Speaker: Prof. Huazhong Tang（汤华中教授）

Time: 10:00-11:00, 11 Jan. 2026 (Sunday)  (Beijing time)

Venue: CC126 (华信书院）

Abstract

This talk introduces two high-order accurate structure-preserving finite difference schemes for the special relativistic hydrodynamics (RHD). The first is the physical-constraints-preserving (PCP) scheme, which preserves the positivity of the rest-mass density and the pressure and the bounds of the fluid velocity and is built on the local Lax-Friedrichs (LxF) splitting, the WENO reconstruction, the PCP flux limiter, and the high-order strong stability preserving time discretization. The key to developing such scheme is to prove the convexity and other properties of the admissible state set and to discover a concave function with respect to the conservative vector. The second is the entropy stable (ES) scheme, whose semi-discrete version satisfies the entropy inequality. The key is to technically construct the affordable entropy conservative (EC) flux of the semi-discrete second-order accurate EC schemes satisfying the semi-discrete entropy equality for the found convex entropy pair. As soon as the EC flux is derived, the dissipation term can be added to give the semi-discrete ES schemes satisfying the semi-discrete entropy inequality. The WENO reconstruction for the scaled entropy variables and the previous time discretization are implemented to obtain the fully-discrete high-order “ES” schemes. The performance of the proposed schemes has been demonstrated by numerical experiments. By the way, we also briefly review other relative works on the structure-preserving schemes for the special RHDs. Those works have been further to the general equation of state and the special relativistic magnetohydrodynamics etc., see our papers listed below for details.

About the Speaker

北京大学数学科学学院博雅特聘教授，博士生导师。2021年10月当选中国工业与应用数学学会的会士。现任International Journal for Numerical Methods in Fluids，East Asia Journal on Applied Mathematics，《计算物理》，《气体物理》和《信息与计算科学丛书》等编委。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，中国工业与应用数学学会副理事长，期刊Journal of Computational Physics的Associate Editor、《计算数学》的副主编。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。