Speaker：Yulong Xing（The Ohio State University）

Time：2021-12-16 10:30

Location：Tencent Meeting ID：211-415-103（No Password）

Abstract:

Shallow water equations (SWEs) with a non-flat bottom topography have been widely used to model flows in rivers and coastal areas. In this presentation, we will talk about the applications of high-order well-balanced and positivity-preserving discontinuous Galerkin methods to this system. With carefully chosen numerical fluxes, we will show that the proposed methods preserve the still water steady state exactly, and at the same time maintain the non-negativity of the water height. For the temporal discretization, we propose a family of second and third order time integration methods for systems of partially stiff ordinary differential equations, and explore their application in solving the shallow water equations with friction. The new temporal discretization methods come from a combination of the traditional Runge-Kutta method (for non-stiff equation) and exponential Runge-Kutta method (for stiff equation), and are shown to have the sign-preserving and steady-state-preserving properties. We demonstrate that the full-discrete schemes are well-balanced, positivity-preserving and sign-preserving. The proposed methods have been tested and validated on one- and two-dimensional shallow water equations, and good numerical results have been observed.