2. Numerical methods for nonlinear acoustic resonators

For the study of pressure waves in an oscillating acoustic resonator, one has to solve the compressible NavierStokes equations. The geometry of the resonator strongly influences its resonance frequencies and the nonlinear standing pressure waveform generated within the cavity. Studying the acoustic wave by real physical experiments would be expensive due to the cost of constructing different resonator configurations. Hence, one relies on numerical simulations to study the pressure wave in oscillating resonators. Numerical studies become more challenging due to a possible need for a high-frequency driving force. In this chapter, we review the numerical methods used to simulate the evolution of the pressure wave in oscillating resonators. We also present a numerical method for optimizing resonator shapes in order to maximize the pressure compression ratio, defined as the ratio of maximum to minimum gas pressure at one end of the oscillating resonator. Correspondence/Reprint request: Dr. Xiaofan Li, Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL60616, USA. E-mail: [email protected] Xiaofan Li & Ganesh Raman 22