论文标题
分析可压缩起泡的流动。第二部分：宏观模型的推导
Analysis of compressible bubbly flows. Part II: Derivation of a macroscopic model
论文作者
论文摘要
本文是两篇论文系列中的第二篇，该论文的重点是用于可压缩气泡流的平均1D模型。为此，我们从微观描述，对大量但有限的小气泡和周围可压缩流体的相互作用之间的相互作用。该微观模型已在第一篇论文中得出和分析。在目前的情况下，根据气泡的数量，提供了物理参数的比例，我们证明了微观模型的解决方案存在于与气泡数量无关的时间跨度。考虑到我们有大量的气泡，我们提出了宏观变量的构造，并得出这些数量满足的平均系统。我们的方法基于在强溶液中的紧凑型方法。在最后一部分中，我们提出了与我们的设置相对应的威廉姆斯 - 博尔兹曼方程的推导。
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.
