GRINS::IncompressibleNavierStokesAdjointStabilization< Viscosity > Class Template Reference

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

#include <inc_navier_stokes_adjoint_stab.h>

Inheritance diagram for GRINS::IncompressibleNavierStokesAdjointStabilization< Viscosity >:

Collaboration diagram for GRINS::IncompressibleNavierStokesAdjointStabilization< Viscosity >:

Public Member Functions
	IncompressibleNavierStokesAdjointStabilization (const GRINS::PhysicsName &physics_name, const GetPot &input)
virtual	~IncompressibleNavierStokesAdjointStabilization ()
virtual void	element_time_derivative (bool compute_jacobian, AssemblyContext &context)
	Time dependent part(s) of physics for element interiors. More...
virtual void	element_constraint (bool compute_jacobian, AssemblyContext &context)
	Constraint 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::IncompressibleNavierStokesStabilizationBase< Viscosity >
	IncompressibleNavierStokesStabilizationBase (const GRINS::PhysicsName &physics_name, const GetPot &input)
virtual	~IncompressibleNavierStokesStabilizationBase ()
virtual void	init_context (AssemblyContext &context)
	Initialize context for added physics variables. More...
Public Member Functions inherited from GRINS::IncompressibleNavierStokesBase< Viscosity >
	IncompressibleNavierStokesBase (const std::string &my_physics_name, const std::string &core_physics_name, const GetPot &input)
	~IncompressibleNavierStokesBase ()
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...
libMesh::Real	get_viscosity_value (AssemblyContext &context, unsigned int qp) const
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	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
	IncompressibleNavierStokesAdjointStabilization ()

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::IncompressibleNavierStokesStabilizationBase< Viscosity >
IncompressibleNavierStokesStabilizationHelper	_stab_helper
Protected Attributes inherited from GRINS::IncompressibleNavierStokesBase< Viscosity >
VelocityVariable &	_flow_vars
PressureFEVariable &	_press_var
libMesh::Number	_rho
	Material parameters, read from input. More...
Viscosity	_mu
	Viscosity object. 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 Viscosity>
class GRINS::IncompressibleNavierStokesAdjointStabilization< Viscosity >

Adds VMS-based stabilization to LowMachNavierStokes physics class.

Definition at line 35 of file inc_navier_stokes_adjoint_stab.h.

Constructor & Destructor Documentation

template<class Mu >

GRINS::IncompressibleNavierStokesAdjointStabilization< Mu >::IncompressibleNavierStokesAdjointStabilization	(	const GRINS::PhysicsName &	physics_name,
		const GetPot &	input
	)

Definition at line 40 of file inc_navier_stokes_adjoint_stab.C.

    : IncompressibleNavierStokesStabilizationBase<Mu>(physics_name,input)
  {}

template<class Viscosity >

virtual GRINS::IncompressibleNavierStokesAdjointStabilization< Viscosity >::~IncompressibleNavierStokesAdjointStabilization ( )

inlinevirtual

Definition at line 41 of file inc_navier_stokes_adjoint_stab.h.

{};

template<class Viscosity >

GRINS::IncompressibleNavierStokesAdjointStabilization< Viscosity >::IncompressibleNavierStokesAdjointStabilization ( )

private

Member Function Documentation

template<class Mu >

void GRINS::IncompressibleNavierStokesAdjointStabilization< Mu >::element_constraint ( bool  , AssemblyContext &    )

virtual

Constraint part(s) of physics for element interiors.

Reimplemented from GRINS::Physics.

Definition at line 369 of file inc_navier_stokes_adjoint_stab.C.

  {
    // 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();

    // The pressure shape functions at interior quadrature points.
    const std::vector<std::vector<libMesh::RealGradient> >& p_dphi =
      context.get_element_fe(this->_press_var.p())->get_dphi();

    // The velocity 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<std::vector<libMesh::RealGradient> >& u_dphi =
      context.get_element_fe(this->_flow_vars.u())->get_dphi();

    const std::vector<std::vector<libMesh::RealTensor> >& u_d2phi =
      context.get_element_fe(this->_flow_vars.u())->get_d2phi();

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

    libMesh::DenseSubMatrix<libMesh::Number> &Kpp =
      context.get_elem_jacobian(this->_press_var.p(), this->_press_var.p()); // J_{pp}
    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->_flow_vars.dim() == 3)
      {
        Kpw = &context.get_elem_jacobian
          (this->_press_var.p(), this->_flow_vars.w()); // J_{pw}
      }

    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->_flow_vars.dim() == 3 )
          {
            U(2) = context.interior_value( this->_flow_vars.w(), qp );
          }

        libMesh::Real tau_M;
        libMesh::Real d_tau_M_d_rho;
        libMesh::Gradient d_tau_M_dU;
        libMesh::Gradient RM_s, d_RM_s_uvw_dgraduvw;
        libMesh::Tensor d_RM_s_dgradp, d_RM_s_dU, d_RM_s_uvw_dhessuvw;

        // Compute the viscosity at this qp
        libMesh::Real _mu_qp = this->_mu(context, qp);

        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 );
            this->_stab_helper.compute_res_momentum_steady_and_derivs
              ( context, qp, this->_rho, _mu_qp,
                RM_s, d_RM_s_dgradp, d_RM_s_dU, d_RM_s_uvw_dgraduvw,
                d_RM_s_uvw_dhessuvw);
          }
        else
          {
            tau_M = this->_stab_helper.compute_tau_momentum( context, qp, g, G, this->_rho, U, _mu_qp, this->_is_steady );
            RM_s = this->_stab_helper.compute_res_momentum_steady( context, qp, this->_rho, _mu_qp );
          }

        // Now a loop over the pressure degrees of freedom.  This
        // computes the contributions of the continuity equation.
        for (unsigned int i=0; i != n_p_dofs; i++)
          {
            Fp(i) += tau_M*(RM_s*p_dphi[i][qp])*JxW[qp];

            if (compute_jacobian)
              {
                const libMesh::Real fixed_deriv =
                  context.get_fixed_solution_derivative();

                const libMesh::TypeVector<libMesh::Number>
                  p_dphiiT_d_RM_s_dgradp =
                  d_RM_s_dgradp.transpose() * p_dphi[i][qp];

                for (unsigned int j=0; j != n_p_dofs; j++)
                  {
                    Kpp(i,j) += tau_M*(p_dphiiT_d_RM_s_dgradp*p_dphi[j][qp])*JxW[qp];
                  }

                for (unsigned int j=0; j != n_u_dofs; j++)
                  {
                    Kpu(i,j) += (
                                 d_tau_M_dU(0)*u_phi[j][qp]*(RM_s*p_dphi[i][qp])
                                 + tau_M*
                                 (
                                  d_RM_s_dU(0,0)*u_phi[j][qp]*p_dphi[i][qp](0) +
                                  d_RM_s_dU(1,0)*u_phi[j][qp]*p_dphi[i][qp](1) +
                                  d_RM_s_dU(2,0)*u_phi[j][qp]*p_dphi[i][qp](2) +
                                  d_RM_s_uvw_dgraduvw*u_dphi[j][qp]*p_dphi[i][qp](0) +
                                  d_RM_s_uvw_dhessuvw.contract(u_d2phi[j][qp])*p_dphi[i][qp](0)
                                  )*fixed_deriv
                                 )*JxW[qp];
                    Kpv(i,j) += (
                                 d_tau_M_dU(1)*u_phi[j][qp]*(RM_s*p_dphi[i][qp])
                                 + tau_M*
                                 (
                                  d_RM_s_dU(0,1)*u_phi[j][qp]*p_dphi[i][qp](0) +
                                  d_RM_s_dU(1,1)*u_phi[j][qp]*p_dphi[i][qp](1) +
                                  d_RM_s_dU(2,1)*u_phi[j][qp]*p_dphi[i][qp](2) +
                                  d_RM_s_uvw_dgraduvw*u_dphi[j][qp]*p_dphi[i][qp](1) +
                                  d_RM_s_uvw_dhessuvw.contract(u_d2phi[j][qp])*p_dphi[i][qp](0)
                                  )*fixed_deriv
                                 )*JxW[qp];
                  }

                if(this->_flow_vars.dim() == 3)
                  {
                    for (unsigned int j=0; j != n_u_dofs; j++)
                      {
                        (*Kpw)(i,j) += (
                                        d_tau_M_dU(2)*u_phi[j][qp]*(RM_s*p_dphi[i][qp])
                                        + tau_M*
                                        (
                                         d_RM_s_dU(0,2)*u_phi[j][qp]*p_dphi[i][qp](0) +
                                         d_RM_s_dU(1,2)*u_phi[j][qp]*p_dphi[i][qp](1) +
                                         d_RM_s_dU(2,2)*u_phi[j][qp]*p_dphi[i][qp](2) +
                                         d_RM_s_uvw_dgraduvw*u_dphi[j][qp]*p_dphi[i][qp](2) +
                                         d_RM_s_uvw_dhessuvw.contract(u_d2phi[j][qp])*p_dphi[i][qp](0)
                                         )*fixed_deriv
                                        )*JxW[qp];
                      }
                  }
              }
          }
      }
  }

template<class Mu >

void GRINS::IncompressibleNavierStokesAdjointStabilization< Mu >::element_time_derivative ( bool  , AssemblyContext &    )

virtual

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

Reimplemented from GRINS::Physics.

Definition at line 47 of file inc_navier_stokes_adjoint_stab.C.

  {
    // 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<std::vector<libMesh::RealGradient> >& p_gradphi =
      context.get_element_fe(this->_press_var.p())->get_dphi();

    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> >& u_gradphi =
      context.get_element_fe(this->_flow_vars.u())->get_dphi();

    const std::vector<std::vector<libMesh::RealTensor> >& u_hessphi =
      context.get_element_fe(this->_flow_vars.u())->get_d2phi();

    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::DenseSubMatrix<libMesh::Number> &Kup =
      context.get_elem_jacobian(this->_flow_vars.u(), this->_press_var.p()); // J_{up}
    libMesh::DenseSubMatrix<libMesh::Number> &Kuu =
      context.get_elem_jacobian(this->_flow_vars.u(), this->_flow_vars.u()); // J_{uu}
    libMesh::DenseSubMatrix<libMesh::Number> &Kuv =
      context.get_elem_jacobian(this->_flow_vars.u(), this->_flow_vars.v()); // J_{uv}
    libMesh::DenseSubMatrix<libMesh::Number> &Kvp =
      context.get_elem_jacobian(this->_flow_vars.v(), this->_press_var.p()); // J_{vp}
    libMesh::DenseSubMatrix<libMesh::Number> &Kvu =
      context.get_elem_jacobian(this->_flow_vars.v(), this->_flow_vars.u()); // J_{vu}
    libMesh::DenseSubMatrix<libMesh::Number> &Kvv =
      context.get_elem_jacobian(this->_flow_vars.v(), this->_flow_vars.v()); // J_{vv}

    libMesh::DenseSubVector<libMesh::Number> *Fw = NULL;
    libMesh::DenseSubMatrix<libMesh::Number> *Kuw = NULL;
    libMesh::DenseSubMatrix<libMesh::Number> *Kvw = NULL;
    libMesh::DenseSubMatrix<libMesh::Number> *Kwp = NULL;
    libMesh::DenseSubMatrix<libMesh::Number> *Kwu = NULL;
    libMesh::DenseSubMatrix<libMesh::Number> *Kwv = NULL;
    libMesh::DenseSubMatrix<libMesh::Number> *Kww = NULL;


    if(this->_flow_vars.dim() == 3)
      {
        Fw = &context.get_elem_residual(this->_flow_vars.w()); // R_{w}
        Kuw = &context.get_elem_jacobian
          (this->_flow_vars.u(), this->_flow_vars.w()); // J_{uw}
        Kvw = &context.get_elem_jacobian
          (this->_flow_vars.v(), this->_flow_vars.w()); // J_{vw}
        Kwp = &context.get_elem_jacobian
          (this->_flow_vars.w(), this->_press_var.p()); // J_{wp}
        Kwu = &context.get_elem_jacobian
          (this->_flow_vars.w(), this->_flow_vars.u()); // J_{wu}
        Kwv = &context.get_elem_jacobian
          (this->_flow_vars.w(), this->_flow_vars.v()); // J_{wv}
        Kww = &context.get_elem_jacobian
          (this->_flow_vars.w(), this->_flow_vars.w()); // J_{ww}
      }

    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->_flow_vars.dim() == 3 )
          {
            U(2) = context.interior_value( this->_flow_vars.w(), qp );
          }

        /*
          libMesh::Gradient grad_u, grad_v, grad_w;
          grad_u = context.interior_gradient(this->_flow_vars.u(), qp);
          grad_v = context.interior_gradient(this->_flow_vars.v(), qp);
          if (_dim == 3)
          grad_w = context.interior_gradient(this->_flow_vars.w(), qp);
        */

        libMesh::Real tau_M, tau_C;
        libMesh::Real d_tau_M_d_rho, d_tau_C_d_rho;
        libMesh::Gradient d_tau_M_dU, d_tau_C_dU;
        libMesh::Gradient RM_s, d_RM_s_uvw_dgraduvw;
        libMesh::Real RC;
        libMesh::Tensor d_RC_dgradU,
          d_RM_s_dgradp, d_RM_s_dU, d_RM_s_uvw_dhessuvw;

        // Compute the viscosity at this qp
        libMesh::Real _mu_qp = this->_mu(context, qp);

        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 );
            this->_stab_helper.compute_tau_continuity_and_derivs
              ( tau_M, d_tau_M_d_rho, d_tau_M_dU,
                g,
                tau_C, d_tau_C_d_rho, d_tau_C_dU );
            this->_stab_helper.compute_res_momentum_steady_and_derivs
              ( context, qp, this->_rho, _mu_qp,
                RM_s, d_RM_s_dgradp, d_RM_s_dU, d_RM_s_uvw_dgraduvw,
                d_RM_s_uvw_dhessuvw);
            this->_stab_helper.compute_res_continuity_and_derivs
              ( context, qp, RC, d_RC_dgradU );
          }
        else
          {
            tau_M = this->_stab_helper.compute_tau_momentum( context, qp, g, G, this->_rho, U, _mu_qp, this->_is_steady );
            tau_C = this->_stab_helper.compute_tau_continuity( tau_M, g );
            RM_s = this->_stab_helper.compute_res_momentum_steady( context, qp, this->_rho, _mu_qp );
            RC = this->_stab_helper.compute_res_continuity( context, qp );
          }

        for (unsigned int i=0; i != n_u_dofs; i++)
          {
            libMesh::Real test_func = this->_rho*U*u_gradphi[i][qp] +
              _mu_qp*( u_hessphi[i][qp](0,0) + u_hessphi[i][qp](1,1) + u_hessphi[i][qp](2,2) );
            libMesh::Gradient d_test_func_dU = this->_rho*u_gradphi[i][qp];

            //libMesh::RealGradient zeroth_order_term = - this->_rho*u_phi[i][qp]*(grad_u + grad_v + grad_w);

            Fu(i) += ( -tau_M*RM_s(0)*test_func - tau_C*RC*u_gradphi[i][qp](0) )*JxW[qp];

            Fv(i) += ( -tau_M*RM_s(1)*test_func - tau_C*RC*u_gradphi[i][qp](1) )*JxW[qp];

            if(this->_flow_vars.dim() == 3)
              {
                (*Fw)(i) += ( -tau_M*RM_s(2)*test_func - tau_C*RC*u_gradphi[i][qp](2) )*JxW[qp];
              }

            if (compute_jacobian)
              {
                const libMesh::Real fixed_deriv =
                  context.get_fixed_solution_derivative();
                for (unsigned int j=0; j != n_p_dofs; j++)
                  {
                    Kup(i,j) += ( -tau_M*
                                  ( d_RM_s_dgradp(0,0) *
                                    p_gradphi[j][qp](0) +
                                    d_RM_s_dgradp(0,1) *
                                    p_gradphi[j][qp](1) +
                                    d_RM_s_dgradp(0,2) *
                                    p_gradphi[j][qp](2)
                                    )*test_func)*fixed_deriv*JxW[qp];
                    Kvp(i,j) += ( -tau_M*
                                  ( d_RM_s_dgradp(1,0) *
                                    p_gradphi[j][qp](0) +
                                    d_RM_s_dgradp(1,1) *
                                    p_gradphi[j][qp](1) +
                                    d_RM_s_dgradp(1,2) *
                                    p_gradphi[j][qp](2)
                                    )*test_func)*fixed_deriv*JxW[qp];
                  }
                for (unsigned int j=0; j != n_u_dofs; j++)
                  {
                    Kuu(i,j) += ( -d_tau_M_dU(0)*RM_s(0)*test_func
                                  -tau_M*d_RM_s_dU(0,0)*test_func
                                  - d_tau_C_dU(0)*RC*u_gradphi[i][qp](0)
                                  )*fixed_deriv*u_phi[j][qp]*JxW[qp];
                    Kuu(i,j) += ( -tau_M*RM_s(0)*d_test_func_dU(0)
                                  )*u_phi[j][qp]*JxW[qp];
                    Kuu(i,j) += ( - tau_C*
                                  (
                                   d_RC_dgradU(0,0)*u_gradphi[j][qp](0) +
                                   d_RC_dgradU(0,1)*u_gradphi[j][qp](1) +
                                   d_RC_dgradU(0,2)*u_gradphi[j][qp](2)
                                   )
                                  *fixed_deriv*u_gradphi[i][qp](0)
                                  )*JxW[qp];
                    Kuu(i,j) += ( -tau_M*test_func*(d_RM_s_uvw_dgraduvw*u_gradphi[j][qp])
                                  )*fixed_deriv*JxW[qp];
                    Kuu(i,j) += ( -tau_M*test_func*(d_RM_s_uvw_dhessuvw.contract(u_hessphi[j][qp]))
                                  )*fixed_deriv*JxW[qp];
                    Kuv(i,j) += ( -d_tau_M_dU(1)*RM_s(0)*test_func
                                  -tau_M*d_RM_s_dU(0,1)*test_func
                                  )*fixed_deriv*u_phi[j][qp]*JxW[qp];
                    Kuv(i,j) += ( -tau_M*RM_s(0)*d_test_func_dU(1)
                                  )*u_phi[j][qp]*JxW[qp];
                    Kuv(i,j) += ( - tau_C*
                                  (
                                   d_RC_dgradU(1,0)*u_gradphi[j][qp](0) +
                                   d_RC_dgradU(1,1)*u_gradphi[j][qp](1) +
                                   d_RC_dgradU(1,2)*u_gradphi[j][qp](2)
                                   )
                                  *fixed_deriv*u_gradphi[i][qp](0)
                                  )*JxW[qp];
                    Kvu(i,j) += ( -d_tau_M_dU(0)*RM_s(1)*test_func
                                  -tau_M*d_RM_s_dU(1,0)*test_func
                                  )*fixed_deriv*u_phi[j][qp]*JxW[qp];
                    Kvu(i,j) += ( -tau_M*RM_s(1)*d_test_func_dU(0)
                                  )*u_phi[j][qp]*JxW[qp];
                    Kvu(i,j) += ( - tau_C*
                                  (
                                   d_RC_dgradU(0,0)*u_gradphi[j][qp](0) +
                                   d_RC_dgradU(0,1)*u_gradphi[j][qp](1) +
                                   d_RC_dgradU(0,2)*u_gradphi[j][qp](2)
                                   )
                                  *fixed_deriv*u_gradphi[i][qp](1)
                                  )*JxW[qp];
                    Kvv(i,j) += ( -d_tau_M_dU(1)*RM_s(1)*test_func
                                  -tau_M*d_RM_s_dU(1,1)*test_func
                                  )*fixed_deriv*u_phi[j][qp]*JxW[qp];
                    Kvv(i,j) += ( -tau_M*RM_s(1)*d_test_func_dU(1)
                                  )*u_phi[j][qp]*JxW[qp];
                    Kvv(i,j) += ( - tau_C*
                                  (
                                   d_RC_dgradU(1,0)*u_gradphi[j][qp](0) +
                                   d_RC_dgradU(1,1)*u_gradphi[j][qp](1) +
                                   d_RC_dgradU(1,2)*u_gradphi[j][qp](2)
                                   )
                                  *fixed_deriv*u_gradphi[i][qp](1)
                                  )*JxW[qp];
                    Kvv(i,j) += ( -tau_M*test_func*(d_RM_s_uvw_dgraduvw*u_gradphi[j][qp])
                                  )*fixed_deriv*JxW[qp];
                    Kvv(i,j) += ( -tau_M*test_func*(d_RM_s_uvw_dhessuvw.contract(u_hessphi[j][qp]))
                                  )*fixed_deriv*JxW[qp];
                  }
                if(this->_flow_vars.dim() == 3)
                  {
                    for (unsigned int j=0; j != n_p_dofs; j++)
                      {
                        (*Kwp)(i,j) += ( -tau_M*
                                         ( d_RM_s_dgradp(2,0) *
                                           p_gradphi[j][qp](0) +
                                           d_RM_s_dgradp(2,1) *
                                           p_gradphi[j][qp](1) +
                                           d_RM_s_dgradp(2,2) *
                                           p_gradphi[j][qp](2)
                                           )*test_func)*fixed_deriv*JxW[qp];
                      }
                    for (unsigned int j=0; j != n_u_dofs; j++)
                      {
                        (*Kuw)(i,j) += ( -d_tau_M_dU(2)*RM_s(0)*test_func
                                         -tau_M*d_RM_s_dU(0,2)*test_func
                                         )*fixed_deriv*u_phi[j][qp]*JxW[qp];
                        (*Kuw)(i,j) += ( -tau_M*RM_s(0)*d_test_func_dU(2)
                                         )*u_phi[j][qp]*JxW[qp];
                        (*Kuw)(i,j) += ( - tau_C*
                                         (
                                          d_RC_dgradU(2,0)*u_gradphi[j][qp](0) +
                                          d_RC_dgradU(2,1)*u_gradphi[j][qp](1) +
                                          d_RC_dgradU(2,2)*u_gradphi[j][qp](2)
                                          )
                                         *fixed_deriv* u_gradphi[i][qp](0)
                                         )*JxW[qp];
                        (*Kvw)(i,j) += ( -d_tau_M_dU(2)*RM_s(1)*test_func
                                         -tau_M*d_RM_s_dU(1,2)*test_func
                                         )*fixed_deriv*u_phi[j][qp]*JxW[qp];
                        (*Kvw)(i,j) += ( -tau_M*RM_s(1)*d_test_func_dU(2)
                                         )*u_phi[j][qp]*JxW[qp];
                        (*Kvw)(i,j) += ( - tau_C*
                                         (
                                          d_RC_dgradU(2,0)*u_gradphi[j][qp](0) +
                                          d_RC_dgradU(2,1)*u_gradphi[j][qp](1) +
                                          d_RC_dgradU(2,2)*u_gradphi[j][qp](2)
                                          )
                                         *fixed_deriv* u_gradphi[i][qp](1)
                                         )*JxW[qp];
                        (*Kwu)(i,j) += ( -d_tau_M_dU(0)*RM_s(2)*test_func
                                         -tau_M*d_RM_s_dU(2,0)*test_func
                                         )*fixed_deriv*u_phi[j][qp]*JxW[qp];
                        (*Kwu)(i,j) += ( -tau_M*RM_s(2)*d_test_func_dU(0)
                                         )*u_phi[j][qp]*JxW[qp];
                        (*Kwu)(i,j) += ( - tau_C*
                                         (
                                          d_RC_dgradU(0,0)*u_gradphi[j][qp](0) +
                                          d_RC_dgradU(0,1)*u_gradphi[j][qp](1) +
                                          d_RC_dgradU(0,2)*u_gradphi[j][qp](2)
                                          )
                                         *fixed_deriv* u_gradphi[i][qp](2)
                                         )*JxW[qp];
                        (*Kwv)(i,j) += ( -d_tau_M_dU(1)*RM_s(2)*test_func
                                         -tau_M*d_RM_s_dU(2,1)*test_func
                                         )*fixed_deriv*u_phi[j][qp]*JxW[qp];
                        (*Kwv)(i,j) += ( -tau_M*RM_s(2)*d_test_func_dU(1)
                                         )*u_phi[j][qp]*JxW[qp];
                        (*Kwv)(i,j) += ( - tau_C*
                                         (
                                          d_RC_dgradU(1,0)*u_gradphi[j][qp](0) +
                                          d_RC_dgradU(1,1)*u_gradphi[j][qp](1) +
                                          d_RC_dgradU(1,2)*u_gradphi[j][qp](2)
                                          )
                                         *fixed_deriv* u_gradphi[i][qp](2)
                                         )*JxW[qp];
                        (*Kww)(i,j) += ( -d_tau_M_dU(2)*RM_s(2)*test_func
                                         -tau_M*d_RM_s_dU(2,2)*test_func
                                         )*fixed_deriv*u_phi[j][qp]*JxW[qp];
                        (*Kww)(i,j) += ( -tau_M*RM_s(2)*d_test_func_dU(2)
                                         )*u_phi[j][qp]*JxW[qp];
                        (*Kww)(i,j) += ( - tau_C*
                                         (
                                          d_RC_dgradU(2,0)*u_gradphi[j][qp](0) +
                                          d_RC_dgradU(2,1)*u_gradphi[j][qp](1) +
                                          d_RC_dgradU(2,2)*u_gradphi[j][qp](2)
                                          )
                                         *fixed_deriv* u_gradphi[i][qp](2)
                                         )*JxW[qp];
                        (*Kww)(i,j) += ( -tau_M*test_func*(d_RM_s_uvw_dgraduvw*u_gradphi[j][qp])
                                         )*fixed_deriv*JxW[qp];
                        (*Kww)(i,j) += ( -tau_M*test_func*(d_RM_s_uvw_dhessuvw.contract(u_hessphi[j][qp]))
                                         )*fixed_deriv*JxW[qp];

                      }
                  }
              }
          }
      }
  }

template<class Mu >

void GRINS::IncompressibleNavierStokesAdjointStabilization< Mu >::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 522 of file inc_navier_stokes_adjoint_stab.C.

  {
    // 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();

    // The pressure shape functions at interior quadrature points.
    const std::vector<std::vector<libMesh::RealGradient> >& p_dphi =
      context.get_element_fe(this->_press_var.p())->get_dphi();

    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> >& u_gradphi =
      context.get_element_fe(this->_flow_vars.u())->get_dphi();

    const std::vector<std::vector<libMesh::RealTensor> >& u_hessphi =
      context.get_element_fe(this->_flow_vars.u())->get_d2phi();

    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;

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

    libMesh::DenseSubMatrix<libMesh::Number> &Kuu =
      context.get_elem_jacobian(this->_flow_vars.u(), this->_flow_vars.u()); // J_{uu}
    libMesh::DenseSubMatrix<libMesh::Number> &Kuv =
      context.get_elem_jacobian(this->_flow_vars.u(), this->_flow_vars.v()); // J_{uv}
    libMesh::DenseSubMatrix<libMesh::Number> &Kvu =
      context.get_elem_jacobian(this->_flow_vars.v(), this->_flow_vars.u()); // J_{vu}
    libMesh::DenseSubMatrix<libMesh::Number> &Kvv =
      context.get_elem_jacobian(this->_flow_vars.v(), this->_flow_vars.v()); // J_{vv}

    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;

    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->_flow_vars.dim() == 3)
      {
        Fw = &context.get_elem_residual(this->_flow_vars.w()); // R_{w}

        Kuw = &context.get_elem_jacobian
          (this->_flow_vars.u(), this->_flow_vars.w()); // J_{uw}
        Kvw = &context.get_elem_jacobian
          (this->_flow_vars.v(), this->_flow_vars.w()); // J_{vw}
        Kwu = &context.get_elem_jacobian
          (this->_flow_vars.w(), this->_flow_vars.u()); // J_{wu}
        Kwv = &context.get_elem_jacobian
          (this->_flow_vars.w(), this->_flow_vars.v()); // J_{wv}
        Kww = &context.get_elem_jacobian
          (this->_flow_vars.w(), this->_flow_vars.w()); // J_{ww}

        Kpw = &context.get_elem_jacobian
          (this->_press_var.p(), this->_flow_vars.w()); // J_{pw}
      }

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

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

        libMesh::RealGradient g = this->_stab_helper.compute_g( fe, context, qp );
        libMesh::RealTensor G = this->_stab_helper.compute_G( fe, context, qp );

        libMesh::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::Gradient grad_u, grad_v, grad_w;
          grad_u = context.interior_gradient(this->_flow_vars.u(), qp);
          grad_v = context.interior_gradient(this->_flow_vars.v(), qp);
          if (_dim == 3)
          grad_w = context.interior_gradient(this->_flow_vars.w(), qp);
        */

        libMesh::Real tau_M;

        libMesh::Real d_tau_M_d_rho;

        libMesh::Gradient d_tau_M_dU;

        libMesh::RealGradient RM_t;

        libMesh::Real d_RM_t_uvw_duvw;

        // Compute the viscosity at this qp
        libMesh::Real _mu_qp = this->_mu(context, qp);

        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,
                false );
            this->_stab_helper.compute_res_momentum_transient_and_derivs
              ( context, qp, this->_rho,
                RM_t, d_RM_t_uvw_duvw );
          }
        else
          {
            tau_M = this->_stab_helper.compute_tau_momentum( context, qp, g, G, this->_rho, U, _mu_qp, false );
            RM_t = this->_stab_helper.compute_res_momentum_transient( context, qp, this->_rho );
          }


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

            if (compute_jacobian)
              {
                const libMesh::Real fixed_deriv =
                  context.get_fixed_solution_derivative();

                for (unsigned int j=0; j != n_u_dofs; j++)
                  {
                    Kpu(i,j) -= d_tau_M_dU(0)*u_phi[j][qp]*RM_t*p_dphi[i][qp]*fixed_deriv*JxW[qp];
                    Kpu(i,j) -= tau_M*d_RM_t_uvw_duvw*u_phi[j][qp]*p_dphi[i][qp](0)*fixed_deriv*JxW[qp];

                    Kpv(i,j) -= d_tau_M_dU(1)*u_phi[j][qp]*RM_t*p_dphi[i][qp]*fixed_deriv*JxW[qp];
                    Kpv(i,j) -= tau_M*d_RM_t_uvw_duvw*u_phi[j][qp]*p_dphi[i][qp](1)*fixed_deriv*JxW[qp];
                  }

                if(this->_flow_vars.dim() == 3)
                  {
                    for (unsigned int j=0; j != n_u_dofs; j++)
                      {
                        (*Kpw)(i,j) -= d_tau_M_dU(2)*u_phi[j][qp]*RM_t*p_dphi[i][qp]*fixed_deriv*JxW[qp];
                        (*Kpw)(i,j) -= tau_M*d_RM_t_uvw_duvw*u_phi[j][qp]*p_dphi[i][qp](2)*fixed_deriv*JxW[qp];
                      }
                  }
              }
          }

        for (unsigned int i=0; i != n_u_dofs; i++)
          {
            libMesh::Real test_func = this->_rho*U*u_gradphi[i][qp] +
              _mu_qp*( u_hessphi[i][qp](0,0) + u_hessphi[i][qp](1,1) + u_hessphi[i][qp](2,2) );
            libMesh::Gradient d_test_func_dU = this->_rho*u_gradphi[i][qp];

            //libMesh::RealGradient zeroth_order_term = - this->_rho*u_phi[i][qp]*(grad_u + grad_v + grad_w);

            Fu(i) -= tau_M*RM_t(0)*test_func*JxW[qp];

            Fv(i) -= tau_M*RM_t(1)*test_func*JxW[qp];

            if(this->_flow_vars.dim() == 3)
              {
                (*Fw)(i) -= tau_M*RM_t(2)*test_func*JxW[qp];
              }

            if (compute_jacobian)
              {
                const libMesh::Real fixed_deriv =
                  context.get_fixed_solution_derivative();

                for (unsigned int j=0; j != n_u_dofs; j++)
                  {
                    Kuu(i,j) -= d_tau_M_dU(0)*u_phi[j][qp]*RM_t(0)*test_func*fixed_deriv*JxW[qp];
                    Kuu(i,j) -= tau_M*d_RM_t_uvw_duvw*u_phi[j][qp]*test_func*fixed_deriv*JxW[qp];
                    Kuu(i,j) -= tau_M*RM_t(0)*d_test_func_dU(0)*u_phi[j][qp]*fixed_deriv*JxW[qp];

                    Kuv(i,j) -= d_tau_M_dU(1)*u_phi[j][qp]*RM_t(0)*test_func*fixed_deriv*JxW[qp];
                    Kuv(i,j) -= tau_M*RM_t(0)*d_test_func_dU(1)*u_phi[j][qp]*fixed_deriv*JxW[qp];

                    Kvu(i,j) -= d_tau_M_dU(0)*u_phi[j][qp]*RM_t(1)*test_func*fixed_deriv*JxW[qp];
                    Kvu(i,j) -= tau_M*RM_t(1)*d_test_func_dU(0)*u_phi[j][qp]*fixed_deriv*JxW[qp];

                    Kvv(i,j) -= d_tau_M_dU(1)*u_phi[j][qp]*RM_t(1)*test_func*fixed_deriv*JxW[qp];
                    Kvv(i,j) -= tau_M*d_RM_t_uvw_duvw*u_phi[j][qp]*test_func*fixed_deriv*JxW[qp];
                    Kvv(i,j) -= tau_M*RM_t(1)*d_test_func_dU(1)*u_phi[j][qp]*fixed_deriv*JxW[qp];
                  }
                if(this->_flow_vars.dim() == 3)
                  {
                    for (unsigned int j=0; j != n_u_dofs; j++)
                      {
                        (*Kuw)(i,j) -= d_tau_M_dU(2)*u_phi[j][qp]*RM_t(0)*test_func*fixed_deriv*JxW[qp];
                        (*Kuw)(i,j) -= tau_M*RM_t(0)*d_test_func_dU(2)*u_phi[j][qp]*fixed_deriv*JxW[qp];

                        (*Kvw)(i,j) -= d_tau_M_dU(2)*u_phi[j][qp]*RM_t(1)*test_func*fixed_deriv*JxW[qp];
                        (*Kvw)(i,j) -= tau_M*RM_t(1)*d_test_func_dU(2)*u_phi[j][qp]*fixed_deriv*JxW[qp];

                        (*Kwu)(i,j) -= d_tau_M_dU(0)*u_phi[j][qp]*RM_t(2)*test_func*fixed_deriv*JxW[qp];
                        (*Kwu)(i,j) -= tau_M*RM_t(2)*d_test_func_dU(0)*u_phi[j][qp]*fixed_deriv*JxW[qp];

                        (*Kwv)(i,j) -= d_tau_M_dU(1)*u_phi[j][qp]*RM_t(2)*test_func*fixed_deriv*JxW[qp];
                        (*Kwv)(i,j) -= tau_M*RM_t(2)*d_test_func_dU(1)*u_phi[j][qp]*fixed_deriv*JxW[qp];

                        (*Kww)(i,j) -= d_tau_M_dU(2)*u_phi[j][qp]*RM_t(2)*test_func*fixed_deriv*JxW[qp];
                        (*Kww)(i,j) -= tau_M*d_RM_t_uvw_duvw*u_phi[j][qp]*test_func*fixed_deriv*JxW[qp];
                        (*Kww)(i,j) -= tau_M*RM_t(2)*d_test_func_dU(2)*u_phi[j][qp]*fixed_deriv*JxW[qp];
                      }
                  }
              }
          }

      }
  }

---

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

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