import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as animation

nx   = 100
nt   = 100
x    = np.linspace(0.,10.,nx)
t    = np.linspace(0.,10.,nt)
q    = np.zeros((nt,nx))
q[0,x<3] = 1.0     # Step function initial condition
v0   = 0.4         # Constant advection velocity
for n in range(0,nt-1):
    dt          = t[n+1] - t[n]
    q[n+1,1:-1] = q[n,1:-1] - dt * v0 * ( q[n,2:] - q[n,:-2] ) / ( x[2:] - x[:-2] )
    q[n+1,0]    = q[n,0]
    q[n+1,-1]   = q[n,-1]

n = 0
def animupdate(frameNum, a0):
    global n,q,x,nt
    y = q[n,:]
    a0.set_data(x, y)
    n = (n + 1) % nt

fig = plt.figure()
ax  = plt.axes(xlim=(x.min(),x.max()),ylim=(0.,1.5))
a0, = ax.plot([], [])
anim = animation.FuncAnimation(fig,animupdate,fargs=(a0,),interval=40)
plt.show()