A Well-Balanced FVC Scheme for 2D Shallow Water Flows on Unstructured Triangular Meshes

A Well-Balanced FVC Scheme for 2D Shallow Water Flows on Unstructured Triangular Meshes

Year:    2023

Author:    Moussa Ziggaf, Imad Kissami, Mohamed Boubekeur, Fayssal Benkhaldoun

Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 5 : pp. 1335–1378

Abstract

This paper aims to present a new well-balanced, accurate and fast finite volume scheme on unstructured grids to solve hyperbolic conservation laws. It is a scheme that combines both finite volume approach and characteristic method. In this study, we consider a shallow water system with Coriolis effect and bottom friction stresses where this new Finite Volume Characteristics (FVC) scheme has been applied. The physical and mathematical properties of the system, including the C-property, have been well preserved.
First, we developed this approach by preserving the advantages of the finite volume discretization such as conservation property and the method of characteristics, in order to avoid Riemann solvers and to enhance the accuracy without any complexity of the MUSCL reconstruction. Afterward, a discretization was applied to the bottom source term that leads to a well-balanced scheme satisfying the steady-state condition of still water. A semi-implicit treatment will also be presented in this study to avoid stability problems due to source terms. Finally, the proposed finite volume method is verified on several benchmark tests and shows good agreement with analytical solutions and experimental results; moreover, it gives a noteworthy accuracy and rapidity improvement compared to the original approaches.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2022-0113

Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 5 : pp. 1335–1378

Published online:    2023-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    44

Keywords:    Shallow water model method of characteristics FVC scheme finite volume method well-balanced scheme.

Author Details

Moussa Ziggaf

Imad Kissami

Mohamed Boubekeur

Fayssal Benkhaldoun

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