THEORETICAL AND NUMERICAL STUDY OF AN IMPLICIT DISCRETIZATION OF A 1D INVISCID MODEL FOR RIVER FLOWS

Abstract

In this paper, we consider a 1D inviscid model to simulate river flows whose unknown are the water elevation, the flow rate and the wet area. We rewrite this model in terms of the wet area and the flow rate. Next, by using a weak formulation and a discretization by characteristics, we derive an implicit semidiscretized scheme that involves a variational inequality. Under suitable hypothesis, we prove that this scheme has at least one solution. We present an algorithm for the numerical solution of the fully discretized problem and the numerical results obtained for channels with parabolic and rectangular sections and variable depth. Finally, we perform a stability analysis for the semidiscretized scheme applied to a similar problem where the convection term has been omitted.