Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-25T13:34:14.184Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  20 August 2015

J. Staudacher  and
É Savin
J. Staudacher*
Affiliation:
ONERA - The French Aerospace Lab, F-92322 Chătillon, France
É Savin*
Affiliation:
ONERA - The French Aerospace Lab, F-92322 Chătillon, France
*
Corresponding author.Email address:[email protected]
Email:[email protected]
Get access

Abstract

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.

Keywords

35L4565M0665M1270H99Acousticshigh-frequencyLiouville equationenergy conservationreflectiontransmission
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 2 , February 2012 , pp. 351 - 366
Copyright
Copyright © Global Science Press Limited 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Bal, G., Keller, J.B., Papanicolaou, G. C. and Ryzhik, L. V., Transport theory for acoustic waves with reflection and transmission at interfaces, Wave Motion, 30 (1999), 303–327.Google Scholar
[2] Gary Cohen, C., Higher-Order Numerical Methods for Transient Wave Equations, Springer, 2002.Google Scholar
[3]Jin, S. and Wen, X., Hamiltonian-preserving schemes for the Liouville equation with discontinuous potentials, Commun. Math. Sci., 3 (2005), 285–315.CrossRefGoogle Scholar
[4]Jin, S. and Wen, X., Hamiltonian preserving schemes for the Liouville equation of geometrical optics with discontinuous local wave speeds, J. Comput. Phys., 214 (2006), 672–697.Google Scholar
[5]Jin, S. and Wen, X., A Hamiltonian-preserving scheme for the Liouville equation of geometrical optics with partial transmissons and reflections, SIAM J. Numer. Anal., 44 (2006), 1801–1828.Google Scholar
[6]Jin, S. and Wen, X., Computation of transmissions and reflections in geometrical optics via the reduced Liouville equation, Wave Motion, 43 (2006), 667–688.Google Scholar
[7]Jin, S. and Yin, D., Computational high frequency waves through curved interfaces via the Liouville equation and geometric theory of diffraction, J. Comput. Phys., 227 (2008), 6106–6139.CrossRefGoogle Scholar
[8] Lawrence Kinsler, E., Frey, Austin R., Coppens, Alan B. and Sanders, James V., Fundamentals of Acoustics, 4th Edition, Wiley, 2000.Google Scholar
[9] Randall LeVeque, J., Numerical Methods for Conservation Laws, Birkhäuser Verlag, 1990.Google Scholar
[10]Miklowitz, J., The Theory of Elastic Waves and Waveguides, North Holland, 1978.Google Scholar
[11]Miller, L., Refraction of high-frequency waves density by sharp interfaces and semiclassical measures at the boundary, J. Math. Pure Appl., 79 (2000), 227–269.CrossRefGoogle Scholar
[12]Ryzhik, L. V., Papanicolaou, G. C. and Keller, J. B., Transport equations for elastic and other waves in random media, Wave Motion, 24 (1996), 327–370.Google Scholar