Simulating the energy cascade of shock wave formation process in a resonator by gas-kinetic scheme

The temporal-spatial evolution of the sound field in a cylindrical resonator driven by a piston was simulated by gas-kinetic scheme (GKS), and periodic shock waves propagating back and forth were observed in the resonator with finite displacement amplitude of the driving piston. It can been seen from the instantaneous spatial distribution of the oscillatory pressure and velocity in the resonator that the oscillatory pressure is a one-dimensional,but the oscillatory velocity exhibits a quasi-one-dimensional distribution due to the effect of the boundary layer.The evolution process of shock wave from the sinusoidal wave to the zigzag wave was demonstrated with the increasing of the driving displacement amplitude of the piston. Especially, simulation results revealed that the acoustic intensity was linearly proportional to the driving displacement amplitude of the piston, rather than the square type. The studied results demonstrated well the process of harmonic energy cascade by the FFT analysis, at the same time, the physical explanations has been also given. The simulation results of acoustic intensity were well consistent with the existing experimental results, which verifies the validity of GKS modeling method.