Abstract: The research of the nonlinear standing waves in resonators is a key technology for the macrosonic seal which is being studied. A nonlinear wave equation for irrotational and compressible Newtonian fluid is carried out from three gasdynamic equations. Based on the discretized nonlinear wave equation, a two-dimensional finite difference algorithm for simulating nonlinear standing waves in resonators is proposed. Based on the process of boundary conditions of the resonators, the proposed two-dimensional finite difference algorithm can be employed to simulate the nonlinear standing waves in resonators. When the cylindrical resonator filled with Refrigerant-12 as working fluid is excited by harmonic motion, the nonlinear standing wave is solved with the finite difference algorithm. Then the absolute pressure wave and a frequency spectrum for the acoustic pressure are obtained. The space distribution of acoustic pressure in the cylindrical resonator is also displayed. The numerical simulation results are in excellent agreement with the other simulation solutions and experiment. So the feasibility of this method is verified. The two-dimensional finite difference algorithm is a solid foundation for the macrosonic seal.

Key words: Finite difference, Macrosonic seal, Nonlinear standing wave, Resonator, Two-dimension