TY - JOUR
T1 - A Second-Order Implicit-Explicit Scheme for the Baroclinic-Barotropic Split System of Primitive Equations
AU - Lan , Rihui
AU - Ju , Lili
AU - Wang , Zhu
AU - Gunzburger , Max
JO - Communications in Computational Physics
VL - 5
SP - 1306
EP - 1331
PY - 2023
DA - 2023/12
SN - 34
DO - http://doi.org/10.4208/cicp.OA-2023-0112
UR - https://global-sci.org/intro/article_detail/cicp/22215.html
KW - Primitive equations, baroclinic-barotropic splitting, implicit-explicit, strong stability preserving RK, SSH reconciliation.
AB - <p style="text-align: justify;">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.</p>