Discrete Boltzmann modeling of Rayleigh-Taylor instability in two-component compressible flows

Abstract

A discrete Boltzmann model (DBM) is proposed to probe the Rayleigh-Taylor instability (RTI) in two-component compressible flows. Each species has a flexible specific heat ratio and is described by one discrete Boltzmann equation (DBE). Independent discrete velocities are adopted for the two DBEs. The collision and force terms in the DBE account for the molecular collision and external force, respectively. Two types of force terms are exploited. In addition to recovering the modified Navier-Stokes equations in the hydrodynamic limit, the DBM has the capability of capturing detailed nonequilibrium effects. Furthermore, we use the DBM to investigate the dynamic process of the RTI. The invariants of tensors for nonequilibrium effects are presented and studied. For low Reynolds numbers, both global nonequilibrium manifestations and the growth rate of the entropy of mixing show three stages (i.e., the reducing, increasing, and then decreasing trends) in the evolution of the RTI. On the other hand, the early reducing tendency is suppressed and even eliminated for high Reynolds numbers. Relevant physical mechanisms are analyzed and discussed.

Discrete Boltzmann modeling of unsteady reactive flows with nonequilibrium effects

“…It should be stressed that kinetic effects are significant and traditional hydrodynamic models are not sufficient for fluid flows with small characteristic scales or large Knudsen numbers [26][27][28][29][30][31][32][33][34][35][36][37][38]. The TNE becomes crucial and even dominant in the evolution of multicomponent flows due to the existence of various complex material and/or mechanical interfaces [26][27][28][29][30][31][32][33][34][35][36][37][38]. In such complicated cases, to investigate the TNE is a significant and convenient way to study the fundamental kinetic processes.…”

Mesoscopic Simulation of the (2 + 1)-Dimensional Wave Equation with Nonlinear Damping and Source Terms Using the Lattice Boltzmann BGK Model

“…From a computational resource perspective, the remarkable merits are brevity of programming, numerical potency, inherent parallelism, and ease treatment of intricate boundary conditions. This kind of method has comprehensive capacities in quite several fields, from phonon transport [13] to approximate incompressible flows [14][15][16][17][18][19][20][21][22][23][24][25], full compressible flows [26][27][28][29][30][31][32][33][34][35][36][37], dendrite growth [38,39] and thermal multiphase flows [40]. Recently, the mesoscopic kinetics method is also becoming increasingly popular in computational mathematics and engineering science for solving certain NPDEs, including Burgers' equations [41,42], Korteweg-de Vries equation [43], Gross-Pitaevskii equation [44], convection-diffusion equation [45][46][47][48][49][50][51], Kuramoto-Sivashinsky equation [52], wave equation [53,54], Dirac equation [55], Poisson equation…”

Knudsen Number Effects on Two-Dimensional Rayleigh–Taylor Instability in Compressible Fluid: Based on a Discrete Boltzmann Method

“…In the same year, Chen et al used a multi-relaxation-time DBM to investigate the effects of viscosity, heat conductivity, and Prandtl number on the 2D RT instability from macroscopic and non-equilibrium viewpoints, and found that viscosity and heat conduction suppress RT instability mainly by suppressing the re-acceleration phase KH instability [ 75 ]. In 2017, Lin et al extended the DBM to the compressible system containing two components with independent specific-heat ratios, and studied the dynamic process of the RT instability with two components [ 76 ]. In 2018, Chen et al adopted a multi-relaxation-time DBM to numerically simulate a 2D Richtmyer–Meshkov (RM) instability and RT instability coexisting system [ 77 ].…”

“…In 2018, Chen et al adopted a multi-relaxation-time DBM to numerically simulate a 2D Richtmyer–Meshkov (RM) instability and RT instability coexisting system [ 77 ]. Around the same time, Li et al used the DBM to study the multi-mode RT instability with discontinuous interface in a compressible flow [ 78 ]. In 2019, Zhang et al made a Lagrangian tracking supplement to the DBM, and studied the RT instability of the two-miscible-fluid system [ 79 ].…”