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                 #numpy is a library for array operations akin to MATLAB
import matplotlib.pyplot as plt    #matplotlib is 2D plotting library

def linearconv(nx):
    dx = 2./(nx-1)
    nt = 20    #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

    u = np.ones(nx)      #defining a numpy array which is nx elements long with every value 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) #initializing our placeholder array, un, to hold the values we calculate for the n+1 timestep

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

linearconv(41) #convection using 41 grid points

linearconv(61)

linearconv(71)

linearconv(85)

import numpy as np
import matplotlib.pyplot as plt

def linearconv(nx):
    dx = 2./(nx-1)
    nt = 20    #nt is the number of timesteps we want to calculate
    c = 1
    sigma = .5
    
    dt = sigma*dx

    u = np.ones(nx) 
    u[.5/dx : 1/dx+1]=2

    un = np.ones(nx)

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

linearconv(41)

linearconv(61)

linearconv(81)

linearconv(101)

linearconv(121)

from IPython.display import YouTubeVideo
YouTubeVideo('Yw1YPBupZxU')

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