CFD Python http://lorenabarba.com/blog/cfd-python-12-steps-to-navier-stokes/

lin-conv.py

# Remember: comments in python are denoted by the pound sign
import numpy as np                 #here we load numpy, calling it 'np' from now on
import matplotlib.pyplot as plt    #here we load matplotlib, calling it 'plt'
import time, sys                   #and load some utilities
from IPython.core.display import clear_output #used for inline animation

nx = 41  # try changing this number from 41 to 81 and Run All ... what happens?
dx = 2./(nx-1)
nt = 25    #nt is the number of timesteps we want to calculate
dt = .025  #dt is the amount of time each timestep covers (delta t)
c = 1.      #assume wavespeed of c = 1

u = np.ones(nx)      #numpy function ones()
u[.5/dx : 1/dx+1]=2  #setting u = 2 between 0.5 and 1 as per our I.C.s
print (u)

plt.plot(np.linspace(0,2,nx), u)
plt.show()

un = np.ones(nx) #initialize a temporary array

for n in range(nt):  #loop for values of n from 0 to nt, so it will run nt times
    un[:] = u[:] ##copy the existing values of u into un
    #for i in range(1,nx): ## you can try commenting this line and...
    for i in range(nx): ## ... uncommenting this line and see what happens!
        u[i] = un[i]-c*dt/dx*(un[i]-un[i-1])

print (u)

plt.plot(np.linspace(0,2,nx),u)
plt.show()