Numerical simulations of 3D free surface flows by a multilayer Saint‐Venant model

We present a multilayer Saint‐Venant system for the simulation of 3D free surface flows with friction and viscosity effects. A vertical discretization of a Navier–Stokes system approximation deduced from a precise analysis of the shallow water assumption leads to a set of coupled Saint‐Venant‐type systems. The idea is to obtain an accurate description of the vertical profile of the horizontal velocity while preserving the robustness and the computational efficiency of the usual Saint‐Venant system. For each time‐dependent layer, a Saint‐Venant‐type system is solved on the same 2D mesh by a kinetic solver using a finite volume framework. The free surface is directly deduced from the sum of layers water depth. We validate the model with some numerical academic and realistic examples. We present comparisons with simulations computed with the hydrostatic Navier–Stokes solver of the Telemac‐3D code developed by Electricité de France. Copyright © 2007 John Wiley & Sons, Ltd.