🌊 Shallow Water

Scenario:

Left height h_L (m): 3.0 Right height h_R (m): 1.0 Manning n (friction): 0.00 CFL number: 0.4

Sim. time (s)0.0

Wave speed c (m/s)—

Max Froude Fr—

Max h (m)—

Mass conserved?✓

Saint-Venant (1D SWE)
∂h/∂t + ∂(hu)/∂x = 0
∂(hu)/∂t + ∂(hu² + ½gh²)/∂x = −ghn·|u|·u/h^4/3

Wave speed: c = √(gh)
Froude: Fr = |u|/c
Fr < 1: subcritical; Fr > 1: supercritical

Lax-Friedrichs finite-difference scheme.

Water surface height h(x,t) — blue fill, bed in brown

Velocity u(x,t) and Froude number Fr(x)