Conservative explicit local time-stepping schemes for the shallow water equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:382

Article

Hoang, Thi-Thao-Phuong^1,4  Leng, Wei²  Ju, Lili¹  Wang, Zhu¹  Pieper, Konstantin³ 

[1] Univ South Carolina, Dept Math, Columbia, SC 29208 USA

[2] Chinese Acad Sci, State Key Lab Sci & Engn Comp, Beijing 100190, Peoples R China

[3] Florida State Univ, Dept Sci Comp, Tallahassee, FL 32306 USA

[4] Auburn Univ, Dept Math & Stat, Auburn, AL 36849 USA

关键词: Shallow water equations;    Local time-stepping;    Strong stability preserving Runge-Kutta;    Finite volume;    Mass conservation;    Potential vorticity;   

DOI  :  10.1016/j.jcp.2019.01.006

来源: Elsevier

【 摘 要 】

In this paper we develop explicit local time-stepping (LTS) schemes with second and third order accuracy for the shallow water equations. The system is discretized in space by a C-grid staggering method, namely the TRiSK scheme adopted in MPAS-Ocean, a global ocean model with the capability of resolving multiple resolutions within a single simulation. The time integration is designed based on the strong stability preserving Runge-Kutta (SSP-RK) methods, but different time step sizes can be used in different regions of the domain through the coupling of coarse-fine time discretizations on the interface, and are only restricted by respective local CFL conditions. The proposed LTS schemes are of predictor-corrector type in which the predictors are constructed based on Taylor series expansions and SSP-RK stepping algorithms. The schemes preserve some important physical quantities in the discrete sense, such as exact conservation of the mass and potential vorticity and conservation of the total energy within time truncation errors. Moreover, they inherit the natural parallelism of the original explicit global time-stepping schemes. Extensive numerical tests are presented to illustrate the performance of the proposed algorithms. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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