High Order Sign-Preserving and Well-Balanced Exponential Runge-Kutta Discontinuous Galerkin Methods for the Shallow Water Equations with Friction

：邢雨龙（美国俄亥俄州立大学）
：2021-12-16 10:30
：腾讯会议ID：211-415-103（无密码）

报告人：邢雨龙（美国俄亥俄州立大学）

时  间：12月16日上午10:30

地  点：腾讯会议ID：211-415-103（无密码）

内容摘要:

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.

个人简介：

Dr. Yulong Xing is a professor in the Department of Mathematics at the Ohio State University. He received his bachelor degree from University of Science and Technology of China in 2002, and Ph.D. in Mathematics from Brown University in 2006 under the supervision of Prof. Chi-Wang Shu. Prior to joining OSU, he worked as a Postdoctoral Researcher at Courant Institute, New York University, a staff scientist at Oak Ridge National Laboratory, a joint assistant professor at University of Tennessee Knoxville, and an assistant professor at University of California Riverside. He works in the area of numerical analysis and scientific computing, wave propagation, computational fluid dynamics. His research focuses on the design, analysis and applications of accurate and efficient numerical methods for partial differential equations. He has received a CAREER Award from the National Science Foundation.

 

联系人：熊涛