#include <navier_stokes_elements_with_singularity.h>

Inheritance diagram for oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >:

Public Types
typedef Vector< double >(*	NavierStokesVelocitySingularFctPt) (const Vector< double > &x)
	Function pointer to the velocity singular function: More...

typedef Vector< Vector< double > >(*	NavierStokesGradVelocitySingularFctPt) (const Vector< double > &x)
	Function pointer to the gradient of the velocity singular function: More...

typedef double(*	NavierStokesPressureSingularFctPt) (const Vector< double > &x)
	Function pointer to the pressure singular function: More...

typedef Vector< double >(*	NavierStokesGradPressureSingularFctPt) (const Vector< double > &x)
	Function pointer to the gradient of the pressure singular function: More...

Public Member Functions
	SingularNavierStokesSolutionElement ()
	Constructor. More...

bool &	singular_function_satisfies_stokes_equation ()

double	c () const
	Find the value of the unknown amplitude C. More...

void	set_c (const double &value)
	Find the value of the unknown amplitude C. More...

void	pin_c ()
	Pin the value of the unknown amplitude C. More...

void	unpin_c ()
	Unpin the value of the unknown amplitude C. More...

void	set_wrapped_navier_stokes_element_pt (WRAPPED_NAVIER_STOKES_ELEMENT wrapped_navier_stokes_el_pt, const Vector< double > &s, unsigned direction_pt)

NavierStokesVelocitySingularFctPt &	velocity_singular_fct_pt ()
	Access function to pointer to velocity singular function. More...

NavierStokesGradVelocitySingularFctPt &	grad_velocity_singular_fct_pt ()
	Access function to pointer to gradient of velocity singular function. More...

NavierStokesPressureSingularFctPt &	pressure_singular_fct_pt ()
	Access function to pointer to pressure singular function. More...

NavierStokesGradPressureSingularFctPt &	grad_pressure_singular_fct_pt ()
	Access function to pointer to gradient of pressure singular function. More...

Vector< double >	velocity_singular_function (const Vector< double > &x) const
	Evaluate velocity singular function at Eulerian position x. More...

Vector< Vector< double > >	grad_velocity_singular_function (const Vector< double > &x) const

double	pressure_singular_function (const Vector< double > &x) const
	Evaluate pressure singular function at Eulerian position x. More...

Vector< double >	grad_pressure_singular_function (const Vector< double > &x) const
	Evaluate gradient of pressure singular function at Eulerian position x. More...

Vector< double >	u_bar (const Vector< double > &x)

Vector< Vector< double > >	grad_u_bar (const Vector< double > &x)

double	p_bar (const Vector< double > &x)

Vector< double >	grad_p_bar (const Vector< double > &x)

void	fill_in_contribution_to_residuals (Vector< double > &residual)
	Compute residual. More...

void	fill_in_contribution_to_jacobian (Vector< double > &residual, DenseMatrix< double > &jacobian)

Public Member Functions inherited from oomph::GeneralisedElement
	GeneralisedElement ()
	Constructor: Initialise all pointers and all values to zero. More...

virtual	~GeneralisedElement ()
	Virtual destructor to clean up any memory allocated by the object. More...

	GeneralisedElement (const GeneralisedElement &)=delete
	Broken copy constructor. More...

void	operator= (const GeneralisedElement &)=delete
	Broken assignment operator. More...

Data *&	internal_data_pt (const unsigned &i)
	Return a pointer to i-th internal data object. More...

Data *const &	internal_data_pt (const unsigned &i) const
	Return a pointer to i-th internal data object (const version) More...

Data *&	external_data_pt (const unsigned &i)
	Return a pointer to i-th external data object. More...

Data *const &	external_data_pt (const unsigned &i) const
	Return a pointer to i-th external data object (const version) More...

unsigned long	eqn_number (const unsigned &ieqn_local) const

int	local_eqn_number (const unsigned long &ieqn_global) const

unsigned	add_external_data (Data *const &data_pt, const bool &fd=true)

bool	external_data_fd (const unsigned &i) const

void	exclude_external_data_fd (const unsigned &i)

void	include_external_data_fd (const unsigned &i)

void	flush_external_data ()
	Flush all external data. More...

void	flush_external_data (Data *const &data_pt)
	Flush the object addressed by data_pt from the external data array. More...

unsigned	ninternal_data () const
	Return the number of internal data objects. More...

unsigned	nexternal_data () const
	Return the number of external data objects. More...

unsigned	ndof () const
	Return the number of equations/dofs in the element. More...

void	dof_vector (const unsigned &t, Vector< double > &dof)
	Return the vector of dof values at time level t. More...

void	dof_pt_vector (Vector< double * > &dof_pt)
	Return the vector of pointers to dof values. More...

void	set_internal_data_time_stepper (const unsigned &i, TimeStepper *const &time_stepper_pt, const bool &preserve_existing_data)

void	assign_internal_eqn_numbers (unsigned long &global_number, Vector< double * > &Dof_pt)

void	describe_dofs (std::ostream &out, const std::string &current_string) const

virtual void	describe_local_dofs (std::ostream &out, const std::string &current_string) const

void	add_internal_value_pt_to_map (std::map< unsigned, double * > &map_of_value_pt)

virtual void	assign_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	complete_setup_of_dependencies ()

virtual void	get_residuals (Vector< double > &residuals)

virtual void	get_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)

virtual void	get_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &mass_matrix)

virtual void	get_jacobian_and_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix)

virtual void	get_dresiduals_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam)

virtual void	get_djacobian_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam)

virtual void	get_djacobian_and_dmass_matrix_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam, DenseMatrix< double > &dmass_matrix_dparam)

virtual void	get_hessian_vector_products (Vector< double > const &Y, DenseMatrix< double > const &C, DenseMatrix< double > &product)

virtual void	get_inner_products (Vector< std::pair< unsigned, unsigned >> const &history_index, Vector< double > &inner_product)

virtual void	get_inner_product_vectors (Vector< unsigned > const &history_index, Vector< Vector< double >> &inner_product_vector)

virtual unsigned	self_test ()

virtual void	compute_norm (Vector< double > &norm)

virtual void	compute_norm (double &norm)

virtual unsigned	ndof_types () const

virtual void	get_dof_numbers_for_unknowns (std::list< std::pair< unsigned long, unsigned >> &dof_lookup_list) const

Private Member Functions
void	fill_in_generic_contribution_to_residuals (Vector< double > &residual, DenseMatrix< double > &jacobian, const unsigned &flag)
	Compute local residual, and, if flag=1, local jacobian matrix. More...

Private Attributes
WRAPPED_NAVIER_STOKES_ELEMENT *	Wrapped_navier_stokes_el_pt
	Pointer to wrapped Navier-Stokes element. More...

NavierStokesVelocitySingularFctPt	Velocity_singular_fct_pt
	Pointer to velocity singular function. More...

NavierStokesGradVelocitySingularFctPt	Grad_velocity_singular_fct_pt

NavierStokesPressureSingularFctPt	Pressure_singular_fct_pt
	Pointer to pressure singular function. More...

NavierStokesGradPressureSingularFctPt	Grad_pressure_singular_fct_pt
	Pointer to gradient of pressure singular function. More...

Vector< double >	S_in_wrapped_navier_stokes_element
	Local coordinates of singulariity in wrapped Navier-Stokes element. More...

unsigned *	Direction_pt
	Direction of the derivative used for the residual of the element. More...

bool	Singular_function_satisfies_stokes_equation

Additional Inherited Members
Static Public Attributes inherited from oomph::GeneralisedElement
static bool	Suppress_warning_about_repeated_internal_data

static bool	Suppress_warning_about_repeated_external_data = true

static double	Default_fd_jacobian_step = 1.0e-8

Protected Member Functions inherited from oomph::GeneralisedElement
unsigned	add_internal_data (Data *const &data_pt, const bool &fd=true)

bool	internal_data_fd (const unsigned &i) const

void	exclude_internal_data_fd (const unsigned &i)

void	include_internal_data_fd (const unsigned &i)

void	clear_global_eqn_numbers ()

void	add_global_eqn_numbers (std::deque< unsigned long > const &global_eqn_numbers, std::deque< double * > const &global_dof_pt)

virtual void	assign_internal_and_external_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	assign_additional_local_eqn_numbers ()

int	internal_local_eqn (const unsigned &i, const unsigned &j) const

int	external_local_eqn (const unsigned &i, const unsigned &j)

void	fill_in_jacobian_from_internal_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian, const bool &fd_all_data=false)

void	fill_in_jacobian_from_internal_by_fd (DenseMatrix< double > &jacobian, const bool &fd_all_data=false)

void	fill_in_jacobian_from_external_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian, const bool &fd_all_data=false)

void	fill_in_jacobian_from_external_by_fd (DenseMatrix< double > &jacobian, const bool &fd_all_data=false)

virtual void	update_before_internal_fd ()

virtual void	reset_after_internal_fd ()

virtual void	update_in_internal_fd (const unsigned &i)

virtual void	reset_in_internal_fd (const unsigned &i)

virtual void	update_before_external_fd ()

virtual void	reset_after_external_fd ()

virtual void	update_in_external_fd (const unsigned &i)

virtual void	reset_in_external_fd (const unsigned &i)

virtual void	fill_in_contribution_to_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &mass_matrix)

virtual void	fill_in_contribution_to_jacobian_and_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix)

virtual void	fill_in_contribution_to_dresiduals_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam)

virtual void	fill_in_contribution_to_djacobian_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam)

virtual void	fill_in_contribution_to_djacobian_and_dmass_matrix_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam, DenseMatrix< double > &dmass_matrix_dparam)

virtual void	fill_in_contribution_to_hessian_vector_products (Vector< double > const &Y, DenseMatrix< double > const &C, DenseMatrix< double > &product)

virtual void	fill_in_contribution_to_inner_products (Vector< std::pair< unsigned, unsigned >> const &history_index, Vector< double > &inner_product)

virtual void	fill_in_contribution_to_inner_product_vectors (Vector< unsigned > const &history_index, Vector< Vector< double >> &inner_product_vector)

Static Protected Attributes inherited from oomph::GeneralisedElement
static DenseMatrix< double >	Dummy_matrix

static std::deque< double * >	Dof_pt_deque

Detailed Description

template<class WRAPPED_NAVIER_STOKES_ELEMENT>
class oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >

We consider a singularity in the solution at the point O.

This class defines the singular functions.

velocity_singularity:

u_bar = C*velocity_singular_function

pressure_singularity:

p_bar = C*pressure_singular_function

and their gradients

The class also defines the function that computes the residual associated to C which is:

R_C = \frac{\partial p_FE}{\partial x_i} (O)

and thus regularises the FE solution by setting the pressure gradient in the coordinate direction x_i to zero. If the amplitude of the singular solution is known, pin C.

Member Typedef Documentation

◆ NavierStokesGradPressureSingularFctPt

template<class WRAPPED_NAVIER_STOKES_ELEMENT >

typedef Vector<double>(* oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::NavierStokesGradPressureSingularFctPt) (const Vector< double > &x)

Function pointer to the gradient of the pressure singular function:

◆ NavierStokesGradVelocitySingularFctPt

template<class WRAPPED_NAVIER_STOKES_ELEMENT >

typedef Vector<Vector<double> >(* oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::NavierStokesGradVelocitySingularFctPt) (const Vector< double > &x)

Function pointer to the gradient of the velocity singular function:

◆ NavierStokesPressureSingularFctPt

template<class WRAPPED_NAVIER_STOKES_ELEMENT >

typedef double(* oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::NavierStokesPressureSingularFctPt) (const Vector< double > &x)

Function pointer to the pressure singular function:

◆ NavierStokesVelocitySingularFctPt

template<class WRAPPED_NAVIER_STOKES_ELEMENT >

typedef Vector<double>(* oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::NavierStokesVelocitySingularFctPt) (const Vector< double > &x)

Function pointer to the velocity singular function:

Constructor & Destructor Documentation

◆ SingularNavierStokesSolutionElement()

template<class WRAPPED_NAVIER_STOKES_ELEMENT >

oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::SingularNavierStokesSolutionElement ( )

inline

Constructor.

   {
    // Initialise Function pointer to velocity singular function to NULL
    Velocity_singular_fct_pt=0;
  
    // Initialise Function pointer to gradient of velocity singular
    // function to NULL
    Grad_velocity_singular_fct_pt=0;
  
    // Initialise Function pointer to pressure singular function to NULL
    Pressure_singular_fct_pt=0;
  
    // Initialise Function pointer to gradient of pressure singular
    // function to NULL
    Grad_pressure_singular_fct_pt=0;
  
    // Initalise pointer to the wrapped Navier-Stokes element which will be
    // used to compute the residual and which includes the point O
    Wrapped_navier_stokes_el_pt=0;
  
    // Initialise the pointer to the direction of the derivative used
    // for the residual of this element
    Direction_pt=0;
  
    // Safe assumption: Singular fct does not satisfy Stokes eqn
    Singular_function_satisfies_stokes_equation=false;
  
    // Create a single item of internal Data, storing one unknown which
    // represents the unknown C.
    add_internal_data(new Data(1));
   }

References oomph::GeneralisedElement::add_internal_data(), oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::Direction_pt, oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::Grad_pressure_singular_fct_pt, oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::Grad_velocity_singular_fct_pt, oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::Pressure_singular_fct_pt, oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::Singular_function_satisfies_stokes_equation, oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::Velocity_singular_fct_pt, and oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::Wrapped_navier_stokes_el_pt.

Member Function Documentation

◆ c()

template<class WRAPPED_NAVIER_STOKES_ELEMENT >

double oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::c ( ) const

inline

Find the value of the unknown amplitude C.

  {
   return internal_data_pt(0)->value(0);
  }

References oomph::GeneralisedElement::internal_data_pt(), and oomph::Data::value().

Referenced by oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::grad_p_bar(), oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::grad_u_bar(), oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::p_bar(), and oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::u_bar().

◆ fill_in_contribution_to_jacobian()

template<class WRAPPED_NAVIER_STOKES_ELEMENT >

void oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::fill_in_contribution_to_jacobian	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian
	)

inlinevirtual

Add the elemental contribution to the jacobian matrix. and the residuals vector. Note that this function will NOT initialise the residuals vector or the jacobian matrix. It must be called after the residuals vector and jacobian matrix have been initialised to zero. The default is to use finite differences to calculate the jacobian

Reimplemented from oomph::GeneralisedElement.

  {
   fill_in_generic_contribution_to_residuals(residual,jacobian,1);
  }

References oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::fill_in_generic_contribution_to_residuals().

◆ fill_in_contribution_to_residuals()

template<class WRAPPED_NAVIER_STOKES_ELEMENT >

void oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::fill_in_contribution_to_residuals ( Vector< double > & residual )

inlinevirtual

Compute residual.

Reimplemented from oomph::GeneralisedElement.

  {
   fill_in_generic_contribution_to_residuals
    (residual,GeneralisedElement::Dummy_matrix,0);
  }

References oomph::GeneralisedElement::Dummy_matrix, and oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::fill_in_generic_contribution_to_residuals().

◆ fill_in_generic_contribution_to_residuals()

template<class WRAPPED_NAVIER_STOKES_ELEMENT >

void oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::fill_in_generic_contribution_to_residuals	(	Vector< double > &	residual,
		DenseMatrix< double > &	jacobian,
		const unsigned &	flag
	)

inlineprivate

Compute local residual, and, if flag=1, local jacobian matrix.

  {
   // Get the local eqn number of our one-and-only
   // unknown
   int eqn_number=internal_local_eqn(0,0);
   if (eqn_number>=0)
    {
     residual[eqn_number] = Wrapped_navier_stokes_el_pt->dpdx_fe_only
      (S_in_wrapped_navier_stokes_element,Direction_pt);  
     
     // Do we want the Jacobian too?
     if (flag)
      {
       // Find the number of pressure dofs in the wrapped Navier-Stokes 
       // element pointed by
       // the SingularNavierStokesSolutionElement class
       unsigned n_pres = Wrapped_navier_stokes_el_pt->npres_nst();
       
       // Find the dimension of the problem
       unsigned cached_dim=Wrapped_navier_stokes_el_pt->dim();
  
       // Set up memory for the pressure shape functions and their derivatives
       Shape psip(n_pres), testp(n_pres);
       DShape dpsipdx(n_pres,cached_dim), dtestpdx(n_pres,cached_dim);
       
       // Compute the pressure shape functions and their derivatives
       // at the local coordinate S_in_wrapped_navier_stokes_element
       // (Test fcts not really needed but nobody's got around to writing
       // a fct that only picks out the basis fcts.
       Wrapped_navier_stokes_el_pt->dpshape_and_dptest_eulerian_nst
        (S_in_wrapped_navier_stokes_element,psip,dpsipdx,testp,dtestpdx);
       
       // Derivs
       for (unsigned j=0;j<n_pres;j++)
        {
         // Unknown
         int local_unknown = Wrapped_navier_stokes_el_pt->p_local_eqn(j);
         
         // If not pinned
         if (local_unknown >= 0)
          {
           // Add the contribution of the node to the local jacobian
           jacobian(eqn_number,local_unknown) = dpsipdx(j,*Direction_pt);
          }
        }
      }
    }
  }

References oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::Direction_pt, oomph::GeneralisedElement::eqn_number(), oomph::GeneralisedElement::internal_local_eqn(), j, oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::S_in_wrapped_navier_stokes_element, and oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::Wrapped_navier_stokes_el_pt.

Referenced by oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::fill_in_contribution_to_jacobian(), and oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::fill_in_contribution_to_residuals().

◆ grad_p_bar()

template<class WRAPPED_NAVIER_STOKES_ELEMENT >

Vector<double> oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::grad_p_bar ( const Vector< double > & x )

inline

Evaluate gradient of pressure singular function (including its amplitude): grad_p_bar = C * grad_pressure_singular

  {
   // Find the value of C
   double c=internal_data_pt(0)->value(0);
  
   // Initialise the gradient of pressure
   Vector<double> grad_p=grad_pressure_singular_function(x);
  
   // Find the dimension of the problem 
   unsigned cached_dim=Wrapped_navier_stokes_el_pt->dim();
  
   // Multiply the components of the gradient of pressure by the unknown C
   for (unsigned d=0;d<cached_dim;d++)
    {
     grad_p[d] *= c;
    }
   
   // Value of grad_p_bar at the position x
   return grad_p;
  }

References oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::c(), oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::grad_pressure_singular_function(), oomph::GeneralisedElement::internal_data_pt(), oomph::Data::value(), oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::Wrapped_navier_stokes_el_pt, and plotDoE::x.

◆ grad_pressure_singular_fct_pt()

template<class WRAPPED_NAVIER_STOKES_ELEMENT >

NavierStokesGradPressureSingularFctPt& oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::grad_pressure_singular_fct_pt ( )

inline

Access function to pointer to gradient of pressure singular function.

198 {return Grad_pressure_singular_fct_pt;}

References oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::Grad_pressure_singular_fct_pt.

◆ grad_pressure_singular_function()

template<class WRAPPED_NAVIER_STOKES_ELEMENT >

Vector<double> oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::grad_pressure_singular_function ( const Vector< double > & x ) const

inline

Evaluate gradient of pressure singular function at Eulerian position x.

   {
 #ifdef PARANOID
    if (Grad_pressure_singular_fct_pt==0)
     {
      std::stringstream error_stream;
      error_stream 
       << "Pointer to gradient of pressure singular function "
       << "hasn't been defined!"
       << std::endl;
      throw OomphLibError(
       error_stream.str(),
       OOMPH_CURRENT_FUNCTION,
       OOMPH_EXCEPTION_LOCATION);
     }
 #endif
    
    // Evaluate gradient of pressure singular function
    return (*Grad_pressure_singular_fct_pt)(x);
   }

References oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::Grad_pressure_singular_fct_pt, OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, and plotDoE::x.

Referenced by oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::grad_p_bar().

◆ grad_u_bar()

template<class WRAPPED_NAVIER_STOKES_ELEMENT >

Vector<Vector<double> > oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::grad_u_bar ( const Vector< double > & x )

inline

Evaluate gradient of velocity singular function (including its amplitude): grad_u_bar = C * grad_velocity_singular; grad[i][j] = du_i/dx_j

   {
    // Find the value of C
    double c=internal_data_pt(0)->value(0);
    
    // Initialise the gradient of velocity vector
    Vector<Vector<double> > grad_u=grad_velocity_singular_function(x);
    
    // Find the dimension of the problem 
    unsigned cached_dim=Wrapped_navier_stokes_el_pt->dim();
    
    // Multiply the components of the gradient of velocity by the unknown C
    for (unsigned d=0;d<cached_dim;d++)
     {
      for (unsigned i=0;i<cached_dim;i++)
       {
        grad_u[d][i] *= c;
       }
     }
    
    // Value of grad_u_bar at the position x
    return grad_u;
   }

References oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::c(), oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::grad_velocity_singular_function(), i, oomph::GeneralisedElement::internal_data_pt(), oomph::Data::value(), oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::Wrapped_navier_stokes_el_pt, and plotDoE::x.

◆ grad_velocity_singular_fct_pt()

template<class WRAPPED_NAVIER_STOKES_ELEMENT >

NavierStokesGradVelocitySingularFctPt& oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::grad_velocity_singular_fct_pt ( )

inline

Access function to pointer to gradient of velocity singular function.

190 {return Grad_velocity_singular_fct_pt;}

References oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::Grad_velocity_singular_fct_pt.

◆ grad_velocity_singular_function()

template<class WRAPPED_NAVIER_STOKES_ELEMENT >

Vector<Vector<double> > oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::grad_velocity_singular_function ( const Vector< double > & x ) const

inline

Evaluate gradient of velocity singular function at Eulerian position x. grad[i][j] = du_i/dx_j

   {
 #ifdef PARANOID
    if (Grad_velocity_singular_fct_pt==0)
     {
      std::stringstream error_stream;
      error_stream 
       << "Pointer to gradient of velocity singular function "
       << "hasn't been defined!"
       << std::endl;
      throw OomphLibError(
       error_stream.str(),
       OOMPH_CURRENT_FUNCTION,
       OOMPH_EXCEPTION_LOCATION);
     }
 #endif
    
    // Evaluate gradient of velocity singular function
    return (*Grad_velocity_singular_fct_pt)(x);
   }

References oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::Grad_velocity_singular_fct_pt, OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, and plotDoE::x.

Referenced by oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::grad_u_bar().

◆ p_bar()

template<class WRAPPED_NAVIER_STOKES_ELEMENT >

double oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::p_bar ( const Vector< double > & x )

inline

Evaluate pressure singular function (including its amplitude): p_bar = C * pressure_singular

  {
   // Find the value of C
   double c=internal_data_pt(0)->value(0);
   
   // Value of p_bar at the position x
   return c*pressure_singular_function(x);
  }

References oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::c(), oomph::GeneralisedElement::internal_data_pt(), oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::pressure_singular_function(), oomph::Data::value(), and plotDoE::x.

◆ pin_c()

template<class WRAPPED_NAVIER_STOKES_ELEMENT >

void oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::pin_c ( )

inline

Pin the value of the unknown amplitude C.

  {
   return internal_data_pt(0)->pin(0);
  }

References oomph::GeneralisedElement::internal_data_pt(), and oomph::Data::pin().

◆ pressure_singular_fct_pt()

template<class WRAPPED_NAVIER_STOKES_ELEMENT >

NavierStokesPressureSingularFctPt& oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::pressure_singular_fct_pt ( )

inline

Access function to pointer to pressure singular function.

194 {return Pressure_singular_fct_pt;}

References oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::Pressure_singular_fct_pt.

◆ pressure_singular_function()

template<class WRAPPED_NAVIER_STOKES_ELEMENT >

double oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::pressure_singular_function ( const Vector< double > & x ) const

inline

Evaluate pressure singular function at Eulerian position x.

  {
 #ifdef PARANOID
   if (Pressure_singular_fct_pt==0)
    {
     std::stringstream error_stream;
     error_stream 
      << "Pointer to pressure singular function hasn't been defined!"
      << std::endl;
     throw OomphLibError(
      error_stream.str(),
      OOMPH_CURRENT_FUNCTION,
      OOMPH_EXCEPTION_LOCATION);
    }
 #endif
   
   // Evaluate pressure singular function
   return (*Pressure_singular_fct_pt)(x);
  }

References OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::Pressure_singular_fct_pt, and plotDoE::x.

Referenced by oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::p_bar().

◆ set_c()

template<class WRAPPED_NAVIER_STOKES_ELEMENT >

void oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::set_c ( const double & value )

inline

Find the value of the unknown amplitude C.

  {
   internal_data_pt(0)->set_value(0,value);
  }

References oomph::GeneralisedElement::internal_data_pt(), oomph::Data::set_value(), and Eigen::value.

◆ set_wrapped_navier_stokes_element_pt()

template<class WRAPPED_NAVIER_STOKES_ELEMENT >

void oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::set_wrapped_navier_stokes_element_pt	(	WRAPPED_NAVIER_STOKES_ELEMENT *	wrapped_navier_stokes_el_pt,
		const Vector< double > &	s,
		unsigned *	direction_pt
	)

inline

Set pointer to associated wrapped Navier-Stokes element which contains the singularity (at local coordinate s). Also specify the direction in which the slope of the FE part of the pressure is set to zero. (Could also set a velocity derivative to zero but this needs to be done with a separate function. Write it if you need it...)

  {
   // Assign the pointer to the variable Wrapped_navier_stokes_el_pt
   Wrapped_navier_stokes_el_pt = wrapped_navier_stokes_el_pt;
   
   // Find number of nodes in the element
   unsigned nnod=wrapped_navier_stokes_el_pt->nnode();
   
   // Loop over the nodes of the element
   for (unsigned j=0;j<nnod;j++)
    {
     // Add the node as external data in the 
     // SingularNavierStokesSolutionElement class. Note that this
     // assumes that the pressure is stored at the nodes (Taylor Hood type
     // NSt elements, which is assumed elsewhere too...)
     add_external_data(Wrapped_navier_stokes_el_pt->node_pt(j));
    }
   
   // Assign the pointer to the local coordinate at which the residual
   // will be computed
   S_in_wrapped_navier_stokes_element = s;
   
   // Assign the pointer to the direction at which the derivative used
   // in the residual will be computed
   Direction_pt = direction_pt;
  }

References oomph::GeneralisedElement::add_external_data(), oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::Direction_pt, j, s, oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::S_in_wrapped_navier_stokes_element, and oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::Wrapped_navier_stokes_el_pt.

◆ singular_function_satisfies_stokes_equation()

template<class WRAPPED_NAVIER_STOKES_ELEMENT >

bool& oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::singular_function_satisfies_stokes_equation ( )

inline

Assert that singular function satisfies the Stokes equations by setting this to true or false.

   {
    return Singular_function_satisfies_stokes_equation;
   }

References oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::Singular_function_satisfies_stokes_equation.

◆ u_bar()

template<class WRAPPED_NAVIER_STOKES_ELEMENT >

Vector<double> oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::u_bar ( const Vector< double > & x )

inline

Evaluate velocity singular function (including its amplitude): u_bar = C * velocity_singular

   {
    // Find the value of C
    double c=internal_data_pt(0)->value(0);
    
    // Initialise the velocity vector
    Vector<double> u=velocity_singular_function(x);
    
    // Find the dimension of the problem
    unsigned cached_dim=Wrapped_navier_stokes_el_pt->dim();
    
    // Multiply the components of the velocity vector by the unknown C
    for (unsigned d=0;d<cached_dim;d++)
     {
      u[d] *= c;
     }
    
    // Value of u_bar at the position x
    return u;
   }

References oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::c(), oomph::GeneralisedElement::internal_data_pt(), oomph::Data::value(), oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::velocity_singular_function(), oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::Wrapped_navier_stokes_el_pt, and plotDoE::x.

◆ unpin_c()

template<class WRAPPED_NAVIER_STOKES_ELEMENT >

void oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::unpin_c ( )

inline

Unpin the value of the unknown amplitude C.

  {
   return internal_data_pt(0)->unpin(0);
  }

References oomph::GeneralisedElement::internal_data_pt(), and oomph::Data::unpin().

◆ velocity_singular_fct_pt()

template<class WRAPPED_NAVIER_STOKES_ELEMENT >

NavierStokesVelocitySingularFctPt& oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::velocity_singular_fct_pt ( )

inline

Access function to pointer to velocity singular function.

186 {return Velocity_singular_fct_pt;}

References oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::Velocity_singular_fct_pt.

◆ velocity_singular_function()

template<class WRAPPED_NAVIER_STOKES_ELEMENT >

Vector<double> oomph::SingularNavierStokesSolutionElement< WRAPPED_NAVIER_STOKES_ELEMENT >::velocity_singular_function ( const Vector< double > & x ) const

inline

Evaluate velocity singular function at Eulerian position x.

   {
 #ifdef PARANOID
    if (Velocity_singular_fct_pt==0)
     {
      std::stringstream error_stream;
      error_stream 
       << "Pointer to velocity singular function hasn't been defined!"
       << std::endl;
      throw OomphLibError(
       error_stream.str(),
       OOMPH_CURRENT_FUNCTION,
       OOMPH_EXCEPTION_LOCATION);
     }
 #endif
    
    // Evaluate velocity singular function
    return (*Velocity_singular_fct_pt)(x);
   }