A real 1D shallow-water wave solver (c = √gh, leapfrog scheme) running a subduction-zone tsunami from seafloor rupture to the coast. Watch the wave slow, shoal and amplify — Green's law emerges naturally — then measure arrival time, wave height at the shore and runup.
Linearised shallow-water equations ∂u/∂t = −g·∂η/∂x and ∂η/∂t = −∂(hu)/∂x, solved by leapfrog with a CFL-stable timestep. Long-wave speed c = √(gh) automatically slows the wave from ~200 m/s in the deep ocean to ~15 m/s at the shore, and shoaling amplification follows Green's law H ∝ h^(−1/4) without being hard-coded. Source: static seafloor displacement ~ 0.3·10^(0.5(M−8)) m, the standard giant-earthquake scaling. Runup = shore height × slope factor (1.2 gentle / 1.6 typical / 2.2 steep).
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