Efficient Outdoor Sound Propagation Modeling with the Finite-Difference Time-Domain (FDTD) Method: A Review

Abstract

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

Meteorological effects on the noise reducing performance of a low parallel wall structure

“…The pressure-velocity (P-V) staggered-in-place (SIP) staggered-in-time (SIT) finite-difference timedomain (FDTD) model [19] is used. When relying on the effective sound speed approach, accurate results can be obtained in the case of wind flowing parallel to flat ground [20], while keeping the computational cost significantly smaller than fully solving the LEE (see also Appendix B).…”

“…On the left, right and upper boundaries, perfectly matched layers [22] are placed to simulate continuation of the propagation region and thus zeroreflection calculation domain termination. The PML equations use the effective sound speed approach as well, by taking the effective sound speeds appearing closest to the inner region of the simulation domain [19].…”

“…The turbule approach is highly suitable in a full-volume discretisation technique like FDTD [19]. The (otherwise uniform) temperature in the sound propagation domain is perturbed, resulting in local variations in the sound speed (see Fig.…”

“…Some small differences are inevitable, since the methods that were used are quite diverse: a frequency-domain technique is opposed to time-domain approaches, and the methods use very different spatial (and temporal) resolutions. In addition, the time-domain techniques use -implicitly -a large number of sound frequencies to constitute the 1/3 octave bands by relying on the response of an acoustic pulse as source excitation [19]. With the BEM technique, a new simulation has to be initiated for each frequency of interest.…”

A Hybrid PSTD/DG Method to Solve the Linearized Euler Equations: Optimization and Accuracy

“…Furthermore, the method is limited to predominantly staircase-like boundary shapes, like in the widely used finite-difference time-domain method (FDTD). 7 Although, a successful development has been presented by Hornikx et al 8 to locally refine the grid using multidomain implementations, its performance is limited when computing complex geometries.…”