u(x,t) — Burgers eq.
Method of Characteristics
Spacetime (x-t) diagram
Viscous vs Inviscid shock
Shock Formation
Amplitude A:
1.0
Viscosity ν:
0.01
Time t:
0.00
IC shape:
Sine wave
Gaussian bump
Step function
Sawtooth
Animate
Reset t=0
Burgers:
∂u/∂t + u·∂u/∂x = ν∂²u/∂x²
Inviscid:
∂u/∂t + u·∂u/∂x = 0
Shock time:
t* = 1/max(-u'₀(x))
Rankine-Hugoniot:
s = (u₊+u₋)/2