This class provides the basic components for assembling the matrix and vector when solving Stokes equations. More...

#include <assemble_stokes.h>

Inheritance diagram for AssembleStokes:

Collaboration diagram for AssembleStokes:

Public Member Functions
	AssembleStokes (EquationSystems &es)
	Constructor. More...

	~AssembleStokes ()
	Destructor. More...

void	assemble_global_K (const std::string &system_name, const std::string &option) override
	Assemble the Global Matrix K. More...

void	assemble_global_F (const std::string &system_name, const std::string &option) override
	Assemble the Global force vector F. More...

void	assemble_element_KIJ (const std::vector< Real > &JxW, const std::vector< std::vector< RealGradient > > &dphi, const unsigned int n_u_dofs, const unsigned int I, const unsigned int J, DenseMatrix< Number > &Kij) override
	Assemble the element matrix K_IJ. More...

void	assemble_element_QI (const std::vector< Real > &JxW, const std::vector< std::vector< RealGradient > > &dphi, const std::vector< std::vector< Real > > &psi, const unsigned int n_v_dofs, const unsigned int n_p_dofs, const unsigned int I, DenseMatrix< Number > &Qi)
	Assemble the element matrices Q_I, i.e., kup, kvp, kwp, for pressure. More...

void	assemble_element_MIJ (const std::vector< Real > &JxW, const std::vector< std::vector< Real > > &phi, const unsigned int n_v_dofs, DenseMatrix< Number > &Mij)
	Assemble the element mass matrix M for preconditioning matrix. More...

void	compute_element_rhs (const Elem *elem, const unsigned int n_u_dofs, FEBase &fe_v, const std::vector< std::size_t > n_list, const bool &pf_flag, const std::string &option, const Real &alpha, DenseVector< Number > &Fe) override
	Assemble function for the right-hand-side in Stokes equation. More...

void	select_boundary_side (const Elem *elem) override
	select sides on the boundary for all elements More...

void	apply_bc_by_penalty (const Elem *elem, const std::string &matrix_or_vector, DenseMatrix< Number > &Ke, DenseVector< Number > &Fe, const std::string &option) override
	Apply BCs by penalty method. More...

Real	boundary_pressure_jump (const std::string &which_side) const
	Define the pressure jump at the inlet and outlet of the channel. More...

Real	boundary_traction (const std::string &which_side) const
	Define the pressure jump at the inlet and outlet of the channel. More...

Public Member Functions inherited from AssembleSystem
	AssembleSystem (EquationSystems &es)
	Constructor. More...

	~AssembleSystem ()
	Destructor. More...

void	assemble_int_force (const Elem *elem, const unsigned int n_u_dofs, FEBase &fe_v)
	Assemble int_force matrix for every element, this includes Gaussian quadrature weights multiplied by shape functions. The product is calculated once and is stored in _int_force. More...

void	penalize_elem_matrix_vector (DenseMatrix< Number > &Ke, DenseVector< Number > &Fe, const std::string &matrix_or_vector, const unsigned int &var_number, const unsigned int &local_node_id, const unsigned int &n_nodes_elem, const Real &penalty, const Real &value)
	Universal function to penalize element matrix or vector with a large number. More...

Additional Inherited Members
Protected Attributes inherited from AssembleSystem
EquationSystems &	_eqn_sys

unsigned int	_dim

MeshBase &	_mesh

const std::vector< boundary_id_type >	_boundary_id_3D = {4,2,1,3,0,5}

const std::vector< std::string >	_boundary_name_3D = {"left", "right", "bottom", "top", "back", "front"}

std::vector< std::vector< Real > >	_int_force

std::vector< std::vector< Point > >	_q_xyz

std::vector< unsigned int >	_n_dofs

std::vector< unsigned int >	_n_u_dofs

std::vector< unsigned int >	_n_p_dofs

std::vector< unsigned int >	_n_uvw_dofs

std::vector< std::vector< dof_id_type > >	_dof_indices

std::vector< std::vector< dof_id_type > >	_dof_indices_u

std::vector< std::vector< dof_id_type > >	_dof_indices_p

std::vector< std::vector< unsigned int > >	_boundary_sides

Detailed Description

This class provides the basic components for assembling the matrix and vector when solving Stokes equations.

For details of the numerical discretization, refer to The finite element method in heat transfer and fluid dynamics (3rd ed) J.N. Reddy and D.K. Gartling. 2010, CRC Press

Constructor & Destructor Documentation

AssembleStokes::AssembleStokes ( EquationSystems & es )

Constructor.

Parameters

[in,out] es EquationSystem

AssembleStokes::~AssembleStokes ( )

Destructor.

Member Function Documentation

void AssembleStokes::apply_bc_by_penalty	(	const Elem *	elem,
		const std::string &	matrix_or_vector,
		DenseMatrix< Number > &	Ke,
		DenseVector< Number > &	Fe,
		const std::string &	option
	)

overridevirtual

Apply BCs by penalty method.

Implements AssembleSystem.

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void AssembleStokes::assemble_element_KIJ	(	const std::vector< Real > &	JxW,
		const std::vector< std::vector< RealGradient > > &	dphi,
		const unsigned int	n_u_dofs,
		const unsigned int	I,
		const unsigned int	J,
		DenseMatrix< Number > &	Kij
	)

overridevirtual

Assemble the element matrix K_IJ.

Reinit and compute the element matrix K_ij, which will be added into K matrix after calling assemble_global_K(). Size of this submatrix is n_u_dofs * n_u_dofs = n_v_dofs * n_v_dofs = n_w_dofs * n_w_dofs

Implements AssembleSystem.

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void AssembleStokes::assemble_element_MIJ	(	const std::vector< Real > &	JxW,
		const std::vector< std::vector< Real > > &	phi,
		const unsigned int	n_v_dofs,
		DenseMatrix< Number > &	Mij
	)

Assemble the element mass matrix M for preconditioning matrix.

This function only exists for Stokes equation.

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void AssembleStokes::assemble_element_QI	(	const std::vector< Real > &	JxW,
		const std::vector< std::vector< RealGradient > > &	dphi,
		const std::vector< std::vector< Real > > &	psi,
		const unsigned int	n_v_dofs,
		const unsigned int	n_p_dofs,
		const unsigned int	I,
		DenseMatrix< Number > &	Qi
	)

Assemble the element matrices Q_I, i.e., kup, kvp, kwp, for pressure.

These element matrices will be added to Ke after calling assemble_global_K(). This function only exists for Stokes equation.

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void AssembleStokes::assemble_global_F	(	const std::string &	system_name,
		const std::string &	option
	)

overridevirtual

Assemble the Global force vector F.

Parameters

[in]	system_name	Name of the system (should be "Stokes")
[in]	option	Options of assembling the system ("disturbed" or "undisturbed")
[out]	Fe	Add rhs vector to system.

Implements AssembleSystem.

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void AssembleStokes::assemble_global_K	(	const std::string &	system_name,
		const std::string &	option
	)

overridevirtual

Assemble the Global Matrix K.

Parameters

[in]	system_name	Name of the system (should be "Stokes")
[in]	Option	options of assembling the system ("disturbed" or "undisturbed")
[out]	Ke	Add element matrix to system

It is a good idea to make sure we are assembling the proper system.

Implements AssembleSystem.

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Real AssembleStokes::boundary_pressure_jump ( const std::string & which_side ) const

Define the pressure jump at the inlet and outlet of the channel.

Real AssembleStokes::boundary_traction ( const std::string & which_side ) const

Define the pressure jump at the inlet and outlet of the channel.

void AssembleStokes::compute_element_rhs	(	const Elem *	elem,
		const unsigned int	n_u_dofs,
		FEBase &	fe_v,
		const std::vector< std::size_t >	n_list,
		const bool &	pf_flag,
		const std::string &	option,
		const Real &	alpha,
		DenseVector< Number > &	Fe
	)