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Evaluation of selected finite-difference and finite-volume approaches to rotational shallow-water flow

Holm, Håvard Heitlo; Brodtkorb, André R.; Brostrøm, Gøran; Christensen, Kai Håkon; Sætra, Martin Lilleeng
Journal article, Peer reviewed
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URI
https://hdl.handle.net/10642/8267
Date
2020-05-24
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Original version
Holm HH, Brodtkorb A, Brostrøm G, Christensen KH, Sætra ML. Evaluation of selected finite-difference and finite-volume approaches to rotational shallow-water flow. Communications in Computational Physics. 2020   https://dx.doi.org/10.4208/cicp.OA-2019-0033
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 finitedifference 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.
Publisher
Global Science Press
Series
Communications in Computational Physics;Volume 27, Issue 4
Journal
Communications in Computational Physics

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