GRINS::Stokes< Viscosity > Class Template Reference

Physics class for Stokes. More...

#include <stokes.h>

Inheritance diagram for GRINS::Stokes< Viscosity >:

Collaboration diagram for GRINS::Stokes< Viscosity >:

Public Member Functions
	Stokes (const std::string &physics_name, const GetPot &input)
	~Stokes ()
virtual void	auxiliary_init (MultiphysicsSystem &system)
	Any auxillary initialization a Physics class may need. More...
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::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	init_context (AssemblyContext &context)
	Initialize context for added physics variables. 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	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...

Protected Attributes
PressurePinning	_p_pinning
bool	_pin_pressure
	Enable pressure pinning. More...
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...

Private Member Functions
	Stokes ()

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...
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::Stokes< Viscosity >

Physics class for Stokes.

This physics class implements the classical Stokes equations.

Definition at line 43 of file stokes.h.

Constructor & Destructor Documentation

template<class Mu >

GRINS::Stokes< Mu >::Stokes	(	const std::string &	physics_name,
		const GetPot &	input
	)

Definition at line 44 of file stokes.C.

References GRINS::Physics::_ic_handler.

    : IncompressibleNavierStokesBase<Mu>(physics_name,
                                         PhysicsNaming::stokes(), /* "core" Physics name */
                                         input),
    _p_pinning(input,physics_name),
    _pin_pressure( input("Physics/"+PhysicsNaming::stokes()+"/pin_pressure", false ) )
  {
    this->_ic_handler = new GenericICHandler( physics_name, input );
  }

template<class Mu >

GRINS::Stokes< Mu >::~Stokes

(

)

Definition at line 55 of file stokes.C.

  {
    return;
  }

template<class Viscosity >

GRINS::Stokes< Viscosity >::Stokes ( )

private

Member Function Documentation

template<class Mu >

void GRINS::Stokes< Mu >::auxiliary_init ( MultiphysicsSystem &  system )

virtual

Any auxillary initialization a Physics class may need.

This is called after all variables are added, so this method can safely query the MultiphysicsSystem about variable information.

Reimplemented from GRINS::Physics.

Definition at line 61 of file stokes.C.

  {
    if( _pin_pressure )
      _p_pinning.check_pin_location(system.get_mesh());
  }

template<class Mu >

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

virtual

Constraint part(s) of physics for element interiors.

Reimplemented from GRINS::Physics.

Definition at line 211 of file stokes.C.

  {
    // 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();
    const unsigned int n_p_dofs = context.get_dof_indices(this->_press_var.p()).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(this->_flow_vars.u())->get_JxW();

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

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

    // The subvectors and submatrices we need to fill:
    //
    // Kpu, Kpv, Kpw, Fp

    libMesh::DenseSubMatrix<libMesh::Number> &Kpu = context.get_elem_jacobian(this->_press_var.p(), this->_flow_vars.u()); // R_{p},{u}
    libMesh::DenseSubMatrix<libMesh::Number> &Kpv = context.get_elem_jacobian(this->_press_var.p(), this->_flow_vars.v()); // R_{p},{v}
    libMesh::DenseSubMatrix<libMesh::Number>* Kpw = NULL;

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


    if( this->_flow_vars.dim() == 3 )
      {
        Kpw = &context.get_elem_jacobian(this->_press_var.p(), this->_flow_vars.w()); // R_{p},{w}
      }

    // Add the constraint given by the continuity equation.
    unsigned int n_qpoints = context.get_element_qrule().n_points();
    for (unsigned int qp=0; qp != n_qpoints; qp++)
      {
        // Compute the velocity gradient at the old Newton iterate.
        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 (this->_flow_vars.dim() == 3)
          grad_w = context.interior_gradient(this->_flow_vars.w(), 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) += JxW[qp] * p_phi[i][qp] *
              (grad_u(0) + grad_v(1));
            if (this->_flow_vars.dim() == 3)
              Fp(i) += JxW[qp] * p_phi[i][qp] *
                (grad_w(2));

            if (compute_jacobian)
              {
                for (unsigned int j=0; j != n_u_dofs; j++)
                  {
                    Kpu(i,j) += context.get_elem_solution_derivative() * JxW[qp]*p_phi[i][qp]*u_gradphi[j][qp](0);
                    Kpv(i,j) += context.get_elem_solution_derivative() * JxW[qp]*p_phi[i][qp]*u_gradphi[j][qp](1);
                    if (this->_flow_vars.dim() == 3)
                      (*Kpw)(i,j) += context.get_elem_solution_derivative() * JxW[qp]*p_phi[i][qp]*u_gradphi[j][qp](2);
                  } // end of the inner dof (j) loop

              } // end - if (compute_jacobian && context.get_elem_solution_derivative())

          } // end of the outer dof (i) loop
      } // end of the quadrature point (qp) loop


    // Pin p = p_value at p_point
    if( _pin_pressure )
      {
        _p_pinning.pin_value( context, compute_jacobian, this->_press_var.p() );
      }
  }

template<class Mu >

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

virtual

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

Reimplemented from GRINS::Physics.

Definition at line 69 of file stokes.C.

  {
    // 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();
    const unsigned int n_p_dofs = context.get_dof_indices(this->_press_var.p()).size();

    // Check number of dofs is same for this->_flow_vars.u(), v_var and w_var.
    libmesh_assert (n_u_dofs == context.get_dof_indices(this->_flow_vars.v()).size());

    if (this->_flow_vars.dim() == 3)
      libmesh_assert (n_u_dofs == context.get_dof_indices(this->_flow_vars.w()).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(this->_flow_vars.u())->get_JxW();

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

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

    // The subvectors and submatrices we need to fill:
    //
    // K_{\alpha \beta} = R_{\alpha},{\beta} = \partial{ R_{\alpha} } / \partial{ {\beta} } (where R denotes residual)
    // e.g., for \alpha = v and \beta = u we get: K{vu} = R_{v},{u}
    // Note that Kpu, Kpv, Kpw and Fp comes as constraint.

    libMesh::DenseSubMatrix<libMesh::Number> &Kuu = context.get_elem_jacobian(this->_flow_vars.u(), this->_flow_vars.u()); // R_{u},{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>* Kww = NULL;

    libMesh::DenseSubMatrix<libMesh::Number> &Kup = context.get_elem_jacobian(this->_flow_vars.u(), this->_press_var.p()); // R_{u},{p}
    libMesh::DenseSubMatrix<libMesh::Number> &Kvp = context.get_elem_jacobian(this->_flow_vars.v(), this->_press_var.p()); // R_{v},{p}
    libMesh::DenseSubMatrix<libMesh::Number>* Kwp = 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;

    if( this->_flow_vars.dim() == 3 )
      {
        Kww = &context.get_elem_jacobian(this->_flow_vars.w(), this->_flow_vars.w()); // R_{w},{w}
        Kwp = &context.get_elem_jacobian(this->_flow_vars.w(), this->_press_var.p()); // R_{w},{p}
        Fw  = &context.get_elem_residual(this->_flow_vars.w()); // R_{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 p, u, v, w;
        p = context.interior_value(this->_press_var.p(), qp);
        u = context.interior_value(this->_flow_vars.u(), qp);
        v = context.interior_value(this->_flow_vars.v(), qp);
        if (this->_flow_vars.dim() == 3)
          w = 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 (this->_flow_vars.dim() == 3)
          grad_w = context.interior_gradient(this->_flow_vars.w(), qp);

        libMesh::NumberVectorValue Uvec (u,v);
        if (this->_flow_vars.dim() == 3)
          Uvec(2) = w;

        // Compute the viscosity at this qp
        libMesh::Real _mu_qp = this->_mu(context, 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++)
          {
            Fu(i) += JxW[qp] *
              ( p*u_gradphi[i][qp](0)              // pressure term
                -_mu_qp*(u_gradphi[i][qp]*grad_u) ); // diffusion term

            Fv(i) += JxW[qp] *
              ( p*u_gradphi[i][qp](1)              // pressure term
                -_mu_qp*(u_gradphi[i][qp]*grad_v) ); // diffusion term
            if (this->_flow_vars.dim() == 3)
              {
                (*Fw)(i) += JxW[qp] *
                  ( p*u_gradphi[i][qp](2)              // pressure term
                    -_mu_qp*(u_gradphi[i][qp]*grad_w) ); // diffusion term
              }

            if (compute_jacobian)
              {
                for (unsigned int j=0; j != n_u_dofs; j++)
                  {
                    // TODO: precompute some terms like:
                    //   (Uvec*vel_gblgradphivec[j][qp]),
                    //   vel_phi[i][qp]*vel_phi[j][qp],
                    //   (vel_gblgradphivec[i][qp]*vel_gblgradphivec[j][qp])

                    Kuu(i,j) += JxW[qp] * context.get_elem_solution_derivative() *
                      (-_mu_qp*(u_gradphi[i][qp]*u_gradphi[j][qp])); // diffusion term

                    Kvv(i,j) += JxW[qp] * context.get_elem_solution_derivative() *
                      (-_mu_qp*(u_gradphi[i][qp]*u_gradphi[j][qp])); // diffusion term

                    if (this->_flow_vars.dim() == 3)
                      {
                        (*Kww)(i,j) += JxW[qp] * context.get_elem_solution_derivative() *
                          (-_mu_qp*(u_gradphi[i][qp]*u_gradphi[j][qp])); // diffusion term
                      }
                  } // end of the inner dof (j) loop

                // Matrix contributions for the up, vp and wp couplings
                for (unsigned int j=0; j != n_p_dofs; j++)
                  {
                    Kup(i,j) += context.get_elem_solution_derivative() * JxW[qp]*u_gradphi[i][qp](0)*p_phi[j][qp];
                    Kvp(i,j) += context.get_elem_solution_derivative() * JxW[qp]*u_gradphi[i][qp](1)*p_phi[j][qp];
                    if (this->_flow_vars.dim() == 3)
                      (*Kwp)(i,j) += context.get_elem_solution_derivative() * JxW[qp]*u_gradphi[i][qp](2)*p_phi[j][qp];
                  } // end of the inner dof (j) loop

              } // end - if (compute_jacobian && context.get_elem_solution_derivative())

          } // end of the outer dof (i) loop
      } // end of the quadrature point (qp) loop
  }

template<class Mu >

void GRINS::Stokes< 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 295 of file stokes.C.

  {
    // Element Jacobian * quadrature weights for interior integration
    // We assume the same for each flow variable
    const std::vector<libMesh::Real> &JxW =
      context.get_element_fe(this->_flow_vars.u())->get_JxW();

    // The shape functions at interior quadrature points.
    // We assume the same for each flow variable
    const std::vector<std::vector<libMesh::Real> >& u_phi =
      context.get_element_fe(this->_flow_vars.u())->get_phi();

    // 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::DenseSubVector<libMesh::Real> &F_u = context.get_elem_residual(this->_flow_vars.u());
    libMesh::DenseSubVector<libMesh::Real> &F_v = context.get_elem_residual(this->_flow_vars.v());
    libMesh::DenseSubVector<libMesh::Real>* F_w = NULL;

    libMesh::DenseSubMatrix<libMesh::Real> &M_uu = context.get_elem_jacobian(this->_flow_vars.u(), this->_flow_vars.u());
    libMesh::DenseSubMatrix<libMesh::Real> &M_vv = context.get_elem_jacobian(this->_flow_vars.v(), this->_flow_vars.v());
    libMesh::DenseSubMatrix<libMesh::Real>* M_ww = NULL;

    if( this->_flow_vars.dim() == 3 )
      {
        F_w  = &context.get_elem_residual(this->_flow_vars.w()); // R_{w}
        M_ww = &context.get_elem_jacobian(this->_flow_vars.w(), this->_flow_vars.w());
      }

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

    for (unsigned int qp = 0; qp != n_qpoints; ++qp)
      {
        // For the mass residual, we need to be a little careful.
        // The time integrator is handling the time-discretization
        // for us so we need to supply M(u_fixed)*u' for the residual.
        // u_fixed will be given by the fixed_interior_value function
        // while u' will be given by the interior_rate function.
        libMesh::Real u_dot, v_dot, w_dot = 0.0;
        context.interior_rate(this->_flow_vars.u(), qp, u_dot);
        context.interior_rate(this->_flow_vars.v(), qp, v_dot);

        if( this->_flow_vars.dim() == 3 )
          context.interior_rate(this->_flow_vars.w(), qp, w_dot);

        for (unsigned int i = 0; i != n_u_dofs; ++i)
          {
            F_u(i) -= JxW[qp]*this->_rho*u_dot*u_phi[i][qp];
            F_v(i) -= JxW[qp]*this->_rho*v_dot*u_phi[i][qp];

            if( this->_flow_vars.dim() == 3 )
              (*F_w)(i) -= JxW[qp]*this->_rho*w_dot*u_phi[i][qp];

            if( compute_jacobian )
              {
                for (unsigned int j=0; j != n_u_dofs; j++)
                  {
                    // Assuming rho is constant w.r.t. u, v, w
                    // and T (if Boussinesq added).
                    libMesh::Real value = context.get_elem_solution_derivative() * JxW[qp]*this->_rho*u_phi[i][qp]*u_phi[j][qp];

                    M_uu(i,j) -= value;
                    M_vv(i,j) -= value;

                    if( this->_flow_vars.dim() == 3)
                      {
                        (*M_ww)(i,j) -= value;
                      }

                  } // End dof loop
              } // End Jacobian check
          } // End dof loop
      } // End quadrature loop

    return;
  }

Member Data Documentation

template<class Viscosity >

PressurePinning GRINS::Stokes< Viscosity >::_p_pinning

protected

Definition at line 70 of file stokes.h.

template<class Viscosity >

bool GRINS::Stokes< Viscosity >::_pin_pressure

protected

Enable pressure pinning.

Definition at line 73 of file stokes.h.

---

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

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