High order well-balanced asymptotic preserving finite difference WENO schemes for the shallow water equations in all Froude numbers

In this paper, high order semi-implicit well-balanced and asymptotic preserving finite difference WENO schemes are proposed for the shallow water equations with a non-flat bottom topography. We consider Froude number ranging from O(1) to 0, which in zero limit becomes "lake equations" balanced flow without gravity waves. apply reconstruction, coupled stiffly accurate implicit-explicit (IMEX) Runge-Kutta time discretization. The resulting scheme can be shown well-balanced, (AP) asymptotically (AA) at same time. Both one- two-dimensional numerical results provided demonstrate accuracy, AP property good performance of methods capturing small perturbations steady state solutions.