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Volume 36, Issue 3
Moving-Water Equilibria Preserving HLL-Type Schemes for the Shallow Water Equations

Christian Klingenberg, Alexander Kurganov, Yongle Liu & Markus Zenk

DOI: 10.4208/cmr.2020-0013

Commun. Math. Res., 36 (2020), pp. 247-271.

Published online: 2020-07

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  • Abstract

We construct new HLL-type moving-water equilibria preserving upwind schemes for the one-dimensional Saint-Venant system of shallow water equations with nonflat bottom topography. The designed first- and second-order schemes are tested on a number of numerical examples, in which we verify the well-balanced property as well as the ability of the proposed schemes to accurately capture small perturbations of moving-water steady states.

  • Keywords

Shallow water equations, Harten-Lax-Van Leer (HLL) scheme, well-balanced method, steady-state solutions (equilibria), moving-water and still-water equilibria.

  • AMS Subject Headings

76M12, 65M08, 35L65, 86-08, 86A05

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{CMR-36-247, author = {Klingenberg , ChristianKurganov , AlexanderLiu , Yongle and Zenk , Markus}, title = {Moving-Water Equilibria Preserving HLL-Type Schemes for the Shallow Water Equations}, journal = {Communications in Mathematical Research }, year = {2020}, volume = {36}, number = {3}, pages = {247--271}, abstract = {

We construct new HLL-type moving-water equilibria preserving upwind schemes for the one-dimensional Saint-Venant system of shallow water equations with nonflat bottom topography. The designed first- and second-order schemes are tested on a number of numerical examples, in which we verify the well-balanced property as well as the ability of the proposed schemes to accurately capture small perturbations of moving-water steady states.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2020-0013}, url = {http://global-sci.org/intro/article_detail/cmr/17848.html} }
TY - JOUR T1 - Moving-Water Equilibria Preserving HLL-Type Schemes for the Shallow Water Equations AU - Klingenberg , Christian AU - Kurganov , Alexander AU - Liu , Yongle AU - Zenk , Markus JO - Communications in Mathematical Research VL - 3 SP - 247 EP - 271 PY - 2020 DA - 2020/07 SN - 36 DO - http://doi.org/10.4208/cmr.2020-0013 UR - https://global-sci.org/intro/article_detail/cmr/17848.html KW - Shallow water equations, Harten-Lax-Van Leer (HLL) scheme, well-balanced method, steady-state solutions (equilibria), moving-water and still-water equilibria. AB -

We construct new HLL-type moving-water equilibria preserving upwind schemes for the one-dimensional Saint-Venant system of shallow water equations with nonflat bottom topography. The designed first- and second-order schemes are tested on a number of numerical examples, in which we verify the well-balanced property as well as the ability of the proposed schemes to accurately capture small perturbations of moving-water steady states.

Klingenberg , ChristianKurganov , AlexanderLiu , Yongle and Zenk , Markus. (2020). Moving-Water Equilibria Preserving HLL-Type Schemes for the Shallow Water Equations. Communications in Mathematical Research . 36 (3). 247-271. doi:10.4208/cmr.2020-0013
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