A Second-Order Implicit-Explicit Scheme for the Baroclinic-Barotropic Split System of Primitive Equations  

作　　者：Rihui Lan Lili Ju Zhu Wang Max Gunzburger 

机构地区：[1]School of Mathematical Sciences,Ocean University of China,Qingdao,Shandong 266100,China [2]Department of Mathematics,University of South Carolina,Columbia,SC 29208,USA [3]Oden Institute for Computational Engineering and Sciences,University of Texas at Austin,Austin,Texas 78712,USA

出　　处：《Communications in Computational Physics》2023年第10期1306-1331,共26页计算物理通讯（英文）

基　　金：partially supported by the U.S.Department of Energy,Office of Science,Office of Biological and Environmental Research through Earth and Environmental System Modeling and Scientific Discovery through Advanced Computing programs under university grants DE-SC0020270 and DE-SC0020418;partially supported by Shandong Excellent Young Scientists Program(Overseas)under the grant 2023HWYQ-064;OUC Youth Talents Project.

摘　　要：The baroclinic-barotropic mode splitting technique is commonly employed in numerical solutions of the primitive equations for ocean modeling to deal with the multiple time scales of ocean dynamics.In this paper,a second-order implicit-explicit(IMEX)scheme is proposed to advance the baroclinic-barotropic split system.Specifically,the baroclinic mode and the layer thickness of fluid are evolved explicitly via the second-order strong stability preserving Runge-Kutta scheme,while the barotropic mode is advanced implicitly using the linearized Crank-Nicolson scheme.At each time step,the baroclinic velocity is first computed using an intermediate barotropic velocity.The barotropic velocity is then corrected by re-advancing the barotropic mode with an improved barotropic forcing.Finally,the layer thickness is updated by coupling the baroclinic and barotropic velocities together.In addition,numerical inconsistencies on the discretized sea surface height caused by the mode splitting are alleviated via a reconciliation process with carefully calculated flux deficits.Temporal truncation error is also analyzed to validate the second-order accuracy of the scheme.Finally,two benchmark tests from the MPAS-Ocean platform are conducted to numerically demonstrate the performance of the proposed IMEX scheme.

关 键 词：Primitive equations baroclinic-barotropic splitting implicit-explicit strong stability preserving RK SSH reconciliation 

分 类 号：O17[理学—数学]