2D versus 1D models for Shallow Water Equations

In this paper we present a general framework to construct 1D width averaged models when the flow is constrained -e.g. by topography-to be almost 1D. We start from two dimensional shallow water equations, perform an asymptotic expansion of the fluid elevation and velocity field in the spirit of wave diffusive equations and establish a set of 1D equations made of a mass, momentum and energy equations which are close to the one usually used in hydraulic engineering. We show that in some special cases, like the U-shaped river bed, that our set of equations reduces to the classical 1d shallow water equations. Out of these configurations, there is an O(1) deviation of our model from the classical one. (C) 2017 The Authors. Published by Elsevier B.V.