报告题目：Structure-preserving arbitrary Lagrangian-Eulerian discontinuous Galerkin methods for hyperbolic conservation law with source term

主讲人：徐岩教授

时  间： 2023年7月14日（周五）8:30-9:30

腾讯会议： 874-445-918

主讲人简介：

  徐岩，中国科学技术大学数学科学学院教授。2005年于中国科学技术大学数学系获计算数学博士学位。2005-2007年在荷兰Twente大学从事博士后研究工作。2009年获得德国洪堡基金会的支持在德国Freiburg大学访问工作一年。主要研究领域为高精度数值计算方法。2008年度获全国优秀博士学位论文奖，2017年获国家自然科学基金委“优秀青年基金”, 2017年获中国数学会计算数学分会第二届“青年创新奖”。徐岩教授主持国家自然科学基金面上项目、德国洪堡基金会研究组合作计划(Research Group Linkage Programme)、霍英东青年教师基础研究课题等科研项目。担任SIAM Journal on Scientific Computing, Journal of Scientific Computing, Advances in Applied Mathematics and Mechanics, Communication on Applied Mathematics and Computation、计算物理等杂志的编委。

摘要：

  We develop the structure-preserving Lagrangian-Eulerian discontinuous Galerkin (ALE-DG) methods for a class of hyperbolic conservation laws with source term, which can preserve a general hydrostatic equilibrium state and positivity-preserving property under a suitable time step at the same time. Such equations mainly include the shallow water equations with non-flat bottom topography and the Euler equations with gravitation. By introducing well-balanced numerical fluxes and corresponding source term approximations, we established well-balanced schemes. We also discuss about the weak positivity property of the proposed schemes, and the positivity-preserving limiter can be applied to effectively enforce the positivity-preserving property. Numerical examples have been provided not only to demonstrate the good properties but also to show the advantages on moving mesh.