TY - JOUR
T1 - A Well-Balanced FVC Scheme for 2D Shallow Water Flows on Unstructured Triangular Meshes
AU - Ziggaf , Moussa
AU - Kissami , Imad
AU - Boubekeur , Mohamed
AU - Benkhaldoun , Fayssal
JO - Advances in Applied Mathematics and Mechanics
VL - 5
SP - 1335
EP - 1378
PY - 2023
DA - 2023/06
SN - 15
DO - http://doi.org/10.4208/aamm.OA-2022-0113
UR - https://global-sci.org/intro/article_detail/aamm/21779.html
KW - Shallow water model, method of characteristics, FVC scheme, finite volume method, well-balanced scheme.
AB - <p style="text-align: justify;">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.<br/>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.</p>