讲座题目：Conservative Explicit Local Time-stepping Schemes for the Shallow Water Equations 主讲人：鞠立力 教授 主持人：羊丹平 教授 开始时间：2019-07-02 10:00:00 结束时间：2019-07-02 11:00:00 讲座地址：闵行数学楼401室 主办单位：数学科学学院
报告人简介： 鞠立力教授，1995年武汉大学学士, 1998年中国科学院硕士，2002年美国爱荷华州立大学博士。2002-2004年美国明尼苏达大学博士后。2004年至今美国南卡莱罗纳大学助理教授、副教授、教授。美国工业与应用数学学会（SIAM）成员，2008-2009年期间担任其东南大西洋分会主席。主要从事数值计算方法与分析，网格优化，图像处理，非局部模型，高性能科学计算，及其在材料与地球科学中的应用等方面的研究工作。至今已发表科研论文80余篇，Google学术引用2400多次。 2012至2017年任SIAM Journal on Numerical Analysis编委。与合作者关于合金微结构演化在“神威·太湖之光”超级计算机上的相场模拟工作入围2016年国际高性能计算应用最高奖—“戈登·贝尔”奖提名。 报告内容： In this talk we present explicit local time-stepping (LTS) schemes with second and third order accuracy for the shallow water equations. The system is discretized in space by a C-grid staggering method, namely the TRiSK scheme adopted in MPAS-Ocean, a global ocean model with the capability of resolving multiple resolutions within a single simulation. The time integration is designed based on the strong stability preserving Runge-Kutta (SSP-RK) methods, but different time step sizes can be used in different regions of the domain through the coupling of coarse-fine time discretizations on the interface, and are only restricted by respective local CFL conditions. The proposed LTS schemes are of predictor-corrector type in which the predictors are constructed based on Taylor series expansions and SSP-RK stepping algorithms. The schemes preserve some important physical quantities in the discrete sense, such as exact conservation of the mass and potential vorticity and conservation of the total energy within time truncation errors. Moreover, they inherit the natural parallelism of the original explicit global time-stepping schemes. Extensive numerical tests are presented to illustrate the performance of the proposed algorithms. |
