PHYSICAL REVIEW E 94, 023106 (2016) Nonequilibrium thermohydrodynamic effects on the Rayleigh-Taylor instability in compressible flows Huilin Lai, 1, 2 Aiguo Xu, 1, 3, * Guangcai Zhang, 1 , † Yanbiao Gan, 1, 4 Yangjun Ying, 1 and Sauro Succi 5 1 National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P. O. Box 8009-26, Beijing 100088, China 2 School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China 3 Center for Applied Physics and Technology, MOE Key Center for High Energy Density Physics Simulations, College of Engineering, Peking University, Beijing 100871, China 4 North China Institute of Aerospace Engineering, Langfang 065000, China 5 Istituto Applicazioni Calcolo, CNR, Viale del Policlinico 137, 00161 Roma, Italy (Received 26 November 2015; revised manuscript received 6 July 2016; published 12 August 2016) The effects of compressibility on Rayleigh-Taylor instability (RTI) are investigated by inspecting the interplay between thermodynamic and hydrodynamic nonequilibrium phenomena (TNE, HNE, respectively) via a discrete Boltzmann model. Two effective approaches are presented, one tracking the evolution of the local TNE effects and the other focusing on the evolution of the mean temperature of the fluid, to track the complex interfaces separating the bubble and the spike regions of the flow. It is found that both the compressibility effects and the global TNE intensity show opposite trends in the initial and the later stages of the RTI. Compressibility delays the initial stage of RTI and accelerates the later stage. Meanwhile, the TNE characteristics are generally enhanced by the compressibility, especially in the later stage. The global or mean thermodynamic nonequilibrium indicators provide physical criteria to discriminate between the two stages of the RTI. DOI: 10.1103/PhysRevE.94.023106 I. INTRODUCTION Rayleigh-Taylor instability (RTI) occurs at the interface between two fluids with different densities, subjected to an ac- celeration directed from the bottom density fluid to the higher density one. A typical case is a heavy fluid resting on the top of a lighter one in the presence of a gravitational field. Under such conditions, density perturbations at the interface grow in time under the effect of gravity. The first detailed study of this instability was conducted by Rayleigh [1] in the 1880s. Later the first study was extended to accelerated fluids by Taylor [2] in 1950. The first experiment was performed by Lewis in the evolution of an unstable air-water interface [3]. Another experiment by Emmons et al. confirmed these findings [4]. Such an instability plays a prominent role in many natural and industrial processes, such as devices for sustainable energy production, say turbines [5], and inertial-confinement fusion (ICF) [6], type-la supernovae [7], hot-wire diagnostics [8], quantum magnetized plasmas [9], colloidal mixtures [10], etc. In the above-mentioned fields, the compressibility effects on RTI are essential and even dominate [11–14], deserving careful investigation. In fact, many theoretical and numerical studies have been performed, especially on the initial linear stage [15–21]. In those studies, the compressibility effects on RTI growth rate are generally probed via changing the ratio of specific heats and the equilibrium pressure at the interface. Specifically, in 2007, Lafay et al. found that, in the isothermal case, the stratification has a stabilizing effect while the compressibility has a destabilizing effect for two mis- cible, viscous and compressible fluids [18]. In 2008, He et al. reported that, in an inviscid case, the influences of the ratio of * Corresponding author: Xu_Aiguo@iapcm.ac.cn † Corresponding author: Zhang_Guangcai@iapcm.ac.cn specific heats are as follows: the ratio mitigates the RTI when the upper heavy fluid is more compressible, while it enhances the RTI when the bottom fluid is more compressible [19]. In 2010, Ye et al. demonstrated that the compressibility has destabilizing effects for inviscid compressible fluid with an exponentially variable density profile [20]. Although the compressibility effects have been studied extensively, several fundamental problems remain open, such as the nonequilibrium effects in RTI, especially for the case of increasing compressibility [21–23]. For the case with strong compressibility, the interfacial dynamics becomes more complicated as the RTI unfolds, resulting in very substantial gradient forces (∇ρ ,∇u, and ∇T ) around the interfaces and very pronounced thermodynamic nonequilibrium (TNE) effects, where ρ , u, and T are the local density, flow velocity, and temperature, respectively. The more pronounced the compressibility, the more complex the interfaces and the TNE effects as well. It is known that the Navier-Stokes model falls short of describing the complex interfaces and TNE effects [24–31]. At the same time, molecular dynamics and Monte Carlo simulations cannot access macroscopic spatial- temporal scales of interest at affordable computational cost. Under such conditions, a kinetic approach based on a suitably simplified model Boltzmann equation is preferable. As a special discretization of the Boltzmann equation, the lattice Boltzmann (LB) method has achieved great success in various complex flows [24,25,32–42]. The LB applications in RTI can be classified into two groups: RTI in incompressible flows [22,23,43–52] and in compressible flows [53–55]. In these studies, the LB method appears as an effective numerical scheme to solve the traditional hydrodynamic models. In recent works [25–31], the LB method was developed to probe the trans- and supercritical fluid behaviors or both the hydrodynamic nonequilibrium (HNE) and TNE behaviors, which has brought some new 2470-0045/2016/94(2)/023106(11) 023106-1 ©2016 American Physical Society