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Application of the Beilis–Tappert parabolic equation method to sound propagation over irregular terrain
J. Acoust. Soc. Am. Volume 131, Issue 2, pp. 1039-1046 (2012); (8 pages)
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Add to FacebookThe Beilis–Tappert (1979) parabolic equation method is attractive for irregular terrain because it treats surface variations in terms of a simple multiplicative factor (“phase screen”). However, implementing the exact sloping-surface impedance condition is problematic if one wants the computational efficiency of a Fourier parabolic equation algorithm. This article investigates an approximate flat-ground impedance condition that allows the Beilis–Tappert phase screen method to be used with a Fourier algorithm without any added complications. The exact sloping-surface impedance condition is derived and applied to propagation predictions over hills with maximum slopes from 5° to 22°. The predictions with the exact impedance condition are compared to predictions using the approximate flat-ground impedance condition. It is found that for slopes less than 15°–20°, the flat-ground impedance condition is sufficiently accurate. For slopes greater than approximately 20°, the limiting factor on numerical accuracy is not the flat-ground impedance approximation, but rather the narrow-angle approximation required by the Beilis–Tappert method. Thus, within the 20° limitation and using the flat-ground impedance condition with a Fourier parabolic equation, sound propagation over irregular terrain can be computed simply, efficiently, and accurately.
© 2012 Acoustical Society of America
ACKNOWLEDGMENT
The authors gratefully acknowledge funding from the U. S. Army TACOM-ARDEC at Picatinny Arsenal, New Jersey.
Article Outline
- INTRODUCTION
- THE PHYSICAL PROBLEM
- THE BEILIS–TAPPERT PARABOLIC EQUATION FOR SOUND PROPAGATION OVER IRREGULAR TERRAIN
- Coordinate transformation
- Wave function transformation
- Split-step solution
- Operator commutivity and the split-step approximation
- IMPEDANCE BOUNDARY CONDITION ON A SLOPE
- Impedance boundary condition on a sloping ground surface
- Sloping-surface impedance condition with a coordinate transformation and the Beilis–Tappert wave function transformation
- Coordinate transformation
- Wave function transformation
- Numerical implementation of the impedance boundary condition on a slope
- Finite difference parabolic equation
- Fourier parabolic equation
- COMPARISON OF THE BEILIS–TAPPERT METHOD WITH BENCHMARK CALCULATIONS AND WITH EXPERIMENTAL MEASUREMENTS
- Benchmark calculations
- Comparison with experiment
- CONCLUSIONS AND DISCUSSION
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History
Received 26 Aug 2011
Accepted 21 Dec 2011
Revised 16 Dec 2011
Accepted 21 Dec 2011
Revised 16 Dec 2011
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