Evaluation of selected finite-difference and finite-volume approaches to rotational shallow-water flow
Journal article, Peer reviewed
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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.