Burgers Equation
u_t + u·u_x = ν·u_xx — shock formation and viscous smoothing
Viscosity ν
0.003
Amplitude A
1.0
Speed ×
1.0
Reset
Initial data: u(x,0) = A·sin(x)
ν=0:
characteristics cross
→ multi-valued → shock forms
at t_shock = 1/(A·max|u_x|)
ν>0:
viscous term ν·u_xx
→ Hopf-Cole solution
→ shock smoothed, stable
Rankine-Hugoniot: shock
speed = ½(u_L + u_R)
t =
0.00