How can I show animation of all points of a meshgrid matrix?

Question

I'm trying to make the animation of a point source diffusion model. The code below only shows the animation of the center point. I'd like to know why my code doesn't show animation of all points of Z matrix.

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation

# Parameters
Dx = 0.00002  # Diffusion coefficient along x (cm2/s)
Dy = 0.00001  # Diffusion coefficient along y (cm2/s)
M = 1000  #Initial mass (gr)
L = 40 # Half of container length (cm)
dt = 0.01  # Time step (s)
T = 20.0  # Total simulation time (s)
num_frames = int(T / dt)

x = np.arange(-L, L + 0.25,0.25)
y = np.arange(-L, L + 0.25,0.25)
X, Y = np.meshgrid(x, y)

def gaussian_circle(X, Y, frame_num):
    c = M*np.exp(-((X ** 2)/(4 * Dx * frame_num * dt) + (Y ** 2)/(4 * Dy * frame_num * dt) )) / ((4 * np.pi * Dx * frame_num * dt) ** 0.5 * (4 * np.pi * Dy * frame_num * dt) ** 0.5) / 10 ** 6
    return c

# Set up the plot
Z = gaussian_circle(X, Y, 1)
fig, ax = plt.subplots()
cax = ax.pcolormesh(X, Y, Z, vmin=0)

def animate(frame):
    global Z
    # Applying the diffusion equation using a Gaussian filter
    next_frame = frame+1
    Z = gaussian_circle(X, Y, next_frame)
    cax.set_array(Z)
    ax.set_title(f'Diffusion at t = {next_frame * dt:.2f} s')
    return cax,


# Creating the animation
animation = FuncAnimation(fig, animate, frames=num_frames, interval=10)

cbar = fig.colorbar(cax) # Add a colorbar to a plot
cbar.set_label('C(ppm)')
ax.set_xlabel('x (cm)')
ax.set_ylabel('y (cm)')
plt.show()

expected result: expected diffusion model

Answer 1

Your animation function works well; it is not the source of the issue. Your problem shows up in the gaussian_circle(...) function. The exponential evaluates to zero for any x/y not equal to zero. The cause seems to be the extremely small values of Dx and Dy. If you change Dx from 2.0E-5 to 2.0E4, which is the correct exponent for conversion from meters to cm^2, then it works well. Do the same with Dy and you will get the following image!

Answer 2

Here's the final code that shows the animation correctly:

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation

# Parameters
Dx = 4 * 10** (-5)  # Diffusion coefficient along x (cm2/s)
Dy = 2 * 10 ** (-5) # Diffusion coefficient along y (cm2/s)
M = 100  #Initial mass (gr)
L = 0.08 # Half of container length (cm)
dt = 0.25  # Time step (s)
T = 40.0  # Total simulation time (s)
mesh_size = 0.001 # Increasing mesh_size leads to lower rendering time
num_frames = int(T / dt)

x = np.arange(-L, L + mesh_size, mesh_size)
y = np.arange(-L, L + mesh_size, mesh_size)
X, Y = np.meshgrid(x, y)

def gaussian_circle(X, Y, frame_num):
    c = M * np.exp(-((X ** 2) / (4 * Dx * frame_num * dt) + (Y ** 2) / (4 * Dy * frame_num * dt))) / (
                (4 * np.pi * Dx * frame_num * dt) ** 0.5 * (4 * np.pi * Dy * frame_num * dt) ** 0.5) / 10 ** 3
    return c

# Setting up the plot
fig, ax = plt.subplots()
# Initializing the animation with t = 0.01
cax = ax.pcolormesh(X , Y, gaussian_circle(X, Y, 1), vmin=0)

#The updating animation fucntion
def animate(frame):    
    Z = gaussian_circle(X, Y, frame + 1)
    ax.set_title(f'Diffusion at t = {(frame + 1) * dt:.2f} s')
    cax = ax.pcolormesh(X , Y, gaussian_circle(X, Y, frame + 1), vmin=0)
    
    # Concentration of the center & the left edge
    print(Z[80, 80], Z[0, 0], frame)
    return cax,

# Creating the animation
animation = FuncAnimation(fig, animate, frames=num_frames, interval=10, repeat=False)

# Adding colorbar & labels to plot
cbar = plt.colorbar(cax) 
cbar.set_label('C(mg/cm2)')
ax.set_xlabel('x (cm)')
ax.set_ylabel('y (cm)')
plt.show()

# #Before saving, comment out plt.show() so u won't have to wait for the animation to be shown)
# animation.save('diff_2X.gif', dpi=300, fps=2/dt)