1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
|
import numpy as np
import scipy.stats as stats
import scipy.constants as const
from scipy.optimize import minimize
import matplotlib
import matplotlib.pyplot as plt
from particles import GasFlow, HardSphereSetup, grid_of_random_velocity_particles
grid_width = 30
radius = 0.002
char_u = 1120
config = HardSphereSetup(radius, char_u, *grid_of_random_velocity_particles(grid_width, radius, char_u))
gas = GasFlow(config)
m_nitrogen = 0.028 / const.N_A
def plot(step, velocities):
velocities = np.array([np.linalg.norm(v) for v in velocities])
maxwellian = stats.maxwell.fit(velocities)
print("T = %.0f K; u_mean = %.0f [m/s]; energy = %.05f" % ((maxwellian[1]**2 / const.k * m_nitrogen, stats.maxwell.mean(*maxwellian), np.sum([x*2 for x in velocities]))))
plt.figure()
plt.ylim(0, 0.003)
plt.ylabel('Probability')
plt.xlim(0, 1.2*char_u)
plt.xlabel('Velocity magnitude [m/s]')
plt.hist(velocities, bins=50, density=True, alpha=0.5, label='Simulated velocities')
xs = np.linspace(0, 1.2*char_u, 100)
plt.plot(xs, stats.maxwell.pdf(xs, *maxwellian), label='Maxwell-Boltzmann distribution')
plt.legend(loc='upper right')
plt.savefig("result/%04d.png" % step)
plt.close()
def simulate(n_steps, section):
for i in range(0, int(n_steps / section)):
print("Plot step %d." % (i * section))
velocities = gas.get_velocities()
for j in range(0,section):
gas.evolve()
plot(i, velocities)
simulate(10000, 500)
|
