Numerical Analysis of Nonlinear Acoustic Wave Propagation in a Rarefied Gas

Unsteady motion of a rarefied gas in a half space, caused by an infinitely wide plate when it starts a longitudinal and harmonic oscillation, is investigated numerically on the basis of the Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation. A deterministic method capable of describing the singularities in the molecular velocity distribution function produced by the oscillating plate, which was developed recently by the authors, is used as a solution method, and the unsteady behavior of the gas is obtained accurately. The streaming motion and the attenuation of the wave, observed in the existing work using the direct simulation Monte Carlo (DSMC) method (T. Ohwada and M. Kunihisa, in Rarefied Gas Dynamics, AIP, Melville, 2003, pp. 202-209), are also obtained. In addition, some pieces of numerical evidence that clarify the long-time behavior of the gas are provided. For example, one-period averages of the momentum and energy fluxes across the oscillating plate tend to approach their values for a periodic state (a constant for the momentum flux and zero for the energy flux) slowly, the rate of approach being likely to be inversely proportional to the square root of time.