Abstract
We consider the problem of rotational shallow-water flow for which non-trivial rotating steady-state solutions are of great importance. In particular, we investigate a high-resolution central-upwind scheme that is well-balanced for a subset of these stationary solutions and show that the well-balanced design is the source of numerical artifacts when applied to more general problems. We propose an alternative flux evaluation that sacrifices the well-balanced property and demonstrate that this gives qualitatively better results for relevant test cases and real-world oceanographic simulations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Brodtkorb, A., Holm, H.: Coastal ocean forecasting on the GPU using a two-dimensional finite-volume scheme. Tellus A. 73(1), 1–22 (2021)
Chertock, A., Dudzinski, M., Kurganov, A., Lukácová-Medvidová, M.: Well-balanced schemes for the shallow water equations with Coriolis forces. Numer. Math. 138(4), 939–973 (2017)
Kurganov, A., Noelle, S., Petrova, G.: Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations. SIAM J. Sci. Comput. 23(3), 707–740 (2001)
Kurganov, A., Petrova, G.: A second-order well-balanced positivity preserving central-upwind scheme for the Saint-Venant system. Commun. Math. Sci. 5(1), 133–160, 03 (2007)
Gottlieb, S., Shu, C.-W.: Total variation diminishing Runge-Kutta schemes. Math. Comput. 67(221), 73–85 (1998)
Lie, K.-A., Noelle, S.: On the artificial compression method for second-order nonoscillatory central difference schemes for systems of conservation laws. SIAM J. Sci. Comput. 24(4), 1157–1174 (2003)
Holm, H., Brodtkorb, A., Broström, G., Christensen, K., Sætra, M.: Evaluation of selected finite-difference and finite-volume approaches to rotational shallow-water flow. Commun Comput. Phys 27(4), 1234–1274 (2020)
Holm, H., Sætra, M., van Leeuwen, P.: Massively parallel implicit equal-weights particle filter for ocean drift trajectory forecasting. J. Comput. Phys. X. 6(0314), 100053 (2020)
Albretsen, J., Sperrevik, A., Staalstrøm, A., Sandvik, A., Vikebø,F.: NorKyst-800 report no. 1: User manual and technical descriptions. Technical Report 2, Fisken og Havet, Institute of Marine Research (2011)
Brodtkorb, A., Holm, H., Sætra, M., Beiser, F.: GPU Ocean (2023). https://doi.org/10.5281/zenodo.7938844
Holm, H., Beiser, F.: Supplementary material for “Reducing numerical artifacts by sacrificing well-balance for rotating shallow-water flow” (2023). https://doi.org/10.5281/zenodo.7938887.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Holm, H.H., Beiser, F. (2023). Reducing Numerical Artifacts by Sacrificing Well-Balance for Rotating Shallow-Water Flow. In: Franck, E., Fuhrmann, J., Michel-Dansac, V., Navoret, L. (eds) Finite Volumes for Complex Applications X—Volume 2, Hyperbolic and Related Problems. FVCA 2023. Springer Proceedings in Mathematics & Statistics, vol 433. Springer, Cham. https://doi.org/10.1007/978-3-031-40860-1_19
Download citation
DOI: https://doi.org/10.1007/978-3-031-40860-1_19
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-40859-5
Online ISBN: 978-3-031-40860-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)