GENERALIZATIONS OF THE ENERGY-FLUX PARABOLIC EQUATION

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.