Rayleigh–Taylor instability under multi-mode perturbation: Discrete Boltzmann modeling with tracers

Abstract

The two-dimensional Rayleigh-Taylor Instability (RTI) under multi-mode perturbation in compressible flow is probed via the Discrete Boltzmann Modeling (DBM) with tracers. The distribution of tracers provides clear boundaries between light and heavy fluids in the position space. Besides, the position-velocity phase space offers a new perspective for understanding the flow behavior of RTI with intuitive geometrical correspondence. The effects of viscosity, acceleration, compressibility, and Atwood number on the mixing of material and momentum and the mean non-equilibrium strength at the interfaces are investigated separately based on both the mixedness defined by the tracers and the non-equilibrium strength defined by the DBM. The mixedness increases with viscosity during early stage but decreases with viscosity at the later stage. Acceleration, compressibility, and Atwood number show enhancement effects on mixing based on different mechanisms. After the system relaxes from the initial state, the mean non-equilibrium strength at the interfaces presents an initially increasing and then declining trend, which is jointly determined by the interface length and the macroscopic physical quantity gradient. We conclude that the four factors investigated all significantly affect early evolution behavior of RTI system, such as the competition between interface length and macroscopic physical quantity gradient. The results contribute to the understanding of the multi-mode RTI evolutionary mechanism and the accompanied kinetic effects.

Effects of Inclined Interface Angle on Compressible Rayleigh–Taylor Instability: A Numerical Study Based on the Discrete Boltzmann Method

“…From the perspective of physical modeling, the DBM is approximately equivalent to a continuous fluid model plus a coarse-grained model describing TNE effects. In recent years, the DBM has been widely used in the numerical study of the RT instability in compressible fluids and has made remarkable progress [31][32][33][34][35][36][37][38][39][40]. For example, Lai et al, studied the impact of compressibility on the RT instability by using the DBM and found that the compressibility effect and the global TNE intensity exhibit opposite tendencies in the early and later stages of the RT instability [31].…”

“…Ye et al, studied the effect of Knudsen number on the RT instability in 2-D compressible fluid using the DBM [37]. Li et al, simulated the nonlinear evolution of the multi-mode compressible RT instability using the DBM [38]. Chen et al, studied the impacts of viscosity, heat conduction, and Prandtl number on 2-D RT instability by using the multi-relaxation time DBM simulation with gravity [39].…”

Nonequilibrium kinetics effects in Richtmyer-Meshkov instability and reshock process

“…Discrete Boltzmann method (DBM) is a modeling and analysis method based on kinetic theory in statistical physics [73][74][75][76][77][78][79][80] . It provides various measures to detect, describe and exhibit the complex Thermodynamic Non-Equilibrium (TNE) behaviors, and has brought a series of new insights in several fields in recent years, such as multiphase flow [81][82][83][84][85] , rarefied gas flow 86,87 , combustion and detonation [88][89][90][91][92][93][94][95][96][97] , hydrodynamic instabilities [98][99][100][101][102][103][104][105] , etc. In contrast to conventional CFD methods, DBM is not restricted by the continuous and nearequilibrium assumptions, and can describe the cases of high Knudsen (Kn) number which contain strong TNE and noncontinuity effects.…”