一、题目
High-Order Multirate Explicit Time-Stepping Schemes for the Baroclinic-Barotropic Split Dynamics in Primitive Equations
二、主讲人
鞠立力
三、摘要
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. We propose second and third order multirate explicit time-stepping schemes for such split system based on the strong stability-preserving Runge-Kutta (SSPRK) framework. Our method allows for a large time step to be used for advancing the three-dimensional (slow) baroclinic mode and a small time step for the two-dimensional (fast) barotropic mode, so that each of the two mode solves only need satisfy their respective CFL condition to maintain numerical stability.
It is well known that the SSPRK method achieves high-order temporal accuracy by utilizing a convex combination of forward-Euler steps. At each time step of our method, the baroclinic velocity is first computed by using the SSPRK scheme with the large time step, then the barotropic velocity is specially corrected by using the same SSPRK scheme with the small time step. Finally, the fluid thickness and the sea surface height perturbation is updated by coupling the predicted baroclinic and barotropic velocities, and the inconsistency on the sea surface height caused by the mode splitting is also resolved via a reconciliation process with carefully calculated flux deficits and velocity adjustments. Two benchmark tests drawn from the ``MPAS-Ocean" platform are used to numerically demonstrate the accuracy and parallel performance of the proposed schemes.
四、主讲人介绍
鞠立力教授，武汉大学数学系获数学学士学位，中国科学院计算数学与科学工程计算研究所硕士学位，美国爱荷华州立大学获得应用数学博士学位。美国明尼苏达大学从事博士后研究。随后进入美国南卡罗莱纳大学工作。主要从事数值方法与分析，高性能科学计算，网格优化，非局部模型，图像处理，深度学习，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120多篇。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年担任国际数值分析领域重要学术期刊SIAM J Numer Anal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最高奖—“戈登·贝尔”奖提名。
五、邀请人
芮洪兴 数学学院教授
六、时间
12月3日（周五）9:00
七、地点
腾讯会议 会议ID：570 424 940 会议密码：211203
八、主办方
山东大学数学学院
