Sharp Interface Limit for Compressible Immiscible Two-Phase Dynamics with Relaxation

IF 1.2 3区 数学 Q2 MATHEMATICS, APPLIED
Yazhou Chen, Yi Peng, Qiaolin He, Xiaoding Shi
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引用次数: 0

Abstract

In this paper, the sharp interface limit for compressible Navier–Stokes/Allen-Cahn system with relaxation is investigated, which is motivated by the Jin-Xin relaxation scheme ([Comm.Pure Appl.Math.,48,1995]). Given any entropy solution which consists of two different families of shocks interacting at some positive time for the immiscible two-phase compressible Euler equations, it is proved that such entropy solution is the singular limit for a family global strong solutions of the compressible Navier–Stokes/Allen-Cahn system with relaxation when the interface thickness of immiscible two-phase flow tends to zero. The weighted estimation and improved anti-derivative method are used in the proof. The results of this singular limit show that, the sharp interface limit of the compressible Navier–Stokes/Allen-Cahn system with relaxation is the immiscible two-phase compressible Euler equations with free interface between phases. Moreover, the interaction of shock waves belong to different families can pass through the two-phase flow interface and maintain the wave strength and wave speed without being affected by the interface for immiscible compressible two-phase flow.

Abstract Image

带松弛的可压缩非混相两相动力学的锐界面极限
本文研究了由Jin-Xin松弛方案驱动的具有松弛的可压缩Navier-Stokes /Allen-Cahn系统的锐界面极限(Comm.Pure appler . math . 48,1995)。给出了非混相两相可压缩欧拉方程的任意熵解,该熵解由两种不同激波族在某正时间相互作用组成,证明了当非混相两相流界面厚度趋于零时,该熵解是具有松弛的可压缩Navier-Stokes /Allen-Cahn系统的一类整体强解的奇异极限。在证明中采用了加权估计和改进的不定积分方法。奇异极限的结果表明,具有弛豫的可压缩Navier-Stokes /Allen-Cahn系统的锐界面极限是两相间具有自由界面的非混相可压缩欧拉方程。此外,在非混相可压缩两相流中,不同族激波的相互作用可以穿过两相流界面,保持波强和波速而不受界面的影响。
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来源期刊
CiteScore
2.00
自引率
15.40%
发文量
97
审稿时长
>12 weeks
期刊介绍: The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.
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