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

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

报告人：熊涛 厦门大学教授、博士生导师

报告时间：2022年9月28日9:00-12: 00

腾讯会议：959-292-542

报告摘要： In this work, 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 the Froude number ranging from O(1) to 0, which in the zero Froude limit becomes the “lake equations” for balanced flow without gravity waves. We apply a well-balanced finite difference WENO reconstruction, coupled with a stiffly accurate implicit-explicit (IMEX) Runge-Kutta time discretization. The resulting semi-implicit scheme can be shown to be well-balanced, asymptotic preserving (AP) and asymptotically accurate (AA) at the same time. Both one- and two-dimensional numerical results are provided to demonstrate the high order accuracy, AP property and good performance of the proposed methods in capturing small perturbations of steady state solutions. (This is a joint work with Guanlan Huang and Yulong Xing.)

报告人简介：熊涛，厦门大学教授，博士生导师，国家高层次青年人才。博士毕业于中国科学技术大学，在美国休斯敦大学从事博士后研究。当前主要研究兴趣是计算流体力学和动理学方程的高精度数值方法。近年来发展了全马赫可压缩欧拉方程组的一致稳定渐近保持有限差分 WENO 方法，多尺度动理学方程的一致稳定渐近保持间断 Galerkin 有限元方法等，成果发表在 SIAM Journal on Scientific Computing 和 Journal of Computational Physics 等杂志上。