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122 | import numpy as np
from py_diff_stokes_flow.env.env_base import EnvBase
from py_diff_stokes_flow.common.common import ndarray
from matplotlib import collections as mc
class FluidicForceDensityEnv2d(EnvBase):
def __init__(self, seed, folder):
np.random.seed(seed)
cell_nums = (64, 48)
E = 100
nu = 0.499
vol_tol = 1e-3
edge_sample_num = 2
EnvBase.__init__(self, cell_nums, E, nu, vol_tol, edge_sample_num, folder)
# Initialize the parametric shapes.
self._parametric_shape_info = [ ('bezier', 8), ('bezier', 8), ( 'bezier', 8 ) ]
# Initialize the node conditions.
self._node_boundary_info = []
inlet_velocity = 10
inlet_range = ndarray([0.45, 0.55])
inlet_lb, inlet_ub = inlet_range * cell_nums[0]
outlet_range = ndarray([0.4, 0.6])
outlet_lb, outlet_ub = outlet_range * cell_nums[1]
for i in range(cell_nums[0] + 1):
if inlet_lb < i < inlet_ub:
self._node_boundary_info.append(((i, 0, 0), 0))
self._node_boundary_info.append(((i, 0, 1), inlet_velocity))
# Initialize the interface.
self._interface_boundary_type = 'free-slip'
# Other data members.
self._inlet_velocity = inlet_velocity
self._inlet_range = inlet_range
self._outlet_range = outlet_range
def _variables_to_shape_params(self, x):
x = ndarray(x).copy().ravel()
# Convert x to the shape parameters.
left = ndarray([
[self._inlet_range[0], 0],
[self._inlet_range[0], self._outlet_range[0]],
[self._inlet_range[0] / 2, self._outlet_range[0]],
[0, self._outlet_range[0]]
])
right = ndarray([
[1, self._outlet_range[0]],
[(self._inlet_range[1] + 1) / 2, self._outlet_range[0]],
[self._inlet_range[1], self._outlet_range[0]],
[self._inlet_range[1], 0]
])
upper = ndarray([
[0, self._outlet_range[1]],
[1 / 3, self._outlet_range[1]],
[2 / 3, self._outlet_range[1]],
[1, self._outlet_range[1]]
])
# Slightly perturb them to avoid singular boundaries.
perturb = 0.01
def get_perturb():
return np.random.normal(scale=perturb)
def get_abs_perturb():
return np.abs(np.random.normal(scale=perturb))
left[0, 0] += get_perturb()
left[0, 1] -= get_abs_perturb()
left[1, 0] += get_perturb()
left[1, 1] += get_perturb()
left[2, 0] += get_perturb()
left[2, 1] += get_perturb()
left[3, 0] -= get_abs_perturb()
left[3, 1] += get_perturb()
right[0, 0] += get_abs_perturb()
right[0, 1] += get_perturb()
right[1, 0] += get_perturb()
right[1, 1] += get_perturb()
right[2, 0] += get_perturb()
right[2, 1] += get_perturb()
right[3, 0] += get_perturb()
right[3, 1] -= get_abs_perturb()
upper[0, 0] -= get_abs_perturb()
upper[0, 1] += get_perturb()
upper[1, 0] += get_perturb()
upper[1, 1] += get_perturb()
upper[2, 0] += get_perturb()
upper[2, 1] += get_perturb()
upper[3, 0] += get_abs_perturb()
upper[3, 1] += get_perturb()
cxy = ndarray(self._cell_nums)
left *= cxy
right *= cxy
upper *= cxy
params = np.concatenate([left.ravel(), right.ravel(), upper.ravel()])
# Jacobian.
J = np.zeros((params.size, x.size))
return ndarray(params).copy(), ndarray(J).copy()
def _loss_and_grad(self, scene, u):
param_size = self._variables_to_shape_params(self.lower_bound())[0].size
grad_param = ndarray(np.zeros(param_size))
return 0, ndarray(np.zeros(u.shape).ravel()), grad_param
def _render_customized_2d(self, scene, u_field, ax):
nx, ny = self._node_nums
lines = []
scale = 0.1
for i in range(nx):
for j in range(ny):
if scene.GetSignedDistance((i, j)) > 0: continue
v_begin = ndarray([i, j])
v_end = v_begin + scale * ndarray(scene.GetFluidicForceDensity((i, j)))
lines.append((v_begin, v_end))
ax.add_collection(mc.LineCollection(lines, colors='tab:red', linestyle='-'))
def sample(self):
return ndarray(np.zeros(24))
|