Abstract:
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.

报告人简介：美国南卡莱罗纳大学教授（ 2013年1月-现在)。2012年-2018年期间兼任北京计算科学研究中心应用与计算数学实验室客座教授，自2018年起兼任中国海洋大学客座教授。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。主持了多项由美国国家科学基金会(NSF)和美国能源部(DOE)等联邦机构资助的科研项目。2012至2017年任数值分析领域国际重要学术期刊SIAM Journal on Numerical Analysis的编委。多次受邀担任美国国家科学基金会计算数学领域基金会审评议组成员。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。