A Well-Balanced FVC Scheme for 2D Shallow Water Flows on Unstructured Triangular Meshes (Advances in Applied Mathematics and Mechanics, 2023)
This paper aims to present a new well-balanced, accurate and fast finitevolume scheme on unstructured grids to solve hyperbolic conservation laws. It is ascheme that combines both finite volume approach and characteristic method. In thisstudy, we consider a shallow water system with Coriolis effect and bottom frictionstresses 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, inorder to avoid Riemann solvers and to enhance the accuracy without any complexityof the MUSCL reconstruction. Afterward, a discretization was applied to the bottomsource term that leads to a well-balanced scheme satisfying the steady-state conditionof still water. A semi-implicit treatment will also be presented in this study to avoidstability problems due to source terms. Finally, the proposed finite volume method isverified on several benchmark tests and shows good agreement with analytical solutions and experimental results; moreover, it gives a noteworthy accuracy and rapidityimprovement compared to the original approaches.