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Journal of the Acoustical Society of America / Volume 117 / Issue 2 / GENERAL LINEAR ACOUSTICS [20]

Equations for finite-difference, time-domain simulation of sound propagation in moving inhomogeneous media and numerical implementation

J. Acoust. Soc. Am. Volume 117, Issue 2, pp. 503-517 (2005); (15 pages)

Vladimir E. Ostashev1,2, D. Keith Wilson3, Lanbo Liu3, David F. Aldridge4, Neill P. Symons4, and David Marlin5

1NOAA/Environmental Technology Laboratory, Boulder, Colorado 80305
2Department of Physics, New Mexico State University, Las Cruces, New Mexico 88003
3U.S. Army Engineer Research and Development Center, Hanover, New Hampshire 03755
4Department of Geophysical Technology, Sandia National Labs., Albuquerque, New Mexico 87185
5U.S. Army Research Laboratory, White Sands Missile Range, New Mexico 88002

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Finite-difference, time-domain (FDTD) calculations are typically performed with partial differential equations that are first order in time. Equation sets appropriate for FDTD calculations in a moving inhomogeneous medium (with an emphasis on the atmosphere) are derived and discussed in this paper. Two candidate equation sets, both derived from linearized equations of fluid dynamics, are proposed. The first, which contains three coupled equations for the sound pressure, vector acoustic velocity, and acoustic density, is obtained without any approximations. The second, which contains two coupled equations for the sound pressure and vector acoustic velocity, is derived by ignoring terms proportional to the divergence of the medium velocity and the gradient of the ambient pressure. It is shown that the second set has the same or a wider range of applicability than equations for the sound pressure that have been previously used for analytical and numerical studies of sound propagation in a moving atmosphere. Practical FDTD implementation of the second set of equations is discussed. Results show good agreement with theoretical predictions of the sound pressure due to a point monochromatic source in a uniform, high Mach number flow and with Fast Field Program calculations of sound propagation in a stratified moving atmosphere. © 2005 Acoustical Society of America.

© 2005 Acoustical Society of America

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KEYWORDS and PACS

Keywords

nonlinear acoustics, sound reproduction, acoustic wave propagation, finite element analysis, fluid dynamics

PACS

  • 43.28.Hr

    Outdoor sound sources

  • 43.28.Js

    Numerical models for outdoor propagation

ARTICLE DATA

History
Received 24 Feb 2004
Accepted 05 Nov 2004
Revised 14 Oct 2004
Digital Object Identifier
http://dx.doi.org/10.1121/1.1841531

PUBLICATION DATA

ISSN

0001-4966 (print)  

Publisher

$abstract.society.value is a Member of CrossRef Acoustical Society of America

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