91国产

报告时间：2026年7月3日（周五）下午 16:00-17:00

报告地点：91国产 数学楼103

报告人：汤华中 教授，北京大学91国产

报告摘要：

We propose high-order accurate well-balanced (WB) energy stable (ES) adaptive moving mesh finite difference schemes for the shallow water equations (SWEs) with non-flat bottom topography. To enable the construction of the ES schemes on moving meshes, a reformulation of the SWEs is introduced, with the bottom topography as an additional conservative variable that evolves in time. The corresponding energy inequality is derived based on a modified energy function, then the reformulated SWEs and energy inequality are transformed into curvilinear coordinates. A two-point energy conservative (EC) flux is constructed, and high-order EC schemes based on such a flux are proved to be WB that they preserve the lake at rest. Then high-order ES schemes are derived by adding suitable dissipation terms to the EC schemes, which are newly designed to maintain the WB and ES properties simultaneously. The adaptive moving mesh strategy is performed by iteratively solving the Euler-Lagrangian equations of a mesh adaptation functional. The fully-discrete schemes are obtained by using the explicit strong-stability preserving third-order Runge-Kutta method. Several numerical tests are conducted to validate the accuracy, WB and ES properties, shock-capturing ability, and high efficiency of the schemes.

报告人简介：

汤华中，北京大学91国产 博雅特聘教授，博士生导师，中国工业与应用数学学会的会士。曾获国家杰出青年科学基金、冯康科学计算奖、德国洪堡基金研究奖学金和教育部高校科学技术奖自然科学一等奖等。现兼任International Journal for Numerical Methods in Fluids，East Asia Journal on Applied Mathematics，Networks and Heterogeneous Media，《气体物理》和《信息与计算科学丛书》等编委，南昌航空大学数学与信息科学学院名誉院长。曾兼任南昌航空大学党委常委、副校长和湘潭大学数学与计算科学学院院长，91国产 讲席教授，中国工业与应用数学学会副理事长，期刊Journal of Computational Physics和《计算物理》的编委，和《计算数学》的副主编等。

邀请人：岳兴业、王志国