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

doi:10.1016/j.jcp.2019.01.006

	Conservative explicit local time-stepping schemes for the shallow water equations
	Hoang, Thi-Thao-Phuong 1,4; Leng, Wei2 ; Ju, Lili 1; Wang, Zhu 1; Pieper, Konstantin 3
	2019-04-01
发表期刊	JOURNAL OF COMPUTATIONAL PHYSICS
ISSN	0021-9991
卷号	382 页码:152-176
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.
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
语种	英语
资助项目	US Department of Energy Office of Science[DE-SC0016540] ; US Department of Energy Office of Science[DE-SC0016591] ; National Natural Science Foundation of China[11501553]
WOS研究方向	Computer Science ; Physics
WOS类目	Computer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号	WOS:000458621600010
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/32607
专题	计算数学与科学工程计算研究所
通讯作者	Ju, Lili
作者单位	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
推荐引用方式 GB/T 7714	Hoang, Thi-Thao-Phuong,Leng, Wei,Ju, Lili,et al. Conservative explicit local time-stepping schemes for the shallow water equations[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2019,382:152-176.
APA	Hoang, Thi-Thao-Phuong,Leng, Wei,Ju, Lili,Wang, Zhu,&Pieper, Konstantin.(2019).Conservative explicit local time-stepping schemes for the shallow water equations.JOURNAL OF COMPUTATIONAL PHYSICS,382,152-176.
MLA	Hoang, Thi-Thao-Phuong,et al."Conservative explicit local time-stepping schemes for the shallow water equations".JOURNAL OF COMPUTATIONAL PHYSICS 382(2019):152-176.