A well-balanced scheme for the shallow-water equations with topography or Manning friction

JOURNAL OF COMPUTATIONAL PHYSICS

卷:335

Article

Michel-Dansac, Victor¹  Berthon, Christophe¹  Clain, Stephane²  Foucher, Francoise^1,3 

[1] Univ Nantes, CNRS, UMR 6629, Lab Math Jean Leray, 2 Rue Houssiniere,BP 92208, F-44322 Nantes 3, France

[2] Univ Minho, Ctr Math, Campus Gualtar, P-4710057 Braga, Portugal

[3] Ecole Cent Nantes, 1 Rue Noe,BP 92101, F-44321 Nantes 3, France

关键词: Shallow-water equations;    Manning friction;    Godunov-type schemes;    Well-balanced schemes;    Moving steady states;   

DOI  :  10.1016/j.jcp.2017.01.009

来源: Elsevier

【 摘 要 】

We consider the shallow-water equations with Manning friction or topography, as well as a combination of both these source terms. The main purpose of this work concerns the derivation of a non-negativity preserving and well-balanced scheme that approximates solutions of the system and preserves the associated steady states, including the moving ones. In addition, the scheme has to deal with vanishing water heights and transitions between wet and dry areas. To address such issues, a particular attention is paid to the study of the steady states related to the friction source term. Then, a Godunov-type scheme is obtained by using a relevant average of the source terms in order to enforce the required well-balance property. An implicit treatment of both topography and friction source terms is also exhibited to improve the scheme while dealing with vanishing water heights. A second-order well-balanced MUSCL extension is designed, as well as an extension for the two-dimensional case. Numerical experiments are performed in order to highlight the properties of the scheme. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free