(untitled) (Advances in Applied Mathematics and Mechanics, 2023)
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.