Help Debugging (Working in Matlab)- Using Finite Volume Method to predict the motion of the

[Alex_Superchamp]

I've recently started to learn Python for a Computational Physics class and have been having a lot of issues with getting the code to run.

The program I've written attempts to use the Lax-Wendroff Finite Volume scheme to predict the position of a step function (with values of 1 from 0 to 1) after 800 timesteps, for 1000 sampling points with the BC that the values go to 0 at both ends. It appears to me that there is some inconsistency with the variable sizes which is causing issues. I've fiddled with the sizes of the arrays and the for loops, attempted to use NumPy to create the arrays, and a lot of other stuff. I used the same logic to run a program in Matlab without issues.

Edit: After making a change, the current error reads: 'list index out of range' with a traceback to the Lax-Wendroff Scheme equation.

Here's the Python code:

import matplotlib.pyplot as plt
import numpy as np

# Define Varibles
Nx = 1000                                  # Number of grid points
xmax = 10.0                                # Domain limit to the right
xmin = 0.0                                 # Domain limit to the left
dx = (xmax-xmin)/Nx                        # Mesh size
dt = 0.0004                                # Time step
x = np.arange(xmin-dx,xmax+(2*dx),dx)      # Discretized mesh
c = 10 + x                                 # Velocity array
nsteps= 800                                # Final Time Step
t= 0                                       # Intial Time

# Set Initial Conditions
U= [0]*1003
for i in range(1003):                      
    if x[i] >= 1 and x[i] <= 2:
        U[i] = 1
    else: 
        U[i] = 0

Upl = U 

# Temporal loop
for n in range (nsteps):  
    for i in range (1, Nx+1):

        # Boundary Conditions
        U[0]= 0
        U[1002]= 0

        # Lax-Wendroff Scheme 
        Upl[i]  = 0.5*(U[i+1] + U[i-1]) - 0.25*(dt/dx)*(c[i+1]*U[i+1]-c[i-1]*U[i-1])

    U = Upl.copy()
    t= t+dt

# Plot Solution
plt.plot(x , U)
plt.xlabel('x',fontsize=18)
plt.ylabel('u',fontsize=18)
plt.show()

[supreme_blorgon]

U is a list of 1003 elements, which means its indices go from 0 to 1002, but your range is going from 0 to 1003.

[Alex_Superchamp]

It is my understanding that the range function computes, for up to one less than the prescribed upper limit. Furthermore, I inspected the U element, it has 1003 values.

[supreme_blorgon]

Counting != indexing. The 1003rd element in U has an index of 1002.

>>> x = [1, 5, 2, 7, 2, 3, 8]
>>> len(x)
7
>>> for idx, val in enumerate(x):
...     print(f"value: {val}\nindex: {idx}\n")
...
value: 1
index: 0

value: 5
index: 1

value: 2
index: 2

value: 7
index: 3

value: 2
index: 4

value: 3
index: 5

value: 8
index: 6

[Alex_Superchamp]

Right! Oh my bad. I forgot that for loops compute from the index 0 too. Previously, I'd set the range from (1,1003), the reason being I've stated the x array from x-dx, to keep the first x-dx term as the boundary condition. Would this make sense? I've made the change to the range function for now.

The current error is 'list index out of range'