Accurate fast field formulation for a uniformly moving source traveling above an impedance plane

Abstract

The Lorentz transform, which can be applied to a uniformly moving source, effectively converts the time-domain wave equation to an equivalent problem in frequency-domain due to a stationary source. Standard fast field program (FFP) implementations apply the property of conjugate symmetry in the wavenumber domain for improved efficiency. Recent literature [D. Dragna et al., AIAA 52, 1928–1939 (2014)] suggests the use of a Dopplerized frequency-dependent impedance model to account for the effects of source motion. Consequently, the FFP kernel function is no longer identical for the positive and negative wavenumbers. Additional complications are introduced by the necessity to compute the positive and negative horizontal separation distances in the Lorentz frame to obtain a complete time history of sound pressures for the source approaching and receding from the receiver. Further development of the FFP algorithm in the Lorentz frame is explored such that a frequency-dependent impedance model is developed. Both moving line and point monopole sources are considered in the current investigation. Results are validated against direct numerical integration schemes and with the published time-domain solutions. Applications for an aircraft operating in cruise condition is also examined in the present study. [Work Sponsored by the Federal Aviation Administration.]