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

Hoang, Thi-Thao-Phuong; Leng, Wei; Ju, Lili; Wang, Zhu; Pieper, Konstantin

doi:10.1016/j.jcp.2019.01.006

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

Journal Article · Mon Jan 21 00:00:00 EST 2019 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2019.01.006· OSTI ID:1594023

Hoang, Thi-Thao-Phuong ^[1]; Leng, Wei ^[2]; Ju, Lili ^[3]; Wang, Zhu ^[3]; ^[4]

Univ. of South Carolina, Columbia, SC (United States); Auburn Univ., AL (United States); University of South Carolina
Chinese Academy of Sciences (CAS), Beijing (China)
Univ. of South Carolina, Columbia, SC (United States)
Florida State Univ., Tallahassee, FL (United States)

Here 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.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of South Carolina, Columbia, SC (United States)

Sponsoring Organization:: National Natural Science Foundation of China (NNSFC); National Natural Science Foundation of China (NSFC); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Biological and Environmental Research (BER)

Grant/Contract Number:: SC0016540; SC0016591

OSTI ID:: 1594023

Alternate ID(s):: OSTI ID: 1635985

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 382; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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