讲座人简介：
张敏，北京大学助理研究员。2020年12月博士毕业于厦门大学计算数学专业，2018年10月至2020年9月在美国堪萨斯大学联合培养，2021年1月至2023年4月在北京大学数学科学学院从事博士后研究工作、博雅博士后。获中国数学会第十七届钟家庆数学奖、入选北京市科协青年人才托举工程项目，现主持国家自然科学青年基金，参与科技部数学和应用研究专项项目。主要研究兴趣包括计算流体力学等问题的高精度数值方法、移动网格方法，以及北太天元科学计算软件的系统仿真技术等，相关研究成果发表在期刊SIAM J. Sci. Comput.、J. Comput. Phys.、J. Sci. Comput.等上，参编教材《北太天元科学计算编程与应用》。
讲座简介：
In this talk a rezoning-type adaptive moving mesh discontinuous Galerkin method is presented for the numerical solution of Ripa model with non-flat bottom topography. The Ripa model is a generalization of the shallow water equations that takes temperature variance into the modeling. The well-balance property is crucial to the simulation of perturbation waves over the lake-at-rest steady state such as waves on a lake and tsunami waves in the deep ocean. To ensure the well-balance and positivity-preservation properties, strategies are discussed in the use of slope limiting, positivity-preservation limiting, and data transferring between meshes. Particularly, it is suggested that a DG-interpolation scheme be used for the interpolation of both the flow variables and bottom topography from the old mesh to the new one and after each application of the positivity-preservation limiting on the water depth, a high-order correction be made to the approximation of the bottom topography according to the modifications in the water depth. Mesh adaptivity is realized using an MMPDE moving mesh method with a metric tensor based on an equilibrium variable and water depth. A motivation for this choice of the metric tensor is to adapt the mesh according to both the perturbations of the lake-at-rest steady state and the water depth distribution (bottom topography structure). Numerical examples of both the shallow water equations and Ripa model are presented to demonstrate the well-balance, high-order accuracy, and positivity-preserving properties of the method and its ability to capture small perturbations of the lake-at-rest steady-state. They also show that the mesh adaptation based on the equilibrium variable and water depth give more accurate results than that based on the commonly used entropy function.
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