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An Object Oriented Finite Element Library

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. More...
 
 NSP2DQ41 (Mesh &ms, Vect< real_t > &u)
 Constructor using mesh data and velocity vector. More...
 
 ~NSP2DQ41 ()
 Destructor.
 
void setPenalty (real_t lambda)
 Define penalty parameter. More...
 
void setInput (EqDataType opt, Vect< real_t > &u)
 Set equation input data. More...
 
void Periodic (real_t coef=1.e20)
 Add contribution of periodic boundary condition (by a penalty technique). More...
 
void build ()
 Build the linear system of equations. More...
 
int runOneTimeStep ()
 Run one time step. More...
 
- Public Member Functions inherited from Equa_Fluid< 4, 8, 2, 4 >
 Equa_Fluid ()
 Default constructor. More...
 
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. More...
 
 Equation (Mesh &mesh, Vect< real_t > &u)
 Constructor with mesh instance and solution vector. More...
 
 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. More...
 
 ~Equation ()
 Destructor.
 
void updateBC (const Element &el, const Vect< real_t > &bc)
 Update Right-Hand side by taking into account essential boundary conditions. More...
 
void DiagBC (DOFSupport dof_type=NODE_DOF, int dof=0)
 Update element matrix to impose bc by diagonalization technique. More...
 
void LocalNodeVector (Vect< real_t > &b)
 Localize Element Vector from a Vect instance. More...
 
void ElementNodeVector (const Vect< real_t > &b, LocalVect< real_t, NEE_ > &be)
 Localize Element Vector from a Vect instance. More...
 
void SideNodeVector (const Vect< real_t > &b, LocalVect< real_t, NSE_ > &bs)
 Localize Side Vector from a Vect instance. More...
 
void SideSideVector (const Vect< real_t > &b, std::valarray< real_t > &bs)
 Localize Side Vector from a Vect instance. More...
 
void ElementNodeVectorSingleDOF (const Vect< real_t > &b, LocalVect< real_t, NEN_ > &be)
 Localize Element Vector from a Vect instance. More...
 
void ElementNodeVector (const Vect< real_t > &b, LocalVect< real_t, NEN_ > &be, int dof)
 Localize Element Vector from a Vect instance. More...
 
void ElementSideVector (const Vect< real_t > &b, LocalVect< real_t, NSE_ > &be)
 Localize Element Vector from a Vect instance. More...
 
void ElementVector (const Vect< real_t > &b, DOFSupport dof_type=NODE_DOF, int flag=0)
 Localize Element Vector. More...
 
void SideVector (const Vect< real_t > &b, std::valarray< real_t > &sb)
 Localize Side Vector. More...
 
void ElementNodeCoordinates ()
 Localize coordinates of element nodes. More...
 
void SideNodeCoordinates ()
 Localize coordinates of side nodes. More...
 
void ElementAssembly (Matrix< real_t > *A)
 Assemble element matrix into global one. More...
 
void ElementAssembly (BMatrix< real_t > &A)
 Assemble element matrix into global one. More...
 
void ElementAssembly (SkSMatrix< real_t > &A)
 Assemble element matrix into global one. More...
 
void ElementAssembly (SkMatrix< real_t > &A)
 Assemble element matrix into global one. More...
 
void ElementAssembly (SpMatrix< real_t > &A)
 Assemble element matrix into global one. More...
 
void ElementAssembly (TrMatrix< real_t > &A)
 Assemble element matrix into global one. More...
 
void DGElementAssembly (Matrix< real_t > *A)
 Assemble element matrix into global one for the Discontinuous Galerkin approximation. More...
 
void DGElementAssembly (SkSMatrix< real_t > &A)
 Assemble element matrix into global one for the Discontinuous Galerkin approximation. More...
 
void DGElementAssembly (SkMatrix< real_t > &A)
 Assemble element matrix into global one for the Discontinuous Galerkin approximation. More...
 
void DGElementAssembly (SpMatrix< real_t > &A)
 Assemble element matrix into global one for the Discontinuous Galerkin approximation. More...
 
void DGElementAssembly (TrMatrix< real_t > &A)
 Assemble element matrix into global one for the Discontinuous Galerkin approximation. More...
 
void SideAssembly (Matrix< real_t > *A)
 Assemble side (edge or face) matrix into global one. More...
 
void SideAssembly (SkSMatrix< real_t > &A)
 Assemble side (edge or face) matrix into global one. More...
 
void SideAssembly (SkMatrix< real_t > &A)
 Assemble side (edge or face) matrix into global one. More...
 
void SideAssembly (SpMatrix< real_t > &A)
 Assemble side (edge or face) matrix into global one. More...
 
void ElementAssembly (Vect< real_t > &v)
 Assemble element vector into global one. More...
 
void SideAssembly (Vect< real_t > &v)
 Assemble side (edge or face) vector into global one. More...
 
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. More...
 
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. More...
 
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. More...
 
- 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.
 
MeshgetMesh () const
 Return reference to Mesh instance. More...
 
LinearSolver< real_t > & 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. More...
 
void setLinearSolver (Iteration ls, Preconditioner pc=IDENT_PREC)
 Choose solver for the linear system. More...
 
void setMatrixType (int t)
 Choose type of matrix. More...
 
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. More...
 
int solveLinearSystem (Vect< real_t > &b, Vect< real_t > &x)
 Solve the linear system with given right-hand side. More...
 

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

Constructor & Destructor Documentation

◆ NSP2DQ41() [1/2]

NSP2DQ41 ( Mesh ms)

Constructor using mesh data.

Parameters
[in]msMesh instance

◆ NSP2DQ41() [2/2]

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

Constructor using mesh data and velocity vector.

Parameters
[in]msMesh instance
[in,out]uVelocity 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]coefValue 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 ( EqDataType  opt,
Vect< real_t > &  u 
)

Set equation input data.

Parameters
[in]optParameter that selects data type for input. This parameter is to be chosen in the enumerated variable EqDataType
[in]uVect instance that contains input vector data List of data types contains INITIAL_FIELD, BOUNDARY_CONDITION_DATA, SOURCE_DATA 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]lambdaPenaly parameter: Large value [Default: 1.e07]





Copyright © 1998-2022 Rachid Touzani