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stencils.py
Martin Bauer authored
stencils.py 11.29 KiB
import sympy as sp
def getStencil(name, ordering='walberla'):
"""
Stencils are tuples of discrete velocities. They are commonly labeled in the 'DxQy' notation, where d is the
dimension (length of the velocity tuples) and y is number of discrete velocities.
:param name: DxQy notation
:param ordering: the LBM literature does not use a common order of the discrete velocities, therefore here
different common orderings are available. All orderings lead to the same method, it just has
to be used consistently. Here more orderings are available to compare intermediate results with
the literature.
"""
try:
return getStencil.data[name.upper()][ordering.lower()]
except KeyError:
errMsg = ""
for stencil, orderingNames in getStencil.data.items():
errMsg += " %s: %s\n" % (stencil, ", ".join(orderingNames.keys()))
raise ValueError("No such stencil available. Available stencils: <stencilName>( <orderingNames> )\n" + errMsg)
getStencil.data = {
'D2Q9': {
'walberla': ((0, 0),
(0, 1), (0, -1), (-1, 0), (1, 0),
(-1, 1), (1, 1), (-1, -1), (1, -1),),
'counterclockwise': ((0, 0),
(1, 0), (0, 1), (-1, 0), (0, -1),
(1, 1), (-1, 1), (-1, -1), (1, -1)),
'braunschweig': ((0, 0),
(-1, 1), (-1, 0), (-1, -1), (0, -1),
(1, -1), (1, 0), (1, 1), (0, 1)),
},
'D3Q15': {
'walberla':
((0, 0, 0),
(0, 1, 0), (0, -1, 0), (-1, 0, 0), (1, 0, 0), (0, 0, 1), (0, 0, -1),
(1, 1, 1), (-1, 1, 1), (1, -1, 1), (-1, -1, 1), (1, 1, -1), (-1, 1, -1), (1, -1, -1), (-1, -1, -1)),
'premnath': ((0, 0, 0),
(1, 0, 0), (-1, 0, 0), (0, 1, 0), (0, -1, 0), (0, 0, 1), (0, 0, -1),
(1, 1, 1), (-1, 1, 1), (1, -1, 1), (-1, -1, 1),
(1, 1, -1), (-1, 1, -1), (1, -1, -1), (-1, -1, -1)),
},
'D3Q19': {
'walberla':((0, 0, 0),
(0, 1, 0), (0, -1, 0), (-1, 0, 0), (1, 0, 0), (0, 0, 1), (0, 0, -1),
(-1, 1, 0), (1, 1, 0), (-1, -1, 0), (1, -1, 0),
(0, 1, 1), (0, -1, 1), (-1, 0, 1), (1, 0, 1),
(0, 1, -1), (0, -1, -1), (-1, 0, -1), (1, 0, -1)),
'braunschweig': ((0, 0, 0),
(1, 0, 0), (-1, 0, 0),
(0, 1, 0), (0, -1, 0),
(0, 0, 1), (0, 0, -1),
(1, 1, 0), (-1, -1, 0),
(1, -1, 0), (-1, 1, 0),
(1, 0, 1), (-1, 0, -1),
(1, 0, -1), (-1, 0, 1),
(0, 1, 1), (0, -1, -1),
(0, 1, -1), (0, -1, 1)),
'premnath': ((0, 0, 0),
(1, 0, 0), (-1, 0, 0), (0, 1, 0), (0, -1, 0), (0, 0, 1), (0, 0, -1),
(1, 1, 0), (-1, 1, 0), (1, -1, 0), (-1, -1, 0),
(1, 0, 1), (-1, 0, 1), (1, 0, -1), (-1, 0, -1),
(0, 1, 1), (0, -1, 1), (0, 1, -1), (0, -1, -1)),
},
'D3Q27': {
'walberla': ((0, 0, 0),
(0, 1, 0), (0, -1, 0), (-1, 0, 0), (1, 0, 0), (0, 0, 1), (0, 0, -1),
(-1, 1, 0), (1, 1, 0), (-1, -1, 0), (1, -1, 0),
(0, 1, 1), (0, -1, 1), (-1, 0, 1), (1, 0, 1),
(0, 1, -1), (0, -1, -1), (-1, 0, -1), (1, 0, -1),
(1, 1, 1), (-1, 1, 1), (1, -1, 1), (-1, -1, 1), (1, 1, -1), (-1, 1, -1), (1, -1, -1), (-1, -1, -1)),
'premnath': ((0, 0, 0),
(1, 0, 0), (-1, 0, 0), (0, 1, 0), (0, -1, 0), (0, 0, 1), (0, 0, -1),
(1, 1, 0), (-1, 1, 0), (1, -1, 0), (-1, -1, 0),
(1, 0, 1), (-1, 0, 1), (1, 0, -1), (-1, 0, -1),
(0, 1, 1), (0, -1, 1), (0, 1, -1), (0, -1, -1),
(1, 1, 1), (-1, 1, 1), (1, -1, 1), (-1, -1, 1),
(1, 1, -1), (-1, 1, -1), (1, -1, -1), (-1, -1, -1))
}
}
def inverseDirection(direction):
"""Returns inverse i.e. negative of given direction tuple"""
return tuple([-i for i in direction])
def isValidStencil(stencil, maxNeighborhood=None):
"""
Tests if a nested sequence is a valid stencil i.e. all the inner sequences have the same length.
If maxNeighborhood is specified, it is also verified that the stencil does not contain any direction components
with absolute value greater than the maximal neighborhood.
"""
expectedDim = len(stencil[0])
for d in stencil:
if len(d) != expectedDim:
return False
if maxNeighborhood is not None:
for d_i in d:
if abs(d_i) > maxNeighborhood:
return False
return True
def isSymmetricStencil(stencil):
"""Tests for every direction d, that -d is also in the stencil"""
for d in stencil:
if inverseDirection(d) not in stencil:
return False
return True
def stencilsHaveSameEntries(s1, s2):
if len(s1) != len(s2):
return False
return len(set(s1) - set(s2)) == 0
# -------------------------------------- Visualization -----------------------------------------------------------------
def visualizeStencil(stencil, **kwargs):
dim = len(stencil[0])
if dim == 2:
visualizeStencil2D(stencil, **kwargs)
else:
slicing = False
if 'slice' in kwargs:
slicing = kwargs['slice']
del kwargs['slice']
if slicing:
visualizeStencil3DBySlicing(stencil, **kwargs)
else:
visualizeStencil3D(stencil, **kwargs)
def visualizeStencil2D(stencil, axes=None, figure=None, data=None, textsize='12', **kwargs):
"""
Creates a matplotlib 2D plot of the stencil
:param stencil: sequence of directions
:param axes: optional matplotlib axes
:param data: data to annotate the directions with, if none given, the indices are used
:param textsize: size of annotation text
"""
from matplotlib.patches import BoxStyle
import matplotlib.pyplot as plt
if axes is None:
if figure is None:
figure = plt.gcf()
axes = figure.gca()
text_box_style = BoxStyle("Round", pad=0.3)
head_length = 0.1
text_offset = 1.25
if data is None:
data = list(range(len(stencil)))
for dir, annotation in zip(stencil, data):
assert len(dir) == 2, "Works only for 2D stencils"
if not(dir[0] == 0 and dir[1] == 0):
axes.arrow(0, 0, dir[0], dir[1], head_width=0.08, head_length=head_length, color='k')
if isinstance(annotation, sp.Basic):
annotation = "$" + sp.latex(annotation) + "$"
else:
annotation = str(annotation)
axes.text(dir[0]*text_offset, dir[1]*text_offset, annotation, verticalalignment='center', zorder=30,
horizontalalignment='center',
size=textsize, bbox=dict(boxstyle=text_box_style, facecolor='#00b6eb', alpha=0.85, linewidth=0))
axes.set_axis_off()
axes.set_aspect('equal')
axes.set_xlim([-text_offset*1.1, text_offset*1.1])
axes.set_ylim([-text_offset * 1.1, text_offset * 1.1])
def visualizeStencil3DBySlicing(stencil, sliceAxis=2, figure=None, data=None, **kwargs):
"""
Visualizes a 3D, first-neighborhood stencil by plotting 3 slices along a given axis
:param stencil: stencil as sequence of directions
:param sliceAxis: 0, 1, or 2 indicating the axis to slice through
:param data: optional data to print as text besides the arrows
:return:
"""
import matplotlib.pyplot as plt
for dir in stencil:
for element in dir:
assert element == -1 or element == 0 or element == 1, "This function can only first neighborhood stencils"
if figure is None:
figure = plt.gcf()
axes = [figure.add_subplot(1, 3, i+1) for i in range(3)]
#f, axes = plt.subplots(1, 3)
splittedDirections = [[], [], []]
splittedData = [[], [], []]
axesNames = ['x', 'y', 'z']
for i, dir in enumerate(stencil):
splitIdx = dir[sliceAxis] + 1
reducedDir = tuple([element for j, element in enumerate(dir) if j != sliceAxis])
splittedDirections[splitIdx].append(reducedDir)
splittedData[splitIdx].append(i if data is None else data[i])
for i in range(3):
visualizeStencil2D(splittedDirections[i], axes=axes[i], data=splittedData[i], **kwargs)
for i in [-1, 0, 1]:
axes[i+1].set_title("Cut at %s=%d" % (axesNames[sliceAxis], i))
def visualizeStencil3D(stencil, figure=None, axes=None, data=None, textsize='8'):
"""
Draws 3D stencil into a 3D coordinate system, parameters are similar to :func:`visualizeStencil2D`
If data is None, no labels are drawn. To draw the labels as in the 2D case, use ``data=list(range(len(stencil)))``
"""
from matplotlib.patches import FancyArrowPatch
from mpl_toolkits.mplot3d import proj3d
import matplotlib.pyplot as plt
from matplotlib.patches import BoxStyle
from itertools import product, combinations
import numpy as np
class Arrow3D(FancyArrowPatch):
def __init__(self, xs, ys, zs, *args, **kwargs):
FancyArrowPatch.__init__(self, (0, 0), (0, 0), *args, **kwargs)
self._verts3d = xs, ys, zs
def draw(self, renderer):
xs3d, ys3d, zs3d = self._verts3d
xs, ys, zs = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)
self.set_positions((xs[0], ys[0]), (xs[1], ys[1]))
FancyArrowPatch.draw(self, renderer)
if axes is None:
if figure is None:
figure = plt.figure()
axes = figure.gca(projection='3d')
axes.set_aspect("equal")
if data is None:
data = [None] * len(stencil)
text_offset = 1.25
text_box_style = BoxStyle("Round", pad=0.3)
# Draw cell (cube)
r = [-1, 1]
for s, e in combinations(np.array(list(product(r, r, r))), 2):
if np.sum(np.abs(s - e)) == r[1] - r[0]:
axes.plot3D(*zip(s, e), color="k", alpha=0.5)
for dir, annotation in zip(stencil, data):
assert len(dir) == 3, "Works only for 3D stencils"
if not(dir[0] == 0 and dir[1] == 0 and dir[2] == 0):
if dir[0] == 0:
color = '#348abd'
elif dir[1] == 0:
color = '#fac364'
elif sum([abs(d) for d in dir]) == 2:
color = '#95bd50'
else:
color = '#808080'
a = Arrow3D([0, dir[0]], [0, dir[1]], [0, dir[2]], mutation_scale=20, lw=2, arrowstyle="-|>", color=color)
axes.add_artist(a)
if annotation:
if isinstance(annotation, sp.Basic):
annotation = "$" + sp.latex(annotation) + "$"
else:
annotation = str(annotation)
axes.text(dir[0]*text_offset, dir[1]*text_offset, dir[2]*text_offset,
annotation, verticalalignment='center', zorder=30,
size=textsize, bbox=dict(boxstyle=text_box_style, facecolor='#777777', alpha=0.6, linewidth=0))
axes.set_xlim([-text_offset*1.1, text_offset*1.1])
axes.set_ylim([-text_offset * 1.1, text_offset * 1.1])
axes.set_zlim([-text_offset * 1.1, text_offset * 1.1])
axes.set_axis_off()