High-Order Multirate Explicit Time-Stepping Schemes for the Baroclinic-Barotropic Split Dynamics in Primitive Equations
Time: 2023-05-16
Published By: Xiaoni Tan
Speaker(s): Lili Ju (University of South Carolina)
Time: 16:00-17:00 June 8, 2023
Venue: Room 9, Quan Zhai, BICMR
Abstract:
To treat the multiple time scales of ocean dynamics in an efficient manner, the baroclinic-barotropic splitting technique has been widely used for solving the primitive equations for ocean modeling. Based on the framework of strong stability-preserving Runge-Kutta approach, we propose two high-order multirate explicit time-stepping schemes (SSPRK2-SE and SSPRK3-SE) for the resulting split system in this paper. The proposed schemes allow for a large time step to be used for the three-dimensional baroclinic (slow) mode and a small time step for the two-dimensional barotropic (fast) mode, in which each of the two mode solves just need to satisfy their respective CFL conditions for numerical stability. Specifically, at each time step, the baroclinic velocity is first computed by advancing the baroclinic mode and fluid thickness of the system with the large time-step and the assistance of some intermediate approximations of the baroctropic mode obtained by substepping with the small time step; then the barotropic velocity is corrected by using the small time step to re-advance the barotropic mode under an improved barotropic forcing produced by interpolation of the forcing terms from the preceding baroclinic mode solves; lastly, the fluid thickness is updated by coupling the baroclinic and barotropic velocities. Additionally, numerical inconsistencies on the discretized sea surface height caused by the mode splitting are relieved via a reconciliation process with carefully calculated flux deficits. Two benchmark tests from the ``MPAS-Ocean" platform are carried out to numerically demonstrate the performance and parallel scalability of the proposed SSPRK-SE schemes.
简介：
鞠立力教授1995年毕业于武汉大学数学系获数学学士学位，1998年在中国科学院计算数学与科学工程计算研究所获得计算数学硕士学位，2002年在美国爱荷华州立大学获得应用数学博士学位。2002-2004年在美国明尼苏达大学数学与应用研究所从事博士后研究。随后进入美国南卡罗莱纳大学工作，历任数学系助理教授（2004-2008），副教授（2008-2012），和教授（2013-现在）。主要从事偏微分方程数值方法与分析，非局部模型与算法，计算机视觉，深度学习算法，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140多篇，Google学术引用约5000多次。自2006年起连续主持了十多项由美国国家科学基金会（NSF）和美国能源部（DOE）资助的科研项目。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。2012至2017年担任SIAM Journal on Numerical Analysis的副编辑，目前是JSC, NMPDE, NMTMA, AAMM等期刊的副编辑。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领域“戈登·贝尔”奖提名。
