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Volume 27, Issue 4
Evaluation of Selected Finite-Difference and Finite-Volume Approaches to Rotational Shallow-Water Flow

Håvard H. Holm, André R. Brodtkorb, Göran Broström, Kai H. Christensen & Martin L. Sætra

Commun. Comput. Phys., 27 (2020), pp. 1234-1274.

Published online: 2020-02

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  • 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.

  • Keywords

Rotational shallow-water simulations, storm surge modelling, hyperbolic conservation laws, high-resolution finite-volume methods, test cases, verification.

  • AMS Subject Headings

76U05, 86A05, 35L65, 65M08

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

Havard.Heitlo.Holm@sintef.no (Håvard H. Holm)

Andre.Brodtkorb@sintef.no (André R. Brodtkorb)

Goran.Brostrom@marine.gu.se (Göran Broström)

kaihc@met.no (Kai H. Christensen)

martinls@met.no (Martin L. Sætra)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-27-1234, author = {Håvard H. and Holm and Havard.Heitlo.Holm@sintef.no and 6668 and SINTEF Digital,MathematicsandCybernetics, P.O.Box124Blindern, NO-0314 Oslo, Norway. and Håvard H. Holm and André R. and Brodtkorb and Andre.Brodtkorb@sintef.no and 6671 and SINTEF Digital,MathematicsandCybernetics, P.O.Box124Blindern, NO-0314 Oslo, Norway. and André R. Brodtkorb and Göran and Broström and Goran.Brostrom@marine.gu.se and 6672 and Norwegian Meteorological Institute, P.O. Box 43 Blindern, NO-0313 Oslo, Norway. and Göran Broström and Kai H. and Christensen and kaihc@met.no and 6673 and Norwegian Meteorological Institute, P.O. Box 43 Blindern, NO-0313 Oslo, Norway. and Kai H. Christensen and Martin L. and Sætra and martinls@met.no and 6674 and Norwegian Meteorological Institute, P.O. Box 43 Blindern, NO-0313 Oslo, Norway. and Martin L. Sætra}, title = {Evaluation of Selected Finite-Difference and Finite-Volume Approaches to Rotational Shallow-Water Flow}, journal = {Communications in Computational Physics}, year = {2020}, volume = {27}, number = {4}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2019-0033}, url = {http://global-sci.org/intro/article_detail/cicp/14849.html} }
TY - JOUR T1 - Evaluation of Selected Finite-Difference and Finite-Volume Approaches to Rotational Shallow-Water Flow AU - Holm , Håvard H. AU - Brodtkorb , André R. AU - Broström , Göran AU - Christensen , Kai H. AU - Sætra , Martin L. JO - Communications in Computational Physics VL - 4 SP - 1234 EP - 1274 PY - 2020 DA - 2020/02 SN - 27 DO - http://doi.org/10.4208/cicp.OA-2019-0033 UR - https://global-sci.org/intro/article_detail/cicp/14849.html KW - Rotational shallow-water simulations, storm surge modelling, hyperbolic conservation laws, high-resolution finite-volume methods, test cases, verification. AB -

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.

Håvard H. Holm, André R. Brodtkorb, Göran Broström, Kai H. Christensen & Martin L. Sætra. (2020). Evaluation of Selected Finite-Difference and Finite-Volume Approaches to Rotational Shallow-Water Flow. Communications in Computational Physics. 27 (4). 1234-1274. doi:10.4208/cicp.OA-2019-0033
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