Builds finite element arrays for incompressible Navier-Stokes equations in 2-D domains using Q₁/P₀ element and a penaly formulation for the incompressibility condition. More...

#include <NSP2DQ41.h>

Inheritance diagram for NSP2DQ41:

Public Member Functions
	NSP2DQ41 (Mesh &ms)
	Constructor using mesh data.

	NSP2DQ41 (Mesh &ms, Vect< real_t > &u)
	Constructor using mesh data and velocity vector.

	~NSP2DQ41 ()
	Destructor.

void	setPenalty (real_t lambda)
	Define penalty parameter.

void	setInput (EType opt, Vect< real_t > &u)
	Set equation input data.

void	Periodic (real_t coef=1.e20)
	Add contribution of periodic boundary condition (by a penalty technique).

void	build ()
	Build the linear system of equations.

int	runOneTimeStep ()
	Run one time step.

Public Member Functions inherited from Equa_Fluid< 4, 8, 2, 4 >
	Equa_Fluid ()
	Default constructor.

virtual	~Equa_Fluid ()
	Destructor.

void	Reynolds (const real_t &Re)
	Set Reynolds number.

void	Viscosity (const real_t &visc)
	Set (constant) Viscosity.

void	Viscosity (const string &exp)
	Set viscosity given by an algebraic expression.

void	Density (const real_t &dens)
	Set (constant) Viscosity.

void	Density (const string &exp)
	Set Density given by an algebraic expression.

void	ThermalExpansion (const real_t *e)
	Set (constant) thermal expansion coefficient.

void	ThermalExpansion (const string &exp)
	Set thermal expansion coefficient given by an algebraic expression.

void	setMaterial ()
	Set material properties.

Public Member Functions inherited from Equation< NEN_, NEE_, NSN_, NSE_ >
	Equation ()

	Equation (Mesh &mesh)
	Constructor with mesh instance.

	Equation (Mesh &mesh, Vect< real_t > &u)
	Constructor with mesh instance and solution vector.

	Equation (Mesh &mesh, Vect< real_t > &u, real_t &init_time, real_t &final_time, real_t &time_step)
	Constructor with mesh instance, matrix and right-hand side.

	~Equation ()
	Destructor.

void	updateBC (const Element &el, const Vect< real_t > &bc)
	Update Right-Hand side by taking into account essential boundary conditions.

void	DiagBC (DOFSupport dof_type=NODE_DOF, int dof=0)
	Update element matrix to impose bc by diagonalization technique.

void	LocalNodeVector (Vect< real_t > &b)
	Localize element vector from a Vect instance.

void	ElementNodeVector (const Vect< real_t > &b, LocalVect< real_t, NEE_ > &be)
	Localize element vector from a Vect instance.

void	SideNodeVector (const Vect< real_t > &b, LocalVect< real_t, NSE_ > &bs)
	Localize side vector from a Vect instance.

void	SideSideVector (const Vect< real_t > &b, vector< real_t > &bs)
	Localize side vector from a Vect instance.

void	ElementNodeVectorSingleDOF (const Vect< real_t > &b, LocalVect< real_t, NEN_ > &be)
	Localize Element Vector from a Vect instance.

void	ElementNodeVector (const Vect< real_t > &b, LocalVect< real_t, NEN_ > &be, int dof)
	Localize Element Vector from a Vect instance.

void	ElementSideVector (const Vect< real_t > &b, LocalVect< real_t, NSE_ > &be)
	Localize Element Vector from a Vect instance.

void	ElementVector (const Vect< real_t > &b, DOFSupport dof_type=NODE_DOF, int flag=0)
	Localize element vector.

void	SideVector (const Vect< real_t > &b, vector< real_t > &sb)
	Localize side vector.

void	ElementNodeCoordinates ()
	Localize coordinates of element nodes.

void	SideNodeCoordinates ()
	Localize coordinates of side nodes.

void	ElementAssembly (Matrix< real_t > *A)
	Assemble element matrix into global one.

void	ElementAssembly (BMatrix< real_t > &A)
	Assemble element matrix into global one.

void	ElementAssembly (SkSMatrix< real_t > &A)
	Assemble element matrix into global one.

void	ElementAssembly (SkMatrix< real_t > &A)
	Assemble element matrix into global one.

void	ElementAssembly (SpMatrix< real_t > &A)
	Assemble element matrix into global one.

void	ElementAssembly (TrMatrix< real_t > &A)
	Assemble element matrix into global one.

void	DGElementAssembly (Matrix< real_t > *A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation.

void	DGElementAssembly (SkSMatrix< real_t > &A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation.

void	DGElementAssembly (SkMatrix< real_t > &A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation.

void	DGElementAssembly (SpMatrix< real_t > &A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation.

void	DGElementAssembly (TrMatrix< real_t > &A)
	Assemble element matrix into global one for the Discontinuous Galerkin approximation.

void	SideAssembly (Matrix< real_t > *A)
	Assemble side (edge or face) matrix into global one.

void	SideAssembly (SkSMatrix< real_t > &A)
	Assemble side (edge or face) matrix into global one.

void	SideAssembly (SkMatrix< real_t > &A)
	Assemble side (edge or face) matrix into global one.

void	SideAssembly (SpMatrix< real_t > &A)
	Assemble side (edge or face) matrix into global one.

void	ElementAssembly (Vect< real_t > &v)
	Assemble element vector into global one.

void	SideAssembly (Vect< real_t > &v)
	Assemble side (edge or face) vector into global one.

void	AxbAssembly (const Element &el, const Vect< real_t > &x, Vect< real_t > &b)
	Assemble product of element matrix by element vector into global vector.

void	AxbAssembly (const Side &sd, const Vect< real_t > &x, Vect< real_t > &b)
	Assemble product of side matrix by side vector into global vector.

size_t	getNbNodes () const
	Return number of element nodes.

size_t	getNbEq () const
	Return number of element equations.

real_t	setMaterialProperty (const string &exp, const string &prop)
	Define a material property by an algebraic expression.

Public Member Functions inherited from Equa
	Equa ()
	Default constructor.

virtual	~Equa ()
	Destructor.

void	setMesh (Mesh &m)
	Define mesh and renumber DOFs after removing imposed ones.

Mesh &	getMesh () const
	Return reference to Mesh instance.

LinearSolver &	getLinearSolver ()
	Return reference to linear solver instance.

Matrix< real_t > *	getMatrix () const
	Return pointer to matrix.

void	setSolver (Iteration ls, Preconditioner pc=IDENT_PREC)
	Choose solver for the linear system.

void	setMatrixType (int t)
	Choose type of matrix.

int	solveLinearSystem (Matrix< real_t > *A, Vect< real_t > &b, Vect< real_t > &x)
	Solve the linear system with given matrix and right-hand side.

int	solveLinearSystem (Vect< real_t > &b, Vect< real_t > &x)
	Solve the linear system with given right-hand side.

void	LinearSystemInfo ()
	Print info on linear system solver.

Detailed Description

Builds finite element arrays for incompressible Navier-Stokes equations in 2-D domains using Q₁/P₀ element and a penaly formulation for the incompressibility condition.

Author: Rachid Touzani

Copyright: GNU Lesser Public License

Constructor & Destructor Documentation

◆ NSP2DQ41() [1/2]

NSP2DQ41 ( Mesh & ms )

Constructor using mesh data.

Parameters

[in] ms Mesh instance

◆ NSP2DQ41() [2/2]

NSP2DQ41	(	Mesh &	ms,
		Vect< real_t > &	u )

Constructor using mesh data and velocity vector.

Parameters

[in]	ms	Mesh instance
[in,out]	u	Velocity vector

Member Function Documentation

◆ build()

void build ( )

Build the linear system of equations.

Before using this function, one must have properly selected appropriate options for:

The choice of a steady state or transient analysis. By default, the analysis is stationary
In the case of transient analysis, the choice of a time integration scheme and a lumped or consistent capacity matrix. If transient analysis is chosen, the lumped capacity matrix option is chosen by default, and the implicit Euler scheme is used by default for time integration.

◆ Periodic()

void Periodic ( real_t coef = 1.e20 )

Add contribution of periodic boundary condition (by a penalty technique).

Boundary nodes where periodic boundary conditions are to be imposed must have codes equal to PERIODIC_A on one side and PERIODIC_B on the opposite side.

Parameters

[in] coef Value of penalty parameter [Default: 1.e20].

◆ runOneTimeStep()

int runOneTimeStep ( )

Run one time step.

This function performs one time step, once a time integration scheme has been selected.

◆ setInput()

void setInput	(	EType	opt,
		Vect< real_t > &	u )

Set equation input data.

Parameters

[in]	opt	Parameter that selects data type for input. This parameter is to be chosen in the enumerated variable EqDataType
[in]	u	Vect instance that contains input vector data List of data types contains `INITIAL`, `BOUNDARY_CONDITION_DATA`, `SOURCE` or `FLUX` with obvious meaning

◆ setPenalty()

void setPenalty ( real_t lambda )

Define penalty parameter.

Penalty parameter is used to enforce the incompressibility constraint

Parameters

[in] lambda Penaly parameter: Large value [Default: 1.e07]

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ NSP2DQ41() [1/2]

◆ NSP2DQ41() [2/2]

Member Function Documentation

◆ build()

◆ Periodic()

◆ runOneTimeStep()

◆ setInput()

◆ setPenalty()