可压缩气泡流分析。第一部分:微观模型的构建。

IF 1.9 3区数学 Q2 Mathematics

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2023-05-25 DOI:10.1051/m2an/2023045

M. Hillairet, H. Mathis, N. Seguin

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引用次数: 3

摘要

在这篇笔记中，我们介绍了气泡在粘性流体中运动的微观模型。通过将气泡解释为具有无限剪切粘度的可压缩流体，我们推导出了一个pde/ode系统，该系统将周围流体中的密度/速度/压力与气泡的线速度/角速度和半径相耦合。我们给出了该系统的一维模拟，并在自然正则框架下构造了该简化系统的存在性理论。论文的第二部分是为推导平均模型或宏观模型做准备工作。

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

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.

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来源期刊

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique 数学-应用数学

CiteScore

2.70

自引率

5.30%

发文量

审稿时长

6-12 weeks

期刊介绍： M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.