Analysis of compressible bubbly flows. Part II: Derivation of a macroscopic model - Archive ouverte HAL
Article Dans Une Revue ESAIM: Mathematical Modelling and Numerical Analysis Année : 2023

Analysis of compressible bubbly flows. Part II: Derivation of a macroscopic model

Hélène Mathis
  • Fonction : Auteur
Nicolas Seguin
  • Fonction : Auteur

Résumé

This paper is the second of the series of two papers, which focuses on the derivation of an averaged 1D model for compressible bubbly flows. For this, we start from a microscopic description of the interactions between a large but finite number of small bubbles with a surrounding compressible fluid. This microscopic model has been derived and analysed in the first paper. In the present one, provided physical parameters scale according to the number of bubbles, we prove that solutions to the microscopic model exist on a timespan independent of the number of bubbles. Considering then that we have a large number of bubbles, we propose a construction of the macroscopic variables and derive the averaged system satisfied by these quantities. Our method is based on a compactness approach in a strong-solution setting. In the last section, we propose the derivation of the Williams–Boltzmann equation corresponding to our setting.
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Dates et versions

hal-04211778 , version 1 (19-09-2023)

Identifiants

Citer

Matthieu Hillairet, Hélène Mathis, Nicolas Seguin. Analysis of compressible bubbly flows. Part II: Derivation of a macroscopic model. ESAIM: Mathematical Modelling and Numerical Analysis, 2023, 57 (5), pp.2865-2906. ⟨10.1051/m2an/2023046⟩. ⟨hal-04211778⟩
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