Title: Kinetics of Rayleigh-Taylor instability in van der Waals fluid: the influence of compressibility Show Chinese title

Title: 瑞利-泰勒不稳定性在范德华流体中的动力学：可压缩性的影响

Abstract: Early studies on Rayleigh-Taylor instability (RTI) primarily relied on the Navier-Stokes (NS) model. As research progresses, it becomes increasingly evident that the kinetic information that the NS model failed to capture is of great value for identifying and even controlling the RTI process; simultaneously, the lack of analysis techniques for complex physical fields results in a significant waste of data information. In addition, early RTI studies mainly focused on the incompressible case and the weakly compressible case. In the case of strong compressibility, the density of the fluid from the upper layer (originally heavy fluid) may become smaller than that of the surrounding (originally light) fluid, thus invalidating the early method of distinguishing light and heavy fluids based on density. In this paper, tracer particles are incorporated into a single-fluid discrete Boltzmann method (DBM) model that considers the van der Waals potential. By using tracer particles to label the matter-particle sources, a careful study of the matter-mixing and energy-mixing processes of the RTI evolution is realized in the single-fluid framework. The effects of compressibility on the evolution of RTI are examined mainly through the analysis of bubble and spike velocities, the ratio of area occupied by heavy fluid, and various entropy generation rates of the system. It is demonstrated that: (1) compressibility has a suppressive effect on the spike velocity, and this suppressive impact diminishes as the Atwood number ($At$) increases. The influence of compressibility on bubble velocity shows a staged behavior with increasing $At$. (2) The impact of compressibility on the entropy production rate associated with the heat flow (${{\dot{S}}_{NOEF}}$) is related to the stages of RTI evolution. Show Chinese abstract

Abstract: 早期对瑞利-泰勒不稳定性（RTI）的研究主要依赖于纳维-斯托克斯（NS）模型。 随着研究的深入，越来越明显的是，NS模型未能捕捉到的动能信息对于识别甚至控制RTI过程具有重要价值；同时，缺乏对复杂物理场的分析技术导致了数据信息的重大浪费。 此外，早期的RTI研究主要集中在不可压缩情况和弱可压缩情况。 在强可压缩情况下，上层流体（原本重流体）的密度可能小于周围流体（原本轻流体）的密度，从而使得基于密度区分轻重流体的早期方法失效。 本文将示踪粒子引入一种考虑范德华势的单流体离散玻尔兹曼方法（DBM）模型。 通过使用示踪粒子标记物质粒子源，在单流体框架下实现了对RTI演化过程中物质混合和能量混合过程的细致研究。 通过分析气泡和尖峰速度、重流体占据的面积比以及系统各种熵生成率，主要考察了可压缩性对RTI演化的影响。 结果表明：（1）可压缩性对尖峰速度有抑制作用，这种抑制作用随着阿特伍德数（$At$）的增加而减弱。 可压缩性对气泡速度的影响随着$At$的增加表现出阶段性行为。 （2）可压缩性对与热流相关的熵产生率（${{\dot{S}}_{NOEF}}$）的影响与RTI演化的阶段有关。