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GENERALIZATIONS OF THE ENERGY-FLUX PARABOLIC EQUATION

DMITRY MIKHIN

Research Engineer, Acacia Research Pty. Ltd, Adelaide, Australia

https://doi.org/10.1142/S0218396X05002724Cited by:6 (Source: Crossref)

Abstract

Parabolic equations written in terms of energy flux are inherently immune to the problem of energy conservation at vertical interfaces. Mikhin [J. Comp. Acoust. 9 (2001) 183–203] achieved exact reciprocity and energy conservation in a finite-difference PE model following this approach. However, his model used the implicit Crank–Nicolson scheme in range that requires a small range step for accurate solution. The present paper generalizes the exponential propagator of Collins [J. Acoust. Soc. Am. 93 (1993) 1736–1742] to solve the energy-flux PE. The obtained solution remains strictly reciprocal and energy conserving, while allowing large range steps. The numerical efficiency is improved by one or two orders of magnitude. A technique is proposed to calculate the acoustic pressure within the large steps, so the solution combines fast advance in range with dense range sampling. Numerical examples are provided.

Part of the material in this paper appeared previously under the same title in "Acoustics 2002 Innovation in Acoustics and Vibration, Annual Conference of the Australian Acoustical Society, 13–15 November 2002, Adelaide, Australia," and was published in the CD-ROM proceedings on pp. 261–270.

Keywords:

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