A Second-Order Implicit-Explicit Scheme for the Baroclinic-Barotropic Split System of Primitive Equations (Communications in Computational Physics, 2023)
The baroclinic-barotropic mode splitting technique is commonly employedin numerical solutions of the primitive equations for ocean modeling to deal with themultiple 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 viathe second-order strong stability preserving Runge-Kutta scheme, while the barotropicmode is advanced implicitly using the linearized Crank-Nicolson scheme. At eachtime step, the baroclinic velocity is first computed using an intermediate barotropic velocity. The barotropic velocity is then corrected by re-advancing the barotropic modewith 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 alleviatedvia a reconciliation process with carefully calculated flux deficits. Temporal truncationerror is also analyzed to validate the second-order accuracy of the scheme. Finally,two benchmark tests from the MPAS-Ocean platform are conducted to numericallydemonstrate the performance of the proposed IMEX scheme.
Keywords: Primitive equations; baroclinic-barotropic splitting; implicit-explicit; strong stability preserving RK; SSH reconciliation.