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

Abstract

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.

Simulating acoustic scattering from atmospheric temperature fluctuations using a k-space method

“…9 In contrast, numerical algorithms such at Finite-Difference-Time-Domain (FDTD) can directly model the scattering of these transient acoustic pulses by a specific temperature and velocity distribution. [10][11][12] Given however that SODARs generally operate in the frequency range 1000-5000 Hz and generally have a range of 100 m upward, FDTD simulation of the entire scattering volume in three dimensions is unfortunately not feasible with currently available computing power.…”

<title>High-fidelity simulation capability for virtual testing of seismic and acoustic sensors</title>

“…This approach and several others can yield highly accurate results, although some efficiency in memory usage and/or calculation time is lost in comparison to the customary leap-frog solution for a nonmoving medium. 13 The accuracy of the stencil shown in Figure 5 has been demonstrated at flow Mach numbers as high as 0.8.…”

Implementing statistical acoustic characterization of urban terrain into a decision support tool

“…implementation of these two relations (expanded to 3 dimensions from 2 dimension description in Wilson and Liu, [7]):…”

“…These parameters were chosen as the simplest and most effective implementation of the extensive research on the effect of porosity on acoustic propagation. Wilson and Liu [7] provide a convenient tabulation of these parameters tortuosity, porosity, and flow resistivity for asphalt, snow, sand, grass, and forest.…”