Acoustic Analogy with High-Order Time Derivatives for Far-Field Acoustic Predictions

Abstract

The numerical method is proposed for predicting the far-field noise using Ffowcs Williams–Hawkings (FW–H) equation with high-order finite-difference method for the time derivative. The results of this method for second-, fourth-, and sixth-order finite difference approximations are compared with that of analytic applications, such as monopole and dipole. It is observed that the use of the high-order time derivatives is an efficient approach to improve the prediction accuracy of the radiated acoustic pressure, particularly when the temporal resolution is not sufficiently high owing to the limited time step size. Our findings in this study provide evidence that for higher-order approximations, the RMS error for the first and second derivatives is smaller. In addition, the RMS error for the sixth-order approximation decreases considerably compared to that for the second-order approximation, with an increase in the number of points per period. This study and its results are expected to serve as a guide for noise prediction, indicating the temporal accuracies of the acoustic analogy according to the high-order approximation of time derivatives.