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

TL;DR

This paper introduces a discrete Boltzmann model to simulate Rayleigh-Taylor instability in two-component compressible flows, capturing detailed nonequilibrium effects and analyzing the influence of Reynolds number on instability evolution.

Contribution

The paper develops a novel discrete Boltzmann model with independent velocities for each species, capable of capturing nonequilibrium effects in RTI of compressible flows.

Findings

RTI exhibits three stages at low Reynolds numbers: reducing, increasing, decreasing.

High Reynolds numbers suppress the initial reducing tendency of RTI.

The model accurately captures nonequilibrium tensor invariants during RTI evolution.

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.