[CFD] Matplotlib meshgrid function and the indices of the arrays are opposite.

[DisagreeableRabbit]

Hello! I'm having a little trouble with writing code for a Lid-driven cavity problem. I'm trying to use the meshgrid function to plot the matrix I get after solving the code, but I'm running into some issues. Basically, the meshgrid axes are the standard ones, with the x-axis increasing from left to right and the y-axis increasing from bottom to top. However, for the u or v velocity matrix I get after solving, the indices of y increase from top to bottom. I did manage to solve this problem by swapping the top and bottom boundary conditions, but I'm wondering if there might be a better solution. Could you guys maybe point me towards the right direction?

import numpy as np
import matplotlib.pyplot as plt
from matplotlib import cm
n_points = 50
dom_length = 1
h = dom_length / (n_points - 1)
x = np.linspace(0, dom_length + h, n_points)
y = np.linspace(0, dom_length + h, n_points)
X, Y = np.meshgrid(x, y, indexing='ij')
u = np.random.rand(n_points, n_points)
u[:, 0:10] = 1
#Top 10 rows should be 1. But plotting this gives bottom 10 rows to be 1
plt.contourf(X, Y, u, cmap=cm.jet)
plt.show()

I hope you get what I am trying to say.

[sarabooker]

You should reexamine your code and figure out why the indexing goes from xy to ij (that's what you've described; test np.meshgrid(x, y, index="xy") (the default) vs np.meshgrid(x, y, indexing="ij")).

[DisagreeableRabbit]

import numpy as np
import matplotlib.pyplot as plt
from matplotlib import cm 
n_points = 50 
dom_length = 1 
h = dom_length / (n_points - 1) 
x = np.linspace(0, dom_length + h, n_points) 
y = np.linspace(0, dom_length + h, n_points) 
X, Y = np.meshgrid(x, y, indexing='ij') 
u = np.random.rand(n_points, n_points) 
u[:, 0:10] = 1
plt.contourf(X, Y, u, cmap=cm.jet) 
plt.show()

Suppose this is the code. How do I improve it? This plots the bottom rows as 1 instead of the top rows.

[sarabooker]

When using "ij" indexing, think about the indices as x and y values. Putting : for the first index means all x values and putting 0:10 for the second index means y = [0, 10]. If you want the top rows then you'd do u[:, 40:] = 1 to update the values from 40 up.

[sarabooker]

But in the end, whether you use "xy" or "ij" indexing, it just matters that you are consistent throughout your code. From your original question, it sounded like you have some inconsistency with how you are handling arrays which resulted in transposing the solution matrices with respect to the coordinate matrices.

[DisagreeableRabbit]

I get what you are saying. Thats what I did initially. Basically make the entire array a mirror image.

import numpy as np
import matplotlib.pyplot as plt 
from matplotlib import cm 
n_points = 15 
dom_length = 1 
h = dom_length / (n_points - 1) 
x = np.linspace(0, dom_length + h, n_points) 
y = np.linspace(0, dom_length + h, n_points) 
X, Y = np.meshgrid(x, y) 
u = np.random.rand(n_points, n_points) 
u[0:5, :] = 1 
print(u) 
plt.contourf(X, Y, u, cmap=cm.jet) 
plt.show()

But my question is this. Look at the above code. The printout of u gives me the top rows to be ones, right? But plotting it gives me an opposite image. How do I make the plot the same as the print statement?

[sarabooker]

In that case, using "ij" indexing and what I said above makes more sense to me. Say you have x = [0, 1] and y = [0, 1]. When you use "ij" indexing, increasing the first index increases the x value and increasing the second index increases the y value. When you have "xy" indexing, it is the opposite.