广西师范大学学报（自然科学版） ›› 2022, Vol. 40 ›› Issue (5): 127-137.doi: 10.16088/j.issn.1001-6600.2021120703

• 综述 • 上一篇    下一篇

可压缩非守恒两相流模型

张映辉*, 叶琴   

  1. 广西师范大学 数学与统计学院, 广西 桂林 541006
  • 收稿日期:2021-12-07 修回日期:2022-01-13 出版日期:2022-09-25 发布日期:2022-10-18
  • 通讯作者: 张映辉(1981—), 男, 湖南祁阳人, 广西师范大学教授, 博导。E-mail: yinghuizhang@gxnu.edu.cn
  • 基金资助:
    国家自然科学基金(11771150, 11571280); 广西自然科学基金(2019JJG110003, 2019AC20214)

Compressible Non-conservative Two-phase Flow Model

ZHANG Yinghui*, YE Qin   

  1. School of Mathematics and Statistics, Guangxi Normal University, Guilin Guangxi 541006, China
  • Received:2021-12-07 Revised:2022-01-13 Online:2022-09-25 Published:2022-10-18

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摘要： 可压缩非守恒两相流模型广泛应用于电力、核能、化学工艺、油气、低温空间、生物医学、微技术等。本文主要介绍流体压强相等且有毛细管效应、压强不相等且无毛细管效应、压强相等且无毛细管效应这3类可压缩非守恒两相流模型及其相关研究成果。特别地, 2种流体压强相等且无毛细管效应的高维可压缩非守恒两相流模型的线性系统含零特征根,使得该问题的数学分析变得十分复杂和困难, 至今, 该模型无任何数学成果, 这将是今后工作的重点。

关键词: 可压缩非守恒两相流模型, 毛细管效应, 柯西问题, 解的适定性, 衰减率

Abstract: The compressible non-conservative two-phase flow models are widely used in industrial applications, such as nuclear, power, chemical-process, oil-and-gas, cryogenics, bio-medical, micro-technology and so on.This paper makes a review on the study of three types of compressible non-conservative two-phase flow models with equal pressure and capillary effect, unequal pressure without capillary effect, and equal pressure without capillary effect. Then, introduces the research developments of these three types of compressible non-conservative two-phase flow models, respectively.In particular, the linear system of the high-dimensional compressible non-conservative two-phase flow model with equal pressure without capillary effect contains zero eigenvalue, which makes the mathematical analysis of this problem very difficult. The new model has no mathematical results so far, and will be the focus of future work.

Key words: compressible non-conservative two-phase flow model, capillary effect, Cauchy problem, well-posedness, decay rate

中图分类号: 

  • O29
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