The adaptive moving mesh method is a powerful tool to improve the efficiency and quality of numerical simulations with localized structures, e.g. sharp transitions or discontinuities in relatively localized regions, which often appear in the solutions in the quasi-linear system of hyperbolic conservation laws. For the governing equations of the fluid flows, the entropy condition should be respected according to the second law of thermodynamics, and it is desirable to seek the entropy stable (ES) schemes satisfying some discrete or semi-discrete entropy conditions. This talk will present the high-order accurate ES adaptive moving mesh methods for the hyperbolic systems and their applications to the 2D and 3D special relativistic (magneto)hydrodynamics and the (multi-component) compressible Euler equations with the stiffened equation of state (EOS). The key is the high-order discretization of the metrics introduced by the coordinate transformation and the construction of the high-order ES fluxes with the discrete metrics. We will also show the mesh iteration redistribution or adaptive moving mesh strategy built on the minimization of the mesh adaption functional. Extensive numerical tests have been conducted in to validate the shock-capturing ability and high efficiency of our methods.

段俊明博士, 瑞士洛桑联邦理工学院(EPFL)博士后, 分别于2016和2021年在北京大学获得理学学士和博士学位。主要研究方向为高精度数值方法和降阶建模, 发展了三维高精度熵稳定的自适应移动网格有限差分方法, 并被用于求解(多组分)可压缩流体力学方程组、狭义相对论（磁）流体力学方程组等, 与固定网格上的相应格式比较, 在数值模拟中可节省高达90%的CPU时间。已发表10余篇论文, 包括在Journal of Computational Physics和Computer Methods in Applied Mechanics and Engineering上发表7篇。曾获北京计算数学学会优秀青年论文一等奖等荣誉。