Commun. Comput. Phys., 11 (2012), pp. 351-366.

Conservative Finite-Difference Scheme for High-Frequency Acoustic Waves Propagating at an Interface Between Two Media

J. Staudacher 1, E. Savin 1*

1 ONERA - The French Aerospace Lab, F-92322 Chatillon, France.

Received 11 December 2009; Accepted (in revised version) 24 July 2010
Available online 24 October 2011


This paper is an introduction to a conservative, positive numerical scheme which takes into account the phenomena of reflection and transmission of high frequency acoustic waves at a straight interface between two homogeneous media. Explicit forms of the interpolation coefficients for reflected and transmitted wave vectors on a two-dimensional uniform grid are derived. The propagation model is a Liouville transport equation solved in phase space.

AMS subject classifications: 35L45, 65M06, 65M12, 70H99

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Key words: Acoustics, high-frequency, Liouville equation, energy conservation, reflection, transmission.

*Corresponding author.
Email: (J. Staudacher), (E. Savin)

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