The use of a subgrid-scale quasi-stationary approximation in finite-difference time-domain simulations to calculate the absorption by Helmholtz resonators

Abstract

To calculate Helmholtz resonators using a finite-difference time-domain (FDTD) simulation technique, one has to deal with two important difficulties. First, the determining structures of a Helmholtz resonator are typically subwavelength geometries with dimensions that are smaller than the FDTD cell size normally used for the wavelengths of interest. Therefore, the FDTD cell size should be reduced, resulting in a very high computational cost. On the other hand, the viscous absorption in the resonator neck influences the resonator behavior a lot and has to be included in the calculation. The first problem was solved by using a coarse FDTD grid but applying detailed simulated quasistationary pressure distribution to modify the FDTD equations in the neighborhood of the resonator neck. For the second problem the analytical solution for viscous boundary layer absorption was introduced into the FDTD equations. However, this solution is only correct for the viscous absorption near an infinite plate. Therefore, the calculated quasi-stationary solutions were applied to correct for the nonuniform velocity distribution in the resonator neck. The results are compared with both analytical solutions and with experimental results.