Kinetic study of compressible Rayleigh–Taylor instability with time-varying acceleration

Rayleigh–Taylor (RT) instability commonly arises in compressible systems with time-dependent acceleration in practical applications. To capture the complex dynamics of such systems, a two-component discrete Boltzmann method is developed to systematically investigate the compressible RT instability driven by variable acceleration. The simulation results are interpreted from three key perspectives: the density gradient, which characterizes the spatial variation in density; the thermodynamic non-equilibrium strength, which quantifies the system's deviation from local thermodynamic equilibrium; and the non-equilibrium region, which captures the spatial distribution of non-equilibrium behaviors. Notably, the fluid system exhibits rich and diverse dynamic patterns resulting from the interplay of multiple competing physical mechanisms, including RT instability, diffusion, and dissipation effects. Specifically, the amplitude, acceleration period, and phase of the time-varying acceleration play an important role in the evolution of the RT instability. In addition, the phase difference determines whether the RT instability is promoted in the initial stage. These findings provide deeper insight into the evolution and regulation of compressible RT instability under complex driving conditions.