# -*- coding: utf-8 -*-
r"""
.. testsetup:: *
import __init__ as ph
from msepy.manifold.predefined.cylinder_channel import _make_an_illustration
_make_an_illustration(
'./source/gallery/msepy_domains_and_meshes/msepy/cylinder_channel_2d.png'
)
None_or_custom_path = './source/gallery/msepy_domains_and_meshes/msepy/cylinder_channel_example.png'
.. testcleanup::
pass
The cylinder channel is a mesh (or domain) in :math:`\mathbb{R}^n`, :math:`n\in\left\lbrace2,3\right\rbrace`.
The 2d domain is illustrated in the following figure.
.. figure:: cylinder_channel_2d.png
:width: 100%
The illustration of the 2d cylinder channel domain.
.. autofunction:: msepy.manifold.predefined.cylinder_channel.cylinder_channel
Boundary units
==============
The cylinder channel domain is divided into 7 regions. The topology of these regions is illusrated in the
following figure.
.. figure:: cylinder_channel_2d_topology.png
:width: 100%
The illustration of the topology of regions in a 2d cylinder channel domain.
Thus, the complete set of boundary units in 2 dimensions is
>>> boundary_units_set = {
... 0: [1, 0, 1, 0],
... 1: [0, 0, 1, 1],
... 2: [0, 1, 1, 0],
... 3: [1, 1, 0, 0],
... 4: [1, 1, 0, 0],
... 5: [1, 0, 0, 1],
... 6: [0, 0, 1, 1],
... 7: [0, 1, 0, 1],
... }
And, for example, if we call the left side the inlet, we can pick up boundary units for the inlet by
>>> boundary_units_inlet = {
... 0: [1, 0, 0, 0],
... 3: [1, 0, 0, 0],
... 5: [1, 0, 0, 0]
... }
The cylinder surface is
>>> boundary_units_inlet = {
... 1: [0, 0, 0, 1],
... 3: [0, 1, 0, 0],
... 4: [1, 0, 0, 0],
... 6: [0, 0, 1, 0]
... }
Examples
========
2d
--
We can generate a mesh in this domain by doing
>>> ph.config.set_embedding_space_dim(2)
>>> manifold = ph.manifold(2)
>>> mesh = ph.mesh(manifold)
>>> msepy, obj = ph.fem.apply('msepy', locals())
>>> manifold = obj['manifold']
>>> mesh = obj['mesh']
>>> msepy.config(manifold)('cylinder_channel')
>>> msepy.config(mesh)(3) # refining factor, a positive integer.
>>> mesh.visualize(saveto=None_or_custom_path) # doctest: +ELLIPSIS
<Figure size ...
.. figure:: cylinder_channel_example.png
:width: 100%
The cylinder_channel mesh of element factor 3.
Note that we configure the mesh with a factor ``3``. Increasing this factor to refine the mesh.
"""
import sys
if './' not in sys.path:
sys.path.append('./')
import numpy as np
from msepy.manifold.predefined._helpers import _LinearTransformation, _Transfinite2
import matplotlib.pyplot as plt
def _make_an_illustration(saveto, r=1, dl=10, dr=25, h=6):
"""Make a picture illustrating the domain."""
fig, ax = plt.subplots(figsize=(8, 6))
ax.set_aspect('equal')
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
ax.spines['left'].set_visible(False)
ax.spines['bottom'].set_visible(False)
plt.tick_params(
axis='both',
which='both',
left=False,
bottom=False,
labelbottom=False,
labelleft=False
)
x = [-dl, dr, dr, -dl, -dl]
y = [-h/2, -h/2, h/2, h/2, -h/2]
angle = np.linspace(0, 2*np.pi, 100)
rx = r * np.cos(angle)
ry = r * np.sin(angle)
plt.plot(x, y, '-k', linewidth=0.8)
plt.plot(rx, ry, '-k', linewidth=0.8)
_r = 1.1*dr
plt.plot([0, _r], [0, 0], '-', linewidth=0.8, color='lightgray')
_ = 0.05 * h
plt.plot([_r - _, _r, _r - _], [_, 0, -_], '-', linewidth=0.8, color='lightgray')
plt.text(_r, 0, r"$x$", c='gray', va='bottom', ha='left')
_y = 1.4 * h / 2
plt.plot([0, 0], [0, _y], '-', linewidth=0.8, color='lightgray')
plt.plot([-_, 0, _], [_y-_, _y, _y-_], '-', linewidth=0.8, color='lightgray')
plt.text(0, _y, r"$y$", c='gray', va='bottom', ha='left')
plt.text(0, 0, r"$r$", c='k', va='bottom', ha='left')
plt.plot([0, r], [0, 0], c='k', linewidth=0.8)
plt.plot([0, 0], [0, -h/2], c='lightgray', linewidth=0.8)
plt.text(-dl, 0, r"$h$", va='center', ha='left')
plt.text(-dl/2, -h/2, r"$d_l$", va='bottom', ha='center')
plt.text(dr/2, -h/2, r"$d_r$", va='bottom', ha='center')
plt.savefig(saveto, bbox_inches='tight', dpi=200)
plt.close()
fig, ax = plt.subplots(figsize=(8, 6))
ax.set_aspect('equal')
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
ax.spines['left'].set_visible(False)
ax.spines['bottom'].set_visible(False)
plt.tick_params(
axis='both',
which='both',
left=False,
bottom=False,
labelbottom=False,
labelleft=False
)
plt.plot(x, y, '-k', linewidth=0.8)
plt.plot([0, _r], [0, 0], '-', linewidth=0.8, color='lightgray')
_ = 0.05 * h
plt.plot([_r - _, _r, _r - _], [_, 0, -_], '-', linewidth=0.8, color='lightgray')
plt.text(_r, 0, r"$x$", c='gray', va='bottom', ha='left')
_y = 1.4 * h / 2
plt.plot([0, 0], [0, _y], '-', linewidth=0.8, color='lightgray')
plt.plot([-_, 0, _], [_y-_, _y, _y-_], '-', linewidth=0.8, color='lightgray')
plt.text(0, _y, r"$y$", c='gray', va='bottom', ha='left')
plt.plot([-r, r, r, -r, -r], [-r, -r, r, r, -r], '-k', linewidth=0.8)
plt.plot([-r, -dl], [-r, -r], '-', linewidth=0.5, color='gray')
plt.plot([r, dr], [-r, -r], '-', linewidth=0.5, color='gray')
plt.plot([-r, -dl], [r, r], '-', linewidth=0.5, color='gray')
plt.plot([r, dr], [r, r], '-', linewidth=0.5, color='gray')
plt.plot([-r, -r], [-r, -h/2], '-', linewidth=0.5, color='gray')
plt.plot([-r, -r], [r, h/2], '-', linewidth=0.5, color='gray')
plt.plot([r, r], [-r, -h/2], '-', linewidth=0.5, color='gray')
plt.plot([r, r], [r, h/2], '-', linewidth=0.5, color='gray')
plt.text(-(dl+r)/2, -(h/2+r)/2, r"$r_0$", c='k', va='center', ha='center')
plt.text(0, -(h/2+r)/2, r"$r_1$", c='k', va='center', ha='center')
plt.text((dr+r)/2, -(h/2+r)/2, r"$r_2$", c='k', va='center', ha='center')
plt.text(-(dl+r)/2, 0, r"$r_3$", c='k', va='center', ha='center')
plt.text((dr+r)/2, 0, r"$r_4$", c='k', va='center', ha='center')
plt.text(-(dl+r)/2, (h/2+r)/2, r"$r_5$", c='k', va='center', ha='center')
plt.text(0, (h/2+r)/2, r"$r_6$", c='k', va='center', ha='center')
plt.text((dr+r)/2, (h/2+r)/2, r"$r_7$", c='k', va='center', ha='center')
saveto = saveto.split('.png')[0] + rf"_topology.png"
plt.savefig(saveto, bbox_inches='tight', dpi=200)
plt.close()
[docs]
def cylinder_channel(r=1, dl=8, dr=25, h=6, w=0, periodic=True):
r"""
Parameters
----------
r : float, default=1
The radius of the cylinder.
dl : float, default=8
The :math:`x` distance from the left boundary to the cylinder center.
dr : float, default=25
The :math:`x` distance from the right boundary to the cylinder center.
h : float, default=6
The height (along :math:`y`-direction, :math:`[-h/2, h/2]`) of the channel; must have
:math:`h/2 > r`.
w : float, default=0
The width (along :math:`z`-direction, :math:`[-w/2, w/2]`) of the channel.
periodic : bool, default=True
When the domain is 3d, whether it is periodic along the :math:`z`-axis? It has no affect
when ``w=0`` (the domain is 2d).
"""
raise Exception(r, dl, dr, h, w, periodic)
# noinspection PyPep8Naming
class _CylinderChannel(object):
r""" ^ y
|
______________|______________________________________
| | |
| _|_ |
| / |r\ |
|h | .--|----------------------------------|----------> x
| \___/ |
| |
|______dl________________________dr_________________|
Regions are distributed as:
^ y
|
__________________________________________
| 5 | 6 | 7 |
|_______|__________|_____________________|
| 3 / \ 4 | --->x
|_______\__________/_____________________|
| 0 | 1 | 2 |
|_______|__________|_____________________|
"""
def __init__(self, mf, r=1, dl=8, dr=25, h=6, w=0, periodic=True):
"""
Parameters
----------
mf
r
dl
dr
h
w
periodic
Returns
-------
"""
self._mf = mf
self._r = r
self._dl = dl
self._dr = dr
self._h = h
self._w = w
self._periodic = periodic
assert dl > 2 * r and (h/2) > 2 * r and dr > 5 * r, f"shape wrong!"
assert mf.esd == mf.ndim, f"_cylinder_channel mesh only works for manifold.ndim == embedding space dimensions."
assert mf.esd in (2, 3), f"_cylinder_channel mesh only works in 2-, 3-dimensions."
esd = mf.esd
self._esd = esd
if w == 0:
assert esd == 2, f"w==0, space must be 2d"
else:
assert w > 0 and esd == 3, f"w>0, space must be 3d"
if esd == 2:
region_map = {
0: [None, 1, None, 3],
1: [0, 2, None, None],
2: [1, None, None, 4],
3: [None, None, 0, 5],
4: [None, None, 2, 7],
5: [None, 6, 3, None],
6: [5, 7, None, None],
7: [6, None, 4, None],
}
elif esd == 3:
if periodic:
region_map = {
0: [None, 1, None, 3, 0, 0],
1: [0, 2, None, None, 1, 1],
2: [1, None, None, 4, 2, 2],
3: [None, None, 0, 5, 3, 3],
4: [None, None, 2, 7, 4, 4],
5: [None, 6, 3, None, 5, 5],
6: [5, 7, None, None, 6, 6],
7: [6, None, 4, None, 7, 7],
}
else:
region_map = {
0: [None, 1, None, 3, None, None],
1: [0, 2, None, None, None, None],
2: [1, None, None, 4, None, None],
3: [None, None, 0, 5, None, None],
4: [None, None, 2, 7, None, None],
5: [None, 6, 3, None, None, None],
6: [5, 7, None, None, None, None],
7: [6, None, 4, None, None, None],
}
else:
raise Exception()
hr = 0.5 * r * np.sqrt(2)
if esd == 2:
tf1 = _Transfinite2(
['straight line', [(-hr, -h/2), (-hr, -hr)]],
['straight line', [(hr, -h/2), (hr, -hr)]],
['straight line', [(-hr, -h/2), (hr, -h/2)]],
['anticlockwise arc', [(0, 0), (-hr, -hr), (hr, -hr)]],
)
tf3 = _Transfinite2(
['straight line', [(-dl, -hr), (-dl, hr)]],
['clockwise arc', [(0, 0), (-hr, -hr), (-hr, hr)]],
['straight line', [(-dl, -hr), (-hr, -hr)]],
['straight line', [(-dl, hr), (-hr, hr)]],
)
tf4 = _Transfinite2(
['anticlockwise arc', [(0, 0), (hr, -hr), (hr, hr)]],
['straight line', [(dr, -hr), (dr, hr)]],
['straight line', [(hr, -hr), (dr, -hr)]],
['straight line', [(hr, hr), (dr, hr)]],
)
tf6 = _Transfinite2(
['straight line', [(-hr, hr), (-hr, h/2)]],
['straight line', [(hr, hr), (hr, h/2)]],
['clockwise arc', [(0, 0), (-hr, hr), (hr, hr)]],
['straight line', [(-hr, h/2), (hr, h/2)]],
)
rm0 = _LinearTransformation(-dl, -hr, -h/2, -hr)
rm1 = tf1
rm2 = _LinearTransformation(hr, dr, -h/2, -hr)
rm3 = tf3
rm4 = tf4
rm5 = _LinearTransformation(-dl, -hr, hr, h/2)
rm6 = tf6
rm7 = _LinearTransformation(hr, dr, hr, h/2)
elif esd == 3:
raise NotImplementedError()
else:
raise Exception()
mapping_dict = {
0: rm0.mapping,
1: rm1.mapping,
2: rm2.mapping,
3: rm3.mapping,
4: rm4.mapping,
5: rm5.mapping,
6: rm6.mapping,
7: rm7.mapping,
}
Jacobian_matrix_dict = {
0: rm0.Jacobian_matrix,
1: rm1.Jacobian_matrix,
2: rm2.Jacobian_matrix,
3: rm3.Jacobian_matrix,
4: rm4.Jacobian_matrix,
5: rm5.Jacobian_matrix,
6: rm6.Jacobian_matrix,
7: rm7.Jacobian_matrix,
}
if esd == 2:
mtype_dict = {
0: rm0.mtype,
1: rm1.mtype, # unique region
2: rm2.mtype,
3: rm3.mtype, # unique region
4: rm4.mtype, # unique region
5: rm5.mtype,
6: rm6.mtype, # unique region
7: rm7.mtype,
}
elif esd == 3:
raise NotImplementedError()
else:
raise Exception()
default_element_layout = self._cylinder_channel_default_element_layout
self._para = (
region_map, mapping_dict, Jacobian_matrix_dict, mtype_dict, default_element_layout
)
def __call__(self, *args, **kwargs):
return self._para
def _cylinder_channel_default_element_layout(self, characteristic_element_number):
"""default_element_layout_maker must return a dict indicating the element layouts in all regions.
When we config the mesh, if only one number argument is provided, this method will be called to
make a default element layout with the only argument being the `characteristic_element_number`.
For this mesh, ``characteristic_element_number`` indicating the element number of
1/4 of the cylinder. Thus, around the cylinder, there will be 4 * ``characteristic_element_number``
elements in total.
"""
assert characteristic_element_number > 0 and characteristic_element_number % 1 == 0, \
f"characteristic_element_number = {characteristic_element_number} is wrong, must be positive integer."
arc_length = 2 * np.pi * self._r * 0.25
hr = 0.5 * self._r * np.sqrt(2)
c_elements = characteristic_element_number
# x-direction of #0, 3, 5
left_elements = int(((self._dl - hr) / arc_length) * characteristic_element_number) + 1
# x-direction of #2, 4, 7
right_elements = int(((self._dr - hr) / arc_length) * characteristic_element_number) + 1
# y-direction of #0, 1, 2, 5, 6, 7
height_elements = int(((self._h/2 - hr) / arc_length) * characteristic_element_number) + 1
if self._esd == 2:
pass
else:
raise NotImplementedError(f"compute z-direction elements.")
element_layout = dict()
if self._esd == 2:
element_layout[0] = [left_elements, height_elements]
element_layout[1] = [c_elements, height_elements]
element_layout[2] = [right_elements, height_elements]
element_layout[3] = [left_elements, c_elements]
element_layout[4] = [right_elements, c_elements]
element_layout[5] = [left_elements, height_elements]
element_layout[6] = [c_elements, height_elements]
element_layout[7] = [right_elements, height_elements]
else:
raise NotImplementedError()
return element_layout
if __name__ == '__main__':
# python msepy/manifold/predefined/cylinder_channel.py
# _make_an_illustration('cylinder_channel.png')
pass
