The finite-difference time-domain (FDTD) method, solving the inhomogeneous, moving medium sound propagation equations, also referred to as the Linearized Euler(ian) Equations (LEE), has become a mature reference outdoor sound propagation model during the last two decades. It combines the ability to account for complex wave-related effects like reflection, scattering and diffraction near or in between arbitrary objects, and complex medium-related effects like convection, refraction and (turbulent) scattering. In addition, it has the general advantages of a time-domain method. It is indicated that the numerical discretisation scheme should be chosen depending on the flow speed of the background medium. Perfectly matched layers, applicable to cases in presence of (non-)uniform flow, are state-ofthe-art perfectly absorbing boundary conditions that are key in outdoor sound propagation applications, where only a small part of the unbounded atmosphere can be numerically described. Various ways to include frequency-dependent outdoor soils are summarized, like time-domain impedance plane boundary conditions and explicitly including the upper part of the soil in the simulation domain. Approaches for long-distance sound propagation, including moving calculation frames and hybrid modeling are discussed. This review deals with linear sound propagation only.
1.INTRODUCTIONDuring the last two decades, time-domain modelling has received a lot of interest as it was shown to have great potential. One of the major advantages is that the response over a broad frequency range can be obtained with a single simulation run only, on condition that a short acoustic pulse is excited at the source position. Clearly, the spatial discretisation will limit the range of frequencies that can be sufficiently resolved. As analysis of a system's response is often more convenient in frequency domain, a Fourier transform can still provide the necessary information in a post-processing step. Time-domain models further allow including non-linear effects that appear near high amplitude sources. A timedomain approach directly models the waveform; therefore, its distortion can be captured, corresponding to a transfer of sound energy in between sound frequencies. The latter is less trivial in a frequency-domain technique, focusing on a single frequency at a time. In time domain, moving sources and related doppler-shifts, as well as transient behavior can be simulated directly. In addition, source localization using time-reversal techniques clearly need a time-domain approach. While traditionally sound propagation is treated in the frequency domain, time-domain approaches emerged in the last two decades mainly due to the increased access to computing power.Moving and inhomogeneous media may strongly effect sound propagation in the near field of realistic sources, as well as in the far field. Near airplanes, e.g., sound is emitted in a flowing medium, and the