Finite Differences. More...

Detailed Description

template<typename Sys_eqs>
class FDScheme< Sys_eqs >

Finite Differences.

This class is able to discretize on a Matrix any system of equations producing a linear system of type \(Ax=b\). In order to create a consistent Matrix it is required that each processor must contain a contiguous range on grid points without holes. In order to ensure this, each processor produce a contiguous local labeling of its local points. Each processor also add an offset equal to the number of local points of the processors with id smaller than him, to produce a global and non overlapping labeling. An example is shown in the figures down, here we have a grid 8x6 divided across four processors each processor label locally its grid points

 *
+--------------------------+
| 1   2   3   4| 1  2  3  4|
|              |           |
| 5   6   7   8| 5  6  7  8|
|              |           |
| 9  10  11  12| 9 10 11 12|
+--------------------------+
|13  14  15| 13 14 15 16 17|
|          |               |
|16  17  18| 18 19 20 21 22|
|          |               |
|19  20  21| 23 24 25 26 27|
+--------------------------+

 *
 *
 *

To the local relabelling is added an offset to make the local id global and non overlapping

 *
+--------------------------+
| 1   2   3   4|23 24 25 26|
|              |           |
| 5   6   7   8|27 28 29 30|
|              |           |
| 9  10  12  13|31 32 33 34|
+--------------------------+
|14  15  16| 35 36 37 38 39|
|          |               |
|17  18  19| 40 41 42 43 44|
|          |               |
|20  21  22| 45 46 47 48 49|
+--------------------------+
 *
 *
 *

Template Parameters

Sys_eqs Definition of the system of equations

Examples

Solve lid-driven cavity 2D for incompressible fluid (inertia=0 --> Re=0)

In this case the system of equation to solve is

\( \left\{ \begin{array}{c} \eta\nabla v_x + \partial_x P = 0 \quad Eq1 \\ \eta\nabla v_y + \partial_y P = 0 \quad Eq2 \\ \partial_x v_x + \partial_y v_y = 0 \quad Eq3 \end{array} \right. \)

and boundary conditions

\( \left\{ \begin{array}{c} v_x = 0, v_y = 0 \quad x = 0 \quad B1\\ v_x = 0, v_y = 1.0 \quad x = L \quad B2\\ v_x = 0, v_y = 0 \quad y = 0 \quad B3\\ v_x = 0, v_y = 0 \quad y = L \quad B4\\ \end{array} \right. \)

with \(v_x\) and \(v_y\) the velocity in x and y and \(P\) Pressure

In order to solve such system first we define the general properties of the system

Define the equations of the system

Define the domain and impose the equations

3D

A 3D case is given in the examples

Definition at line 126 of file FDScheme.hpp.

#include <FDScheme.hpp>

Data Structures
struct	constant_b
	Encapsulation of the b term as constant. More...

struct	grid_b
	Encapsulation of the b term as grid. More...

struct	key_and_eq
	Equation id + space position. More...

Public Types
typedef grid_dist_id< Sys_eqs::dims, typename Sys_eqs::stype, aggregate< size_t >, typename Sys_eqs::b_grid::decomposition::extended_type >	g_map_type
	Distributed grid map.

typedef Sys_eqs	Sys_eqs_typ
	Type that specify the properties of the system of equations.

Public Member Functions
void	setStagPos (comb< Sys_eqs::dims >(&sp)[Sys_eqs::nvar])
	set the staggered position for each property

void	computeStag ()
	compute the staggered position for each property

const Padding< Sys_eqs::dims > &	getPadding ()
	Get the specified padding.

const g_map_type &	getMap ()
	Return the map between the grid index position and the position in the distributed vector.

	FDScheme (const Ghost< Sys_eqs::dims, long int > &stencil, const Box< Sys_eqs::dims, typename Sys_eqs::stype > &domain, const typename Sys_eqs::b_grid &b_g)
	Constructor.

	FDScheme (Padding< Sys_eqs::dims > &pd, const Ghost< Sys_eqs::dims, long int > &stencil, const Box< Sys_eqs::dims, typename Sys_eqs::stype > &domain, const typename Sys_eqs::b_grid &b_g)
	Constructor.

template<typename T >
void	impose (const T &op, typename Sys_eqs::stype num, long int id, const long int(&start)[Sys_eqs::dims], const long int(&stop)[Sys_eqs::dims], bool skip_first=false)
	Impose an operator.

void	new_b ()
	In case we want to impose a new b re-using FDScheme we have to call This function.

void	new_A ()
	In case we want to impose a new A re-using FDScheme we have to call This function.

template<unsigned int prp, typename b_term , typename iterator >
void	impose_dit_b (b_term &b_t, const iterator &it_d, long int id=0)
	Impose an operator.

template<typename T >
void	impose_dit (const T &op, typename Sys_eqs::stype num, long int id, grid_dist_iterator_sub< Sys_eqs::dims, typename g_map_type::d_grid > it_d)
	Impose an operator.

template<typename T , typename bop , typename iterator >
void	impose_git_gmap (const T &op, bop num, long int id, iterator &it)
	Impose an operator.

template<typename T , typename bop , typename iterator >
void	impose_git (const T &op, bop num, long int id, const iterator &it_d, bool skip_first=false)
	Impose an operator.

template<unsigned int prp, typename T , typename b_term , typename iterator >
void	impose_dit (const T &op, b_term &b_t, const iterator &it_d, long int id=0)
	Impose an operator.

Sys_eqs::SparseMatrix_type &	getA ()
	produce the Matrix

Sys_eqs::Vector_type &	getB ()
	produce the B vector

template<unsigned int ... pos, typename Vct , typename Grid_dst >
void	copy (Vct &v, const long int(&start)[Sys_eqs_typ::dims], const long int(&stop)[Sys_eqs_typ::dims], Grid_dst &g_dst)
	Copy the vector into the grid.

template<unsigned int ... pos, typename Vct , typename Grid_dst >
void	copy (Vct &v, Grid_dst &g_dst)
	Copy the vector into the grid.

Data Fields
Sys_eqs::SparseMatrix_type	A
	type of the sparse matrix

Private Types
typedef Sys_eqs::SparseMatrix_type::triplet_type	triplet
	Sparse matrix triplet type.

Private Member Functions
key_and_eq	from_row_to_key (size_t row)
	From the row Matrix position to the spatial position.

const std::vector< size_t >	padding (const size_t(&sz)[Sys_eqs::dims], Padding< Sys_eqs::dims > &pd)
	calculate the mapping grid size with padding

void	consistency ()
	Check if the Matrix is consistent.

template<typename Vct , typename Grid_dst , unsigned int ... pos>
void	copy_staggered (Vct &v, Grid_dst &g_dst, grid_key_dx< Grid_dst::dims > &start_d, grid_key_dx< Grid_dst::dims > &stop_d)
	Copy a given solution vector in a staggered grid.

template<typename Vct , typename Grid_dst , unsigned int ... pos>
void	copy_normal (Vct &v, Grid_dst &g_dst)
	Copy a given solution vector in a normal grid.

template<typename bop , typename iterator >
void	impose_dit_b (bop num, long int id, const iterator &it_d)
	Impose an operator.

template<typename T , typename bop , typename iterator >
void	impose_dit (const T &op, bop num, long int id, const iterator &it_d)
	Impose an operator.

void	construct_gmap ()
	Construct the gmap structure.

void	Initialize (const Box< Sys_eqs::dims, typename Sys_eqs::stype > &domain)

Private Attributes
Padding< Sys_eqs::dims >	pd
	Padding.

Sys_eqs::Vector_type	b
	Vector b.

const grid_sm< Sys_eqs::dims, void > &	gs
	Domain Grid informations.

Sys_eqs::stype	spacing [Sys_eqs::dims]
	Get the grid spacing.

g_map_type	g_map
	mapping grid

size_t	row
	row of the matrix

size_t	row_b
	row on b

openfpm::vector< size_t >	pnt
	Grid points that has each processor.

comb< Sys_eqs::dims >	s_pos [Sys_eqs::nvar]
	Staggered position for each property.

size_t	s_pnt

Member Typedef Documentation

◆ g_map_type

template<typename Sys_eqs >

typedef grid_dist_id<Sys_eqs::dims,typename Sys_eqs::stype,aggregate<size_t>,typename Sys_eqs::b_grid::decomposition::extended_type> FDScheme< Sys_eqs >::g_map_type

Distributed grid map.

Definition at line 131 of file FDScheme.hpp.

◆ Sys_eqs_typ

template<typename Sys_eqs >

typedef Sys_eqs FDScheme< Sys_eqs >::Sys_eqs_typ

Type that specify the properties of the system of equations.

Definition at line 134 of file FDScheme.hpp.

◆ triplet

template<typename Sys_eqs >

typedef Sys_eqs::SparseMatrix_type::triplet_type FDScheme< Sys_eqs >::triplet

private

Sparse matrix triplet type.

Definition at line 202 of file FDScheme.hpp.

Constructor & Destructor Documentation

◆ FDScheme() [1/2]

template<typename Sys_eqs >

FDScheme< Sys_eqs >::FDScheme	(	const Ghost< Sys_eqs::dims, long int > &	stencil,
		const Box< Sys_eqs::dims, typename Sys_eqs::stype > &	domain,
		const typename Sys_eqs::b_grid &	b_g
	)

inline

Constructor.

The periodicity is given by the grid b_g

Parameters

stencil	maximum extension of the stencil on each directions
domain	the domain
b_g	object grid that will store the solution

Definition at line 694 of file FDScheme.hpp.

◆ FDScheme() [2/2]

template<typename Sys_eqs >

FDScheme< Sys_eqs >::FDScheme	(	Padding< Sys_eqs::dims > &	pd,
		const Ghost< Sys_eqs::dims, long int > &	stencil,
		const Box< Sys_eqs::dims, typename Sys_eqs::stype > &	domain,
		const typename Sys_eqs::b_grid &	b_g
	)

inline

Constructor.

The periodicity is given by the grid b_g

Parameters

pd	Padding, how many points out of boundary are present
stencil	maximum extension of the stencil on each directions
domain	the domain
b_g	object grid that will store the solution

Definition at line 712 of file FDScheme.hpp.

Member Function Documentation

◆ computeStag()

template<typename Sys_eqs >

void FDScheme< Sys_eqs >::computeStag ( )

inline

compute the staggered position for each property

This is compute from the value_type stored by Sys_eqs::b_grid::value_type the position of the staggered properties

Definition at line 652 of file FDScheme.hpp.

◆ consistency()

template<typename Sys_eqs >

void FDScheme< Sys_eqs >::consistency ( )

inlineprivate

Check if the Matrix is consistent.

Definition at line 297 of file FDScheme.hpp.

◆ construct_gmap()

template<typename Sys_eqs >

void FDScheme< Sys_eqs >::construct_gmap ( )

inlineprivate

Construct the gmap structure.

Definition at line 565 of file FDScheme.hpp.

◆ copy() [1/2]

template<typename Sys_eqs >

template<unsigned int ... pos, typename Vct , typename Grid_dst >

void FDScheme< Sys_eqs >::copy	(	Vct &	v,
		const long int(&)	start[Sys_eqs_typ::dims],
		const long int(&)	stop[Sys_eqs_typ::dims],
		Grid_dst &	g_dst
	)

inline

Copy the vector into the grid.

Copy the solution into the grid

Template Parameters

scheme	Discretization scheme
Grid_dst	type of the target grid
pos	target properties

Parameters

v	Vector that contain the solution of the system
start	point
stop	point
g_dst	Destination grid

Definition at line 1079 of file FDScheme.hpp.

◆ copy() [2/2]

template<typename Sys_eqs >

template<unsigned int ... pos, typename Vct , typename Grid_dst >

void FDScheme< Sys_eqs >::copy	(	Vct &	v,
		Grid_dst &	g_dst
	)

inline

Copy the vector into the grid.

Copy the solution into the grid

Template Parameters

scheme	Discretization scheme
Grid_dst	type of the target grid
pos	target properties

Parameters

v	Vector that contain the solution of the system
g_dst	Destination grid

Definition at line 1141 of file FDScheme.hpp.

◆ copy_normal()

template<typename Sys_eqs >

template<typename Vct , typename Grid_dst , unsigned int ... pos>

void FDScheme< Sys_eqs >::copy_normal	(	Vct &	v,
		Grid_dst &	g_dst
	)

inlineprivate

Copy a given solution vector in a normal grid.

Template Parameters

Vct	Vector type
Grid_dst	target grid
pos	set of property

Parameters

v	Vector
g_dst	target normal grid

Definition at line 397 of file FDScheme.hpp.

◆ copy_staggered()

template<typename Sys_eqs >

template<typename Vct , typename Grid_dst , unsigned int ... pos>

void FDScheme< Sys_eqs >::copy_staggered	(	Vct &	v,
		Grid_dst &	g_dst,
		grid_key_dx< Grid_dst::dims > &	start_d,
		grid_key_dx< Grid_dst::dims > &	stop_d
	)

inlineprivate

Copy a given solution vector in a staggered grid.

Template Parameters

Vct	Vector type
Grid_dst	target grid
pos	set of properties

Parameters

v	Vector
g_dst	target staggered grid

Definition at line 353 of file FDScheme.hpp.

◆ from_row_to_key()

template<typename Sys_eqs >

key_and_eq FDScheme< Sys_eqs >::from_row_to_key ( size_t row )

inlineprivate

From the row Matrix position to the spatial position.

Parameters

row	Matrix row

Returns: spatial position + equation id

Definition at line 253 of file FDScheme.hpp.

◆ getA()

template<typename Sys_eqs >

Sys_eqs::SparseMatrix_type & FDScheme< Sys_eqs >::getA ( )

inline

produce the Matrix

Returns: the Sparse matrix produced

Definition at line 1036 of file FDScheme.hpp.

◆ getB()

template<typename Sys_eqs >

Sys_eqs::Vector_type & FDScheme< Sys_eqs >::getB ( )

inline

produce the B vector

Returns: the vector produced

Definition at line 1054 of file FDScheme.hpp.

◆ getMap()

template<typename Sys_eqs >

const g_map_type & FDScheme< Sys_eqs >::getMap ( )

inline

Return the map between the grid index position and the position in the distributed vector.

It is the map explained in the intro of the FDScheme

Returns: the map

Definition at line 680 of file FDScheme.hpp.

◆ getPadding()

template<typename Sys_eqs >

const Padding< Sys_eqs::dims > & FDScheme< Sys_eqs >::getPadding ( )

inline

Get the specified padding.

Returns: the padding specified

Definition at line 668 of file FDScheme.hpp.

◆ impose()

template<typename Sys_eqs >

template<typename T >

void FDScheme< Sys_eqs >::impose	(	const T &	op,
		typename Sys_eqs::stype	num,
		long int	id,
		const long int(&)	start[Sys_eqs::dims],
		const long int(&)	stop[Sys_eqs::dims],
		bool	skip_first = `false`
	)

inline

Impose an operator.

This function impose an operator on a box region to produce the system

Ax = b

Stokes equation, lid driven cavity with one splipping wall

Parameters

op	Operator to impose (A term)
num	right hand side of the term (b term)
id	Equation id in the system that we are imposing
start	starting point of the box
stop	stop point of the box
skip_first	skip the first point

Definition at line 738 of file FDScheme.hpp.

◆ impose_dit() [1/3]

template<typename Sys_eqs >

template<unsigned int prp, typename T , typename b_term , typename iterator >

void FDScheme< Sys_eqs >::impose_dit	(	const T &	op,
		b_term &	b_t,
		const iterator &	it_d,
		long int	id = `0`
	)

inline

Impose an operator.

This function impose an operator on a particular grid region to produce the system

Ax = b

Stokes equation 2D, lid driven cavity with one splipping wall

Parameters

op	Operator to impose (A term)
num	right hand side of the term (b term)
id	Equation id in the system that we are imposing
it_d	iterator that define where you want to impose

Definition at line 1018 of file FDScheme.hpp.

◆ impose_dit() [2/3]

template<typename Sys_eqs >

template<typename T , typename bop , typename iterator >

void FDScheme< Sys_eqs >::impose_dit	(	const T &	op,
		bop	num,
		long int	id,
		const iterator &	it_d
	)

inlineprivate

Impose an operator.

This function impose an operator on a particular grid region to produce the system

Ax = b

Stokes equation 2D, lid driven cavity with one splipping wall

Parameters

op	Operator to impose (A term)
num	right hand side of the term (b term)
id	Equation id in the system that we are imposing
it_d	iterator that define where you want to impose

Definition at line 495 of file FDScheme.hpp.

◆ impose_dit() [3/3]

template<typename Sys_eqs >

template<typename T >

void FDScheme< Sys_eqs >::impose_dit	(	const T &	op,
		typename Sys_eqs::stype	num,
		long int	id,
		grid_dist_iterator_sub< Sys_eqs::dims, typename g_map_type::d_grid >	it_d
	)

inline

Impose an operator.

This function impose an operator on a particular grid region to produce the system

Ax = b

Stokes equation 2D, lid driven cavity with one splipping wall

Parameters

op	Operator to impose (A term)
num	right hand side of the term (b term)
id	Equation id in the system that we are imposing
it_d	iterator that define where you want to impose

Definition at line 828 of file FDScheme.hpp.

◆ impose_dit_b() [1/2]

template<typename Sys_eqs >

template<unsigned int prp, typename b_term , typename iterator >

void FDScheme< Sys_eqs >::impose_dit_b	(	b_term &	b_t,
		const iterator &	it_d,
		long int	id = `0`
	)

inline

Impose an operator.

This function impose an operator on a particular grid region to produce the system

Ax = b

Stokes equation 2D, lid driven cavity with one splipping wall

Parameters

op	Operator to impose (A term)
num	right hand side of the term (b term)
id	Equation id in the system that we are imposing
it_d	iterator that define where you want to impose

Definition at line 804 of file FDScheme.hpp.

◆ impose_dit_b() [2/2]

template<typename Sys_eqs >

template<typename bop , typename iterator >

void FDScheme< Sys_eqs >::impose_dit_b	(	bop	num,
		long int	id,
		const iterator &	it_d
	)

inlineprivate

Impose an operator.

This function the RHS no matrix is imposed. This function is usefull if the Matrix has been constructed and only the right hand side b must be changed

Ax = b

Parameters

num	right hand side of the term (b term)
id	Equation id in the system that we are imposing
it_d	iterator that define where you want to impose

Definition at line 454 of file FDScheme.hpp.

◆ impose_git()

template<typename Sys_eqs >

template<typename T , typename bop , typename iterator >

void FDScheme< Sys_eqs >::impose_git	(	const T &	op,
		bop	num,
		long int	id,
		const iterator &	it_d,
		bool	skip_first = `false`
	)

inline

Impose an operator.

This function impose an operator on a particular grid region to produce the system

Ax = b

Stokes equation 2D, lid driven cavity with one splipping wall

Parameters

op	Operator to impose (A term)
num	right hand side of the term (b term)
id	Equation id in the system that we are imposing
it_d	iterator that define where you want to impose

Definition at line 929 of file FDScheme.hpp.

◆ impose_git_gmap()

template<typename Sys_eqs >

template<typename T , typename bop , typename iterator >

void FDScheme< Sys_eqs >::impose_git_gmap	(	const T &	op,
		bop	num,
		long int	id,
		iterator &	it
	)

inline

Impose an operator.

This function impose an operator on a particular grid region to produce the system

Ax = b

Stokes equation 2D, lid driven cavity with one splipping wall

Parameters

op	Operator to impose (A term)
num	right hand side of the term (b term)
id	Equation id in the system that we are imposing
it_d	iterator that define where you want to impose

Definition at line 853 of file FDScheme.hpp.

◆ Initialize()

template<typename Sys_eqs >

void FDScheme< Sys_eqs >::Initialize ( const Box< Sys_eqs::dims, typename Sys_eqs::stype > & domain )

inlineprivate

\initialize the object FDScheme

Parameters

domain simulation domain

Definition at line 611 of file FDScheme.hpp.

◆ new_A()

template<typename Sys_eqs >

void FDScheme< Sys_eqs >::new_A ( )

inline

In case we want to impose a new A re-using FDScheme we have to call This function.

Definition at line 785 of file FDScheme.hpp.

◆ new_b()

template<typename Sys_eqs >

void FDScheme< Sys_eqs >::new_b ( )

inline

In case we want to impose a new b re-using FDScheme we have to call This function.

Definition at line 778 of file FDScheme.hpp.

◆ padding()

template<typename Sys_eqs >

const std::vector< size_t > FDScheme< Sys_eqs >::padding	(	const size_t(&)	sz[Sys_eqs::dims],
		Padding< Sys_eqs::dims > &	pd
	)

inlineprivate

calculate the mapping grid size with padding

Parameters

sz	original grid size
pd	padding

Returns: padded grid size

Definition at line 284 of file FDScheme.hpp.

◆ setStagPos()

template<typename Sys_eqs >

void FDScheme< Sys_eqs >::setStagPos ( comb< Sys_eqs::dims >(&) sp[Sys_eqs::nvar] )

inline

set the staggered position for each property

Parameters

sp	vector containing the staggered position for each property

Definition at line 639 of file FDScheme.hpp.

Field Documentation

◆ A

template<typename Sys_eqs >

Sys_eqs::SparseMatrix_type FDScheme< Sys_eqs >::A

type of the sparse matrix

Definition at line 1029 of file FDScheme.hpp.

◆ b

template<typename Sys_eqs >

Sys_eqs::Vector_type FDScheme< Sys_eqs >::b

private

Vector b.

Definition at line 205 of file FDScheme.hpp.

◆ g_map

template<typename Sys_eqs >

g_map_type FDScheme< Sys_eqs >::g_map

private

mapping grid

Definition at line 214 of file FDScheme.hpp.

◆ gs

template<typename Sys_eqs >

const grid_sm<Sys_eqs::dims,void>& FDScheme< Sys_eqs >::gs

private

Domain Grid informations.

Definition at line 208 of file FDScheme.hpp.

◆ pd

template<typename Sys_eqs >

Padding<Sys_eqs::dims> FDScheme< Sys_eqs >::pd

private

Padding.

Definition at line 199 of file FDScheme.hpp.

◆ pnt

template<typename Sys_eqs >

openfpm::vector<size_t> FDScheme< Sys_eqs >::pnt

private

Grid points that has each processor.

Definition at line 223 of file FDScheme.hpp.

◆ row

template<typename Sys_eqs >

size_t FDScheme< Sys_eqs >::row

private

row of the matrix

Definition at line 217 of file FDScheme.hpp.

◆ row_b

template<typename Sys_eqs >

size_t FDScheme< Sys_eqs >::row_b

private

row on b

Definition at line 220 of file FDScheme.hpp.

◆ s_pnt

template<typename Sys_eqs >

size_t FDScheme< Sys_eqs >::s_pnt

private

Each point in the grid has a global id, to decompose correctly the Matrix each processor contain a contiguos range of global id, example processor 0 can have from 0 to 234 and processor 1 from 235 to 512 no processors can have holes in the sequence, this number indicate where the sequence start for this processor

Definition at line 232 of file FDScheme.hpp.

◆ s_pos

template<typename Sys_eqs >

comb<Sys_eqs::dims> FDScheme< Sys_eqs >::s_pos[Sys_eqs::nvar]

private

Staggered position for each property.

Definition at line 226 of file FDScheme.hpp.

◆ spacing

template<typename Sys_eqs >

Sys_eqs::stype FDScheme< Sys_eqs >::spacing[Sys_eqs::dims]

private

Get the grid spacing.

Definition at line 211 of file FDScheme.hpp.

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

openfpm_numerics/src/FiniteDifference/FDScheme.hpp

Detailed Description

Examples

Solve lid-driven cavity 2D for incompressible fluid (inertia=0 --> Re=0)

Define the equations of the system

Define the domain and impose the equations

3D

Data Structures

Public Types

Public Member Functions

Data Fields

Private Types

Private Member Functions

Private Attributes

Member Typedef Documentation

◆ g_map_type

◆ Sys_eqs_typ

◆ triplet

Constructor & Destructor Documentation

◆ FDScheme() [1/2]

◆ FDScheme() [2/2]

Member Function Documentation

◆ computeStag()

◆ consistency()

◆ construct_gmap()

◆ copy() [1/2]

Copy the solution into the grid

◆ copy() [2/2]

Copy the solution into the grid

◆ copy_normal()

◆ copy_staggered()

◆ from_row_to_key()

◆ getA()

◆ getB()

◆ getMap()

◆ getPadding()

◆ impose()

Stokes equation, lid driven cavity with one splipping wall

◆ impose_dit() [1/3]

Stokes equation 2D, lid driven cavity with one splipping wall

◆ impose_dit() [2/3]

Stokes equation 2D, lid driven cavity with one splipping wall

◆ impose_dit() [3/3]

Stokes equation 2D, lid driven cavity with one splipping wall

◆ impose_dit_b() [1/2]

Stokes equation 2D, lid driven cavity with one splipping wall

◆ impose_dit_b() [2/2]

◆ impose_git()

Stokes equation 2D, lid driven cavity with one splipping wall

◆ impose_git_gmap()

Stokes equation 2D, lid driven cavity with one splipping wall

◆ Initialize()

◆ new_A()

◆ new_b()

◆ padding()

◆ setStagPos()

Field Documentation

◆ A

◆ b

◆ g_map

◆ gs

◆ pd

◆ pnt

◆ row

◆ row_b

◆ s_pnt

◆ s_pos

◆ spacing