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Derivation and Closure of Baer and Nunziato Type Multiphase Models by Averaging a Simple Stochastic Model

Vincent Perrier 1 Enrique Gutiérrez 1
1 CAGIRE - Computational AGility for internal flows sImulations and compaRisons with Experiments
Inria Bordeaux - Sud-Ouest, UPPA - Université de Pau et des Pays de l'Adour
Abstract : In this article, we show how to derive a multiphase model of Baer and Nunziato type with a simple stochastic model. Baer and Nunziato models are known to be unclosed, namely, they depend on modeling parameters, as interfacial velocity and pressure, and relaxation terms, whose exact expression is still an open question. We prove that with a simple stochastic model, interfacial and relaxation terms are equivalent to the evaluation of an integral, which cannot be explicitly computed in general. However, in different particular case matching with a large range of applications (topology of the bubbles/droplets, or special flow regime conditions), the interfacial and relaxation parameters can be explicitly computed, leading to different models that are either nonlinear versions or slight modifications of previously proposed models. The validity domains of previously proposed models are clarified, and some modeling parameters of the averaged system are linked with the local topology of the flow. Last, we prove that usual properties like entropy dissipation are ensured with the new closures found.
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Submitted on : Tuesday, April 27, 2021 - 1:27:38 PM
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Vincent Perrier, Enrique Gutiérrez. Derivation and Closure of Baer and Nunziato Type Multiphase Models by Averaging a Simple Stochastic Model. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Society for Industrial and Applied Mathematics, 2021, 19 (1), pp.401-439. ⟨10.1137/19M1306609⟩. ⟨hal-03209659⟩



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