Discontinuous Galerkin methods with local time stepping for the nonlinear shallow water equations

 Speaker: Yulong Xing (Ohio State University)

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 the high order ADER-differential transform approach. Local time stepping strategy will also be studied to allow elements of different sizes to use different time steps. One- and two-dimensional numerical tests are performed to verify the well-balanced property, high-order accuracy, and good resolution for general solutions.

Time: March 19, 2021 3:30pm-4:30pm
Location: Virtually via Zoom
Host: Lili Ju