Analysis of compressible bubbly flows. Part I: construction of a microscopic model

被引：1

作者：

Hillairet, Matthieu ^{[1
]}

Mathis, Helene ^{[1
]}

Seguin, Nicolas ^{[2
,3
]}

机构：

[1] Univ Montpellier, Inst Montpellierain Alexander Grothendieck, CNRS, Montpellier, France

[2] Univ Montpellier, INRIA, CNRS, Montpellier, France

[3] Univ Montpellier, Inst Montpellierain Alexander Grothendieck, CNRS, Montpellier, France

来源：

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS | 2023年 / 57卷 / 05期

关键词：

Two-phase flows; compressible Navier-Stokes equations; Cauchy theory; RIGID BODIES; MOTION; SYSTEM;

D O I：

10.1051/m2an/2023045

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note, we introduce a microscopic model for the motion of gas bubbles in a viscous fluid. By interpreting a bubble as a compressible fluid with infinite shear viscosity, we derive a pde/ode system coupling the density/velocity/pressure in the surrounding fluid with the linear/angular velocities and radii of the bubbles. We provide a 1D analogue of the system and construct an existence theory for this simplified system in a natural regularity framework. The second part of the paper is a preparatory work for the derivation of an averaged or macroscopic model.

引用

页码：2835 / 2863

页数：29

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