Kinetic entropy for the layer-averaged hydrostatic Navier-Stokes equations

2017/10/11 by Emmanuel Audusse, Marie-Odile Bristeau, Audusse, Emmanuel +4
Engineering · Mathematics · #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1710.04054

openalex publication_date 2017/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We are interested in the numerical approximation of the hydrostatic free surface incompressible Navier-Stokes equations. By using a layer-averaged version of the equations, we are able to extend previous results obtained for shallow water system. We derive a vertically implicit / horizontally explicit finite volume kinetic scheme that ensures the positivity of the approximated water depth, the well-balancing and a fully discrete energy inequality.

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