pyLBM.stencil.Stencil¶

class pyLBM.stencil.Stencil(dico)¶

Create the stencil of velocities used by the scheme(s).

The numbering of the velocities follows the convention for 1D and 2D.

Parameters:

Parameters:	dico : a dictionary that contains the following key:value dim : the value of the spatial dimension (1, 2 or 3) schemes : a list of the dictionaries that contain the key:value velocities [{‘velocities’:[...]}, {‘velocities’:[...]}, {‘velocities’:[...]}, ...]

dico : a dictionary that contains the following key:value

dim : the value of the spatial dimension (1, 2 or 3)

schemes : a list of the dictionaries that contain the key:value velocities

[{‘velocities’:[...]}, {‘velocities’:[...]}, {‘velocities’:[...]}, ...]

Notes

The velocities for each schemes are defined as a Python list.

Examples

>>> s = Stencil({'dim': 1,
             'schemes':[{'velocities': range(9)}, ],
                })
>>> s
Stencil informations
  * spatial dimension: 1
  * maximal velocity in each direction: [4 None None]
  * minimal velocity in each direction: [-4 None None]
  * Informations for each elementary stencil:
        stencil 0
        - number of velocities:  9
        - velocities: (0: 0), (1: 1), (2: -1), (3: 2), (4: -2), (5: 3), (6: -3), (7: 4), (8: -4),

>>> s = Stencil({'dim': 2,
                 'schemes':[{'velocities':range(9)},
                            {'velocities':range(50)},
                           ],
                })
>>> s
Stencil informations
  * spatial dimension: 2
  * maximal velocity in each direction: [4 3 None]
  * minimal velocity in each direction: [-3 -3 None]
  * Informations for each elementary stencil:
        stencil 0
        - number of velocities:  9
        - velocities: (0: 0, 0), (1: 1, 0), (2: 0, 1), (3: -1, 0), (4: 0, -1), (5: 1, 1), (6: -1, 1), (7: -1, -1), (8: 1, -1),
        stencil 1
        - number of velocities: 50
        - velocities: (0: 0, 0), (1: 1, 0), (2: 0, 1), (3: -1, 0), (4: 0, -1), (5: 1, 1), (6: -1, 1), (7: -1, -1), (8: 1, -1), (9: 2, 0), (10: 0, 2), (11: -2, 0), (12: 0, -2), (13: 2, 2), (14: -2, 2), (15: -2, -2), (16: 2, -2), (17: 2, 1), (18: 1, 2), (19: -1, 2), (20: -2, 1), (21: -2, -1), (22: -1, -2), (23: 1, -2), (24: 2, -1), (25: 3, 0), (26: 0, 3), (27: -3, 0), (28: 0, -3), (29: 3, 3), (30: -3, 3), (31: -3, -3), (32: 3, -3), (33: 3, 1), (34: 1, 3), (35: -1, 3), (36: -3, 1), (37: -3, -1), (38: -1, -3), (39: 1, -3), (40: 3, -1), (41: 3, 2), (42: 2, 3), (43: -2, 3), (44: -3, 2), (45: -3, -2), (46: -2, -3), (47: 2, -3), (48: 3, -2), (49: 4, 0),

get the x component of the unique velocities

>>> s.uvx
array([ 0,  1,  0, -1,  0,  1, -1, -1,  1,  2,  0, -2,  0,  2, -2, -2,  2,
        2,  1, -1, -2, -2, -1,  1,  2,  3,  0, -3,  0,  3, -3, -3,  3,  3,
        1, -1, -3, -3, -1,  1,  3,  3,  2, -2, -3, -3, -2,  2,  3,  4])

get the y component of the velocity for the second stencil

>>> s.vy[1]
array([ 0,  0,  1,  0, -1,  1,  1, -1, -1,  0,  2,  0, -2,  2,  2, -2, -2,
        1,  2,  2,  1, -1, -2, -2, -1,  0,  3,  0, -3,  3,  3, -3, -3,  1,
        3,  3,  1, -1, -3, -3, -1,  2,  3,  3,  2, -2, -3, -3, -2,  0])

Attributes

`uvx`	the x component of the unique velocities.
`uvy`	the y component of the unique velocities.
`uvz`	the z component of the unique velocities.
`unum`	the numbering of the unique velocities.
`vmax`	the maximal velocity in norm for each spatial direction.
`vmin`	the minimal velocity in norm for each spatial direction.
`vx`	vx[k] the x component of the velocities for the stencil k.
`vy`	vy[k] the y component of the velocities for the stencil k.
`vz`	vz[k] the z component of the velocities for the stencil k.
`num`	num[k] the numbering of the velocities for the stencil k.
`unvtot`	the number of unique velocities involved in the stencils.

dim	(int) the spatial dimension (1, 2 or 3).
unique_velocities	(NumPy array) array of all velocities involved in the stencils. Each unique velocity appeared only once.
nstencils	(int) the number of elementary stencils.
nv	(list of integers) the number of velocities for each elementary stencil.
v	(list of velocities) list of all the velocities for each elementary stencil.
nv_ptr	(list of integers) used to obtain the list of the velocities involved in a stencil. For instance, the list for the kth stencil is v[nv_ptr[k]:nv_ptr[k+1]]

Methods

`append`	L.append(object) – append object to end
`count`(...)
`extend`	L.extend(iterable) – extend list by appending elements from the iterable
`get_all_velocities`()	get all the velocities for all the stencils in one array
`get_stencil`(k)
`get_symmetric`([axis])	get the symetrics velocities.
`index`((value, [start, ...)	Raises ValueError if the value is not present.
`insert`	L.insert(index, object) – insert object before index
`is_symmetric`()	check if all the velocities have their symetric.
`pop`(...)	Raises IndexError if list is empty or index is out of range.
`remove`	L.remove(value) – remove first occurrence of value.
`reverse`	L.reverse() – reverse IN PLACE
`sort`	L.sort(cmp=None, key=None, reverse=False) – stable sort IN PLACE;
`visualize`([viewer_mod, k, unique_velocities])	plot the velocities

pyLBM.stencil.Stencil¶

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