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An energy-consistent depth-averaged Euler system: derivation and properties.

Abstract : In this paper, we present an original derivation process of a non-hydrostatic shallow water-type model which aims at approximating the incompressible Euler and Navier-Stokes systems with free surface. The closure relations are obtained by a minimal energy constraint instead of an asymptotic expansion. The model slightly differs from the well-known Green-Naghdi model and is confronted with stationary and analytical solutions of the Euler system corresponding to rotational flows. At the end of the paper, we give time-dependent analytical solutions for the Euler system that are also analytical solutions for the proposed model but that are not solutions of the Green-Naghdi model. We also give and compare analytical solutions of the two non-hydrostatic shallow water models.
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https://hal.inria.fr/hal-01011691
Contributor : Jacques Sainte-Marie <>
Submitted on : Monday, August 22, 2016 - 11:12:58 AM
Last modification on : Wednesday, June 30, 2021 - 9:40:13 PM
Long-term archiving on: : Wednesday, November 23, 2016 - 11:58:38 AM

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  • HAL Id : hal-01011691, version 2
  • ARXIV : 1406.6565

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Marie-Odile Bristeau, Anne Mangeney, Jacques Sainte-Marie, Nicolas Seguin. An energy-consistent depth-averaged Euler system: derivation and properties.. Discrete and Continuous Dynamical Systems - Series B, American Institute of Mathematical Sciences, 2015, 20 (4), pp.28. ⟨hal-01011691v2⟩

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