Communications in Mathematical Sciences

Volume 15 (2017)

Number 5

Layer-averaged Euler and Navier–Stokes equations

Pages: 1221 – 1246

DOI: https://dx.doi.org/10.4310/CMS.2017.v15.n5.a3

Authors

M.-O. Bristeau (Inria, Paris, France; and UPMC, Sorbonne Universités, Paris, France)

C. Guichard (Inria, Paris, France; and UPMC, Sorbonne Universités, Paris, France)

B. di Martino (Université de Corte, France; Inria, Paris, France; and UPMC, Sorbonne Universités, Paris, France)

J. Sainte-Marie (Inria, Paris, France; and UPMC, Sorbonne Universités, Paris, France)

Abstract

In this paper we propose a strategy to approximate incompressible hydrostatic free surface Euler and Navier–Stokes models. The main advantage of the proposed models is that the water depth is a dynamical variable of the system and hence the model is formulated over a fixed domain. The proposed strategy extends previous works approximating the Euler and Navier–Stokes systems using a multilayer description. Here, the needed closure relations are obtained using an energy-based optimality criterion instead of an asymptotic expansion. Moreover, the layer-averaged description is successfully applied to the Navier–Stokes system with a general form of the Cauchy stress tensor.

Keywords

incompressible Navier–Stokes equations, incompressible Euler equations, free surface flows, Newtonian fluids, complex rheology

2010 Mathematics Subject Classification

35Q30, 35Q35, 76D05

Full Text (PDF format)

The work presented in this paper was supported in part by the Inria Project Lab “Algae in Silico” and the CNRS-INSU, TelluS-INSMI-MI program, project CORSURF. It was realised during the secondment of the third author in the ANGE Inria team.

Received 5 August 2016

Published 26 June 2017