Finite volume schemes and residual distribution schemes for pollutant transport on unstructured grids

Abstract

In this work, a recent residual distribution scheme and a second-order finite volume method are compared to model the transport of a pollutant in free surface flows. The phenomenon is described in two dimensions using the shallow water (SW) system augmented by a scalar conservation law for the pollutant transport. The two numerical methods are developed to minimize the numerical diffusion which is a critical problem for transport phenomena. The conservation of the mass and the monotonicity of the solution are two other important numerical requirements necessary to reproduce the physics of the problem. These three features (low numerical diffusion—mass conservation—monotonicity) will be theoretically analyzed and then numerically verified through a series of test cases. Both methods are used on completely unstructured grids, but the regularity of the grid with respect to the streamlines direction produces for the two methods different behaviours which will be studied. This work has been realized within the Telemac-2D system, constituted by a finite element kernel and a finite volume kernel. Telemac2D uses several numerical schemes, including the new schemes presented here. The aim of this paper is to present state-of-the-art research in the field of finite volumes (FV) and of residual distribution schemes for advection problems.