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

IF 2.6 3区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL Communications in Computational Physics Pub Date : 2023-12-01 DOI:10.4208/cicp.oa-2023-0112
Rihui Lan,Lili Ju,Zhu Wang, Max Gunzburger
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Abstract

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.
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巴洛克-各向同性分裂原始方程系统的二阶隐含-显式方案
在海洋建模的原始方程数值求解中,通常采用条带-各向同性模式分裂技术来处理海洋动力学的多时间尺度问题。本文提出了一种二阶隐式-显式(IMEX)方案来推进巴氏-各向同性分裂系统。具体地说,利用二阶强稳定性 Runge-Kutta 方案显式地演化条带模式和流体层厚度,而利用线性化 Crank-Nicolson 方案隐式地推进条带模式。在每个时间步,首先使用中间气压速度计算气压线速度。然后用改进的气压作用力重新推进气压模式,修正气压速度。最后,通过将气压速度和各向同性速度耦合在一起来更新层厚度。此外,由于模式分裂造成的离散海面高度的数值不一致,通过与精心计算的通量赤字的调节过程得到了缓解。还分析了时间截断误差,以验证方案的二阶精度。最后,在 MPAS 海洋平台上进行了两次基准测试,从数值上证明了所提出的 IMEX 方案的性能。
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来源期刊
Communications in Computational Physics
Communications in Computational Physics 物理-物理:数学物理
CiteScore
4.70
自引率
5.40%
发文量
84
审稿时长
9 months
期刊介绍: Communications in Computational Physics (CiCP) publishes original research and survey papers of high scientific value in computational modeling of physical problems. Results in multi-physics and multi-scale innovative computational methods and modeling in all physical sciences will be featured.
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