Buckley-Leverett equation (a nonconvex flux)

Observe that setting setting 
    method(1) = 0
    dtv(1) < dx/2.1
results in a stable method that gives good results, while setting
    method(1) = 1
    cflv(1) = 1
    cflv(2) = 0.8
results in poor results because the estimate of CFL used by clawpack
is not sufficient in this case to keep the actual Courant number below 1.
This is because the nonconvexity of f(q) hides points where f'(q) is greater
than the observed shock speed calculated by 
    s = (f(Q_i) - f(Q_{i-1})) / (Q_i - Q_{i-1})

    

WARNING: This example was modified February, 2006 to use
Version 4.3 of clawpack and the associated matlab scripts.