Approximation of the hydrostatic Navier-Stokes system for density stratified flows by a multilayer model. Kinetic interpretation and numerical solution.

Abstract : We present a multilayer Saint-Venant system for the numerical simulation of free surface density-stratified flows over variable topography. The proposed model formally approxi- mates the hydrostatic Navier-Stokes equations with a density that varies depending on the spatial and temporal distribution of a transported quantity such as temperature or salinity. The derivation of the multilayer model is obtained by a Galerkin-type vertical dis- cretization of the Navier-Stokes system with piecewise constant basis functions. In con- trast with classical multilayer models in the literature that assume immiscible fluids, we allow here for mass exchange between layers. We show that the multilayer system admits a kinetic interpretation, and we use this result to formulate a robust finite volume scheme for its numerical approximation. Several numerical experiments are presented, including simulations of wind-driven stratified flows.
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https://hal.inria.fr/hal-00654642
Contributor : Jacques Sainte-Marie <>
Submitted on : Thursday, December 22, 2011 - 3:32:38 PM
Last modification on : Wednesday, May 15, 2019 - 4:14:03 AM

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Emmanuel Audusse, Marie-Odile Bristeau, Marica Pelanti, Jacques Sainte-Marie. Approximation of the hydrostatic Navier-Stokes system for density stratified flows by a multilayer model. Kinetic interpretation and numerical solution.. Journal of Computational Physics, Elsevier, 2011, 230, pp.3453-3478. ⟨10.1016/j.jcp.2011.01.042⟩. ⟨hal-00654642⟩

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