Numerical study of two-dimensional resonant gas oscillation with shock waves

We study the nonlinear resonant gas oscillation and the propagation of shock waves in a rectangular region bounded by solid walls by numerically solving the system of Navier–Stokes equations for compressible flows of an ideal gas. The numerical method is the fourth-order central difference in space and the fourth-order backward difference in time. The resonant gas oscillation is supposed to be excited by the harmonic oscillation of solid walls with a resonant frequency. Our main objective is to study the peculiarities of long-time phenomena caused by the accumulation of small nonlinear effects due to shock waves. In particular, we show that the flow pattern of acoustic streaming is affected by shock–shock and shock–boundary layer interactions.