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: Finite-difference time-domain (FDTD) techniques hold much promise for performing realistic simulations of sound propagation through complex dynamic outdoor environments. This report focuses on a key aspect of FDTD in the atmosphere namely the incorporation of a moving background medium (wind and turbulence in the atmosphere) into the calculations. Appropriate differential equations for FDTD simulation of sound propagation in a moving fluid are discussed. It is shown that FDTD calculations are not possible with this equation set when using the staggered grid "leap-frog" approach which is common for FDTD simulation of other types of wave propagation. Various finite-difference operators that are valid for a moving medium such as Runge-Kutta and an unstaggered leap-frog approach are discussed and compared. It is shown that a rigorous FDTD solution in a moving medium requires storing the field variables over at least two time steps thereby requiring at least twice as much computer memory as the customary staggered grid. Several other topics pertinent to FDTD simulation of sound propagation in the atmosphere are discussed including implementation of porous ground layers absorbing boundaries and rigid surfaces. Example calculations demonstrate the performance of the various finite-difference operators for a high Mach number uniform flow. Other example calculations show FDTD calculations for propagation above rigid and porous ground surfaces over rigid barriers and through turbulence. With sufficiently dense spatial grids very good agreement can be obtained between the FDTD calculations and known theoretical solutions.

Finite-Difference, Time-Domain Simulation of Sound Propagation in a Dynamic Atmosphere