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Journal Articles Communications in Mathematical Sciences Year : 2017

Layer-averaged Euler and Navier-Stokes equations


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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Dates and versions

hal-01202042 , version 1 (18-09-2015)
hal-01202042 , version 2 (21-09-2015)
hal-01202042 , version 3 (27-06-2016)



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