Text and code provided under a Creative Commons Attribution license, CC-BY. (c) Lorena A. Barba, 2013. Thanks: Gilbert Forsyth for help writing the notebooks. NSF for support via CAREER award #1149784.
import numpy as np                 #loading our favorite library
import matplotlib.pyplot as plt    #and the useful plotting library


nx = 41
dx = 2./(nx-1)
nt = 20    #the number of timesteps we want to calculate
nu = 0.3   #the value of viscosity
sigma = .2 #sigma is a parameter, we'll learn more about it later
dt = sigma*dx**2/nu #dt is defined using sigma ... more later!


u = np.ones(nx)      #a numpy array with nx elements all equal to 1.
u[.5/dx : 1/dx+1]=2  #setting u = 2 between 0.5 and 1 as per our I.C.s

un = np.ones(nx) #our placeholder array, un, to advance the solution in time

for n in range(nt):  #iterate through time
    un[:] = u[:] ##copy the existing values of u into un
    for i in range(1,nx-1):
        u[i] = un[i] + nu*dt/dx**2*(un[i+1]-2*un[i]+un[i-1])
        
plt.plot(np.linspace(0,2,nx), u)

from IPython.display import YouTubeVideo
YouTubeVideo('y2WaK7_iMRI')

from IPython.core.display import HTML
def css_styling():
    styles = open("../styles/custom.css", "r").read()
    return HTML(styles)
css_styling()