Three-dimensional shallow water system: A relaxation approach

JOURNAL OF COMPUTATIONAL PHYSICS

卷:333

Article

Liu, Xin¹  Mohammadian, Abdolmajid¹  Sedano, Julio Angel Infante¹  Kurganov, Alexander^2,3 

[1] Univ Ottawa, Dept Civil Engn, Ottawa, ON K1N 6N5, Canada

[2] Southern Univ Sci & Technol China, Dept Math, Shenzhen 518055, Peoples R China

[3] Tulane Univ, Dept Math, New Orleans, LA 70118 USA

关键词: Three-dimensional shallow water equations;    Central-upwind scheme;    Relaxation approach;    Well-balanced;    Positivity preserving;    Finite-volume method;   

DOI  :  10.1016/j.jcp.2016.12.030

来源: Elsevier

【 摘 要 】

We study a three-dimensional shallow water system, which is obtained from the three-dimensional Navier-Stokes equations after Reynolds averaging and under the simplifying hydrostatic pressure assumption. Since the three-dimensional shallow water system is generically not hyperbolic, it cannot be numerically solved using hyperbolic shock capturing schemes. At the same time, existing simple finite-difference and finite-volume methods may fail in simulations of unsteady flows with sharp gradients, such as dam break and flood flows. To overcome this limitation, we propose a novel numerical method, which is based on a relaxation approach utilized to hyperbolize the three-dimensional shallow water system. The extended relaxation system is hyperbolic and we develop a second-order semi-discrete central-upwind scheme for it. The proposed numerical method can preserve lake at rest steady states and positivity of water depth over irregular bottom topography. The accuracy, stability and robustness of the developed numerical method is verified on five numerical experiments. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free