Phase-error analysis of high-order finite difference time domain scheme and its influence on calculation results of impulse response in closed sound field

To obtain accurate impulse responses in a sound field by numerical analysis, a high-order finite difference time domain (FDTD) method was formulated on the basis of a simple Taylor expansion. The accuracy of the FDTD scheme was evaluated by Von Neumann and Richtmyer dispersion analysis. It was found that the unavoidable phase error obtained from the conventional FDTD algorithm is reduced using the high-order scheme with 8 or more reference points. When using higher orders in the scheme used in this study, the time resolution should be small to reduce the phase error. To validate the FDTD scheme for calculating the impulse response in a closed sound field, the numerical result was compared with an analytical solution obtained by the separation of variables method. It was found that the phase error for a low-order FDTD appeared as fluctuations of the arriving pulses and that the fluctuations can be reduced using the high-order scheme with a small time resolution. The accuracy of the FDTD calculation for a large-scale sound field or a long-time calculation, which we should consider when making a sound field analysis of room acoustics or outdoor noise propagation, is strongly influenced by the phase error and therefore the error should be considered when performing such numerical analyses.