Abstract

Due to the importance of the shallow-water equations in models of real-life phenomena, in recent years the study and model of problems that involve them have been the object of interest of many people. By reason of this, it is imperative to have efficient numerical methods to obtain an approximation of the solutions of the shallow-water equations.

Several authors have worked in approximations using the well-known finite volume and finite element methods, nevertheless, even when these methods compute good approximations to real-life behavior, the computational cost is usually high, which could be a limitation to the application of these methods.

This paper presents an explicit Generalized Finite Difference-Volume Hybrid approximation to the solution of the shallow-water equations, solved on irregular regions meshed with logically rectangular grids; the numerical results show the accuracy obtained with a low-cost implementation. The proposed scheme is a hybridization of a generalized finite difference scheme with the finite volume method.

Abstract

Today we faced the problem of solving equations for shallow bodies of water in irregular regions; These equations are very important to be able to model the behavior of liquids that have the characteristic that their extension is much greater than their depth. One of the important blocks to solve these equations is the advection equation. In this work, some schemes are proposed to approximate the solution of the advection equation in irregular regions in the plane, using a variation of the finite difference method in convex and structured meshes.

Abstract