Evaluation of Selected Finite-Difference and Finite-Volume Approaches to Rotational Shallow-Water Flow
Year: 2020
Author: Håvard H. Holm, André R. Brodtkorb, Göran Broström, Kai H. Christensen, Martin L. Sætra
Communications in Computational Physics, Vol. 27 (2020), Iss. 4 : pp. 1234–1274
Abstract
The shallow-water equations in a rotating frame of reference are important for capturing geophysical flows in the ocean. In this paper, we examine and compare two traditional finite-difference schemes and two modern finite-volume schemes for simulating these equations. We evaluate how well they capture the relevant physics for problems such as storm surge and drift trajectory modelling, and the schemes are put through a set of six test cases. The results are presented in a systematic manner through several tables, and we compare the qualitative and quantitative performance from a cost-benefit perspective. Of the four schemes, one of the traditional finite-difference schemes performs best in cases dominated by geostrophic balance, and one of the modern finite-volume schemes is superior for capturing gravity-driven motion. The traditional finite-difference schemes are significantly faster computationally than the modern finite-volume schemes.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2019-0033
Communications in Computational Physics, Vol. 27 (2020), Iss. 4 : pp. 1234–1274
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 41
Keywords: Rotational shallow-water simulations storm surge modelling hyperbolic conservation laws high-resolution finite-volume methods test cases verification.
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