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 effects like reflection, scattering and diffraction near arbitrary objects, and complex medium 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-of-the-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 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.
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