseSubVector<libMesh::Number> *Fw = NULL;
      if(this->_flow_vars.dim() == 3)
      {
      Fw = &context.get_elem_residual(this->_flow_vars.w()); // R_{w}
      }
    */

    libMesh::DenseSubVector<libMesh::Number> &FT = context.get_elem_residual(this->_temp_vars.T()); // R_{T}
    libMesh::DenseSubMatrix<libMesh::Number> &KTT =
      context.get_elem_jacobian(this->_temp_vars.T(), this->_temp_vars.T()); // J_{TT}
    libMesh::DenseSubMatrix<libMesh::Number> &KTu =
      context.get_elem_jacobian(this->_temp_vars.T(), this->_flow_vars.u()); // J_{Tu}
    libMesh::DenseSubMatrix<libMesh::Number> &KTv =
      context.get_elem_jacobian(this->_temp_vars.T(), this->_flow_vars.v()); // J_{Tv}
    libMesh::DenseSubMatrix<libMesh::Number> *KTw = NULL;

    if(this->_flow_vars.dim() == 3)
      {
        KTw = &context.get_elem_jacobian
          (this->_temp_vars.T(), this->_flow_vars.w()); // J_{Tw}
      }

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

    for (unsigned int qp=0; qp != n_qpoints; qp++)
      {
        libMesh::FEBase* fe = context.get_element_fe(this->_temp_vars.T());

        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 );
          }

        //libMesh::RealGradient grad_T = context.interior_gradient( this->_temp_vars.T(), qp );

        libMesh::Real tau_E, RE_s;
        libMesh::Real d_tau_E_dT_rho, d_RE_s_dT;
        libMesh::Gradient d_tau_E_dU, d_RE_s_dgradT, d_RE_s_dU;
        libMesh::Tensor d_RE_s_dhessT;

        // Compute the conductivity at this qp
        libMesh::Real _k_qp = this->_k(context, qp);

        if (compute_jacobian)
          {
            this->_stab_helper.compute_tau_energy_and_derivs
              ( context, G, this->_rho, this->_Cp, _k_qp,  U,
                tau_E, d_tau_E_dT_rho, d_tau_E_dU, this->_is_steady );
            this->_stab_helper.compute_res_energy_steady_and_derivs
              ( context, qp, this->_rho, this->_Cp, _k_qp,
                RE_s, d_RE_s_dT, d_RE_s_dgradT, d_RE_s_dhessT,
                d_RE_s_dU );
          }
        else
          {
            tau_E = this->_stab_helper.compute_tau_energy
              ( context, G, this->_rho, this->_Cp, _k_qp,  U, this->_is_steady );

            RE_s = this->_stab_helper.compute_res_energy_steady
              ( context, qp, this->_rho, this->_Cp, _k_qp );
          }

        /*
          for (unsigned int i=0; i != n_u_dofs; i++)
          {
          Fu(i) += -tau_E*RE_s*this->_rho*this->_Cp*u_phi[i][qp]*grad_T(0)*JxW[qp];
          Fv(i) += -tau_E*RE_s*this->_rho*this->_Cp*u_phi[i][qp]*grad_T(1)*JxW[qp];
          if( this->_flow_vars.dim() == 3 )
          {
          (*Fw)(i) += -tau_E*RE_s*this->_rho*this->_Cp*u_phi[i][qp]*grad_T(2)*JxW[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]
                                   + _k_qp*(T_hessphi[i][qp](0,0) + T_hessphi[i][qp](1,1) + T_hessphi[i][qp](2,2))
                                   )*JxW[qp];
            if (compute_jacobian)
              {
                for (unsigned int j=0; j != n_T_dofs; ++j)
                  {
                    KTT(i,j) += -tau_E*
                      (d_RE_s_dT*T_phi[j][qp] +
                       d_RE_s_dgradT*T_gradphi[j][qp] +
                       d_RE_s_dhessT.contract(T_hessphi[j][qp])
                       ) *
                      ( this->_rho*this->_Cp*U*T_gradphi[i][qp]
                        + _k_qp*(T_hessphi[i][qp](0,0) +
                                 T_hessphi[i][qp](1,1) +
                                 T_hessphi[i][qp](2,2))
                        )*JxW[qp]
                      * context.get_fixed_solution_derivative();
                  }
                for (unsigned int j=0; j != n_u_dofs; ++j)
                  {
                    KTu(i,j) += -tau_E*RE_s*
                      ( this->_rho*this->_Cp*u_phi[j][qp]*T_gradphi[i][qp](0) )*JxW[qp]
                      * context.get_fixed_solution_derivative();
                    KTu(i,j) +=
                      -(tau_E*d_RE_s_dU(0)+d_tau_E_dU(0)*RE_s)*u_phi[j][qp]*
                      ( this->_rho*this->_Cp*U*T_gradphi[i][qp]
                        + _k_qp*(T_hessphi[i][qp](0,0) +
                                 T_hessphi[i][qp](1,1) +
                                 T_hessphi[i][qp](2,2))
                        )*JxW[qp]
                      * context.get_fixed_solution_derivative();
                    KTv(i,j) += -tau_E*RE_s*
                      ( this->_rho*this->_Cp*u_phi[j][qp]*T_gradphi[i][qp](1) )*JxW[qp]
                      * context.get_fixed_solution_derivative();
                    KTv(i,j) +=
                      -(tau_E*d_RE_s_dU(1)+d_tau_E_dU(1)*RE_s)*u_phi[j][qp]*
                      ( this->_rho*this->_Cp*U*T_gradphi[i][qp]
                        + _k_qp*(T_hessphi[i][qp](0,0) +
                                 T_hessphi[i][qp](1,1) +
                                 T_hessphi[i][qp](2,2))
                        )*JxW[qp]
                      * context.get_fixed_solution_derivative();
                  }
                if(this->_flow_vars.dim() == 3)
                  {
                    for (unsigned int j=0; j != n_u_dofs; ++j)
                      {
                        (*KTw)(i,j) += -tau_E*RE_s*
                          ( this->_rho*this->_Cp*u_phi[j][qp]*T_gradphi[i][qp](2) )*JxW[qp]
                          * context.get_fixed_solution_derivative();
                        (*KTw)(i,j) +=
                          -(tau_E*d_RE_s_dU(2)+d_tau_E_dU(2)*RE_s)*u_phi[j][qp]*
                          ( this->_rho*this->_Cp*U*T_gradphi[i][qp]
                            + _k_qp*(T_hessphi[i][qp](0,0) +
                                     T_hessphi[i][qp](1,1) +
                                     T_hessphi[i][qp](2,2))
                            )*JxW[qp]
                          * context.get_fixed_solution_derivative();
                      }
                  }
              }
          }
      }
  }

template<class K >

void GRINS::HeatTransferAdjointStabilization< K >::mass_residual ( bool  , AssemblyContext &    )

virtual

Mass matrix part(s) for element interiors. All boundary terms lie within the time_derivative part.

Reimplemented from GRINS::Physics.

Definition at line 233 of file heat_transfer_adjoint_stab.C.

  {
    // 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();
    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->_temp_vars.T())->get_JxW();

    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::Real> >& T_phi =
      context.get_element_fe(this->_temp_vars.T())->get_phi();

    const std::vector<std::vector<libMesh::RealGradient> >& T_gradphi =
      context.get_element_fe(this->_temp_vars.T())->get_dphi();

    const std::vector<std::vector<libMesh::RealTensor> >& T_hessphi =
      context.get_element_fe(this->_temp_vars.T())->get_d2phi();

    /*
      const unsigned int n_u_dofs = context.get_dof_indices(this->_flow_vars.u()).size();

      const std::vector<std::vector<libMesh::Real> >& u_phi =
      context.get_element_fe(this->_flow_vars.u())->get_phi();

      libMesh::DenseSubVector<libMesh::Number> &Fu = context.get_elem_residual(this->_flow_vars.u()); // R_{p}
      libMesh::DenseSubVector<libMesh::Number> &Fv = context.get_elem_residual(this->_flow_vars.v()); // R_{p}
      libMesh::DenseSubVector<libMesh::Number> *Fw = NULL;
      if(this->_flow_vars.dim() == 3)
      {
      Fw = &context.get_elem_residual(this->_flow_vars.w()); // R_{w}
      }
    */

    libMesh::DenseSubVector<libMesh::Number> &FT = context.get_elem_residual(this->_temp_vars.T()); // R_{T}
    libMesh::DenseSubMatrix<libMesh::Number> &KTT =
      context.get_elem_jacobian(this->_temp_vars.T(), this->_temp_vars.T()); // J_{TT}
    libMesh::DenseSubMatrix<libMesh::Number> &KTu =
      context.get_elem_jacobian(this->_temp_vars.T(), this->_flow_vars.u()); // J_{Tu}
    libMesh::DenseSubMatrix<libMesh::Number> &KTv =
      context.get_elem_jacobian(this->_temp_vars.T(), this->_flow_vars.v()); // J_{Tv}
    libMesh::DenseSubMatrix<libMesh::Number> *KTw = NULL;

    if(this->_flow_vars.dim() == 3)
      {
        KTw = &context.get_elem_jacobian
          (this->_temp_vars.T(), this->_flow_vars.w()); // J_{Tw}
      }

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

    for (unsigned int qp=0; qp != n_qpoints; qp++)
      {
        libMesh::FEBase* fe = context.get_element_fe(this->_temp_vars.T());

        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.fixed_interior_value( this->_flow_vars.u(), qp ),
                                 context.fixed_interior_value( this->_flow_vars.v(), qp ) );
        if( this->_flow_vars.dim() == 3 )
          U(2) = context.fixed_interior_value( this->_flow_vars.w(), qp );

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

        libMesh::Real tau_E, RE_t;
        libMesh::Real d_tau_E_d_rho, d_RE_t_dT;
        libMesh::Gradient d_tau_E_dU;

        // Compute the conductivity at this qp
        libMesh::Real _k_qp = this->_k(context, qp);

        if (compute_jacobian)
          {
            this->_stab_helper.compute_tau_energy_and_derivs
              ( context, G, this->_rho, this->_Cp, _k_qp,  U,
                tau_E, d_tau_E_d_rho, d_tau_E_dU, false );
            this->_stab_helper.compute_res_energy_transient_and_derivs
              ( context, qp, this->_rho, this->_Cp,
                RE_t, d_RE_t_dT );
          }
        else
          {
            tau_E = this->_stab_helper.compute_tau_energy
              ( context, G, this->_rho, this->_Cp, _k_qp,  U, false );

            RE_t = this->_stab_helper.compute_res_energy_transient
              ( context, qp, this->_rho, this->_Cp );
          }


        /*
          for (unsigned int i=0; i != n_u_dofs; i++)
          {
          Fu(i) += -tau_E*RE_t*this->_rho*this->_Cp*u_phi[i][qp]*grad_T(0)*JxW[qp];
          Fv(i) += -tau_E*RE_t*this->_rho*this->_Cp*u_phi[i][qp]*grad_T(1)*JxW[qp];
          if( this->_flow_vars.dim() == 3 )
          {
          (*Fw)(i) += -tau_E*RE_t*this->_rho*this->_Cp*u_phi[i][qp]*grad_T(2)*JxW[qp];
          }
          }
        */

        for (unsigned int i=0; i != n_T_dofs; i++)
          {
            FT(i) -= tau_E*RE_t*( this->_rho*this->_Cp*U*T_gradphi[i][qp]
                                  + _k_qp*(T_hessphi[i][qp](0,0) + T_hessphi[i][qp](1,1) + T_hessphi[i][qp](2,2))
                                  )*JxW[qp];
            if (compute_jacobian)
              {
                const libMesh::Real fixed_deriv =
                  context.get_fixed_solution_derivative();

                for (unsigned int j=0; j != n_T_dofs; ++j)
                  {
                    KTT(i,j) -=
                      (tau_E*d_RE_t_dT)*T_phi[j][qp]*
                      ( this->_rho*this->_Cp*U*T_gradphi[i][qp]
                        + _k_qp*(T_hessphi[i][qp](0,0) +
                                 T_hessphi[i][qp](1,1) +
                                 T_hessphi[i][qp](2,2))
                        )*JxW[qp];
                  }
                for (unsigned int j=0; j != n_u_dofs; ++j)
                  {
                    KTu(i,j) -=
                      d_tau_E_dU(0)*u_phi[j][qp]*RE_t*
                      ( this->_rho*this->_Cp*U*T_gradphi[i][qp]
                        + _k_qp*(T_hessphi[i][qp](0,0) +
                                 T_hessphi[i][qp](1,1) +
                                 T_hessphi[i][qp](2,2))
                        )*fixed_deriv*JxW[qp];
                    KTu(i,j) -=
                      tau_E*RE_t*
                      ( this->_rho*this->_Cp*u_phi[j][qp]*T_gradphi[i][qp](0)*fixed_deriv
                        )*JxW[qp];
                    KTv(i,j) -=
                      d_tau_E_dU(1)*u_phi[j][qp]*RE_t*
                      ( this->_rho*this->_Cp*U*T_gradphi[i][qp]
                        + _k_qp*(T_hessphi[i][qp](0,0) +
                                 T_hessphi[i][qp](1,1) +
                                 T_hessphi[i][qp](2,2))
                        )*fixed_deriv*JxW[qp];
                    KTv(i,j) -=
                      tau_E*RE_t*
                      ( this->_rho*this->_Cp*u_phi[j][qp]*T_gradphi[i][qp](1)*fixed_deriv
                        )*JxW[qp];
                  }
                if(this->_flow_vars.dim() == 3)
                  {
                    for (unsigned int j=0; j != n_u_dofs; ++j)
                      {
                        (*KTw)(i,j) -=
                          d_tau_E_dU(2)*u_phi[j][qp]*RE_t*
                          ( this->_rho*this->_Cp*U*T_gradphi[i][qp]
                            + _k_qp*(T_hessphi[i][qp](0,0) +
                                     T_hessphi[i][qp](1,1) +
                                     T_hessphi[i][qp](2,2))
                            )*fixed_deriv*JxW[qp];
                        (*KTw)(i,j) -=
                          tau_E*RE_t*
                          ( this->_rho*this->_Cp*u_phi[j][qp]*T_gradphi[i][qp](2)*fixed_deriv
                            )*JxW[qp];
                      }
                  }
              }
          }

      }
  }

---

The documentation for this class was generated from the following files:

• src/physics/include/grins/heat_transfer_adjoint_stab.h
• src/physics/src/heat_transfer_adjoint_stab.C