The study of shallow water flow with bottom topography by high-order compact gas-kinetic scheme on unstructured mesh

A well-balanced compact high-order gas-kinetic scheme (GKS) on unstructured mesh is first developed for solving the shallow water equations with source terms. The distinguishable feature of finite volume GKS that based formulation, a time-accurate gas distribution function can be constructed, from which both fluxes and flow variables explicitly evaluated at cell interface. As result, besides update cell-averaged conservative variables, slopes updated as well. Equipped their slopes, fourth-order spatial reconstruction obtained initial condition beginning each time step. For flow, in order to preserve property, advection terms flux have balanced properly. current achieves accuracy, keeps has super-robustness simulation bore waves. used studies, such dam breaking wave propagation. In addition, pollution transport, morphodynamics, bottom friction been included scheme. end, discharge Pearl River estuary dam-break experiment movable bed topography simulated.