Abstract: A finite volume algorithm for solving nonlinear standing waves in cylindrical acoustic resonator is presented. The fluid is initially at rest and excited by the harmonic motion at the entire resonator, when excitation frequency is in accord with natural frequency of acoustic field in the resonator, nonlinear standing acoustic waves can be generated. The final discretized equations are built based on SIMPLEC scheme that is one pressure based finite volume method and a staggered grid manner in the time domain by integrating the one-dimensional Navier-Stokes model equations for an unsteady compressible thermoviscous Newtonian fluid. The cylindrical resonator excited by harmonic motion is filled with R-12. The nonlinear standing waves in resonators are solved with the finite volume algorithm. The numerical simulation results are excellent agreement with the Galerkin method. So the feasibility of this method is verified. The physical properties, including The absolute pressure wave, temperature wave and a frequency pressure spectrum et al, are displayed. Meanwhile, the velocity waves in the different positions in resonator are obtained. It is shown that the sharp velocity spikes appear at the two ends of the cylindrical resonator. The Numerical Algorithm will provide a solid foundation for solving nonlinear standing waves for the macrosonic seal.

Key words: Finite volume algorithm, Macrosonic seal, Nonlinear standing wave, Resonator