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Layer-averaged Euler and Navier-Stokes equations

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.
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https://hal.inria.fr/hal-01202042
Contributor : Jacques Sainte-Marie <>
Submitted on : Monday, June 27, 2016 - 5:50:32 PM
Last modification on : Monday, March 29, 2021 - 11:58:08 AM

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Marie-Odile Bristeau, Cindy Guichard, Bernard Di Martino, Jacques Sainte-Marie. Layer-averaged Euler and Navier-Stokes equations. Communications in Mathematical Sciences, International Press, 2017, ⟨10.4310/CMS.2017.v15.n5.a3⟩. ⟨hal-01202042v3⟩

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