Structure-preserving finite volume arbitrary Lagrangian-Eulerian WENO schemes for the shallow water equations

This paper develops the structure-preserving finite volume weighted essentially non-oscillatory (WENO) hybrid schemes for shallow water equations under arbitrary Lagrangian-Eulerian (ALE) framework, dubbed as ALE-WENO schemes. The WENO reconstruction is adopted on moving meshes, which distinguishes smooth, non-smooth, and transition stencils by a simple smoothness detector. To maintain positivity preserving well-balanced properties of schemes, we adapt limiter approaches static meshes to meshes. rigorous theoretical analysis numerical examples demonstrate high order accuracy positivity-preserving property ALE framework. For it successful in unique exact equilibrium preservation capturing small perturbations hydrostatic state well without oscillations near discontinuity. Moreover, our have an advantage over simulations due higher resolution interface tracking fluid motion.