Commun. Comput. Phys.,
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Volume 3.


Wave Propagation Simulation Using the CIP Method of Characteristic Equations

Kazuya Shiraishi 1*, Toshifumi Matsuoka 1

1 Department of Civil & Earth Resources Engineering, Kyoto University, Kyotodaigaku-Katsura, Nishikyo-ku, Kyoto 615-8540, Japan.

Received 19 September 2006; Accepted (in revised version) 6 June 2007
Available online 14 September 2007

Abstract

We apply the CIP (Cubic Interpolated Profile) scheme to the numerical simulation of the acoustic wave propagation based on characteristic equations.The CIP scheme is based on a concept that both the wavefield and its spatial derivative propagate along the same characteristic curves derived from a hyperbolic differential equation. We describe the derivation of the characteristic equations for the acoustic waves from the basic equations by means of the directional splitting and the diagonalization of the coefficient matrix, and establish geophysical boundary conditions. Since the CIP scheme calculates both the wavefield and its spatial derivatives, it is easy to realize the boundary conditions theoretically. We also show some numerical simulation examples and the CIP can simulate acoustic wave propagation with high stability and less numerical dispersion. The method of characteristics with the CIP scheme is a very powerful technique to deal with the wave propagation in complex geophysical problems.

AMS subject classifications: 35L05, 65M25, 81T80

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Key words: Acoustic wave, characteristic equation, CIP.

*Corresponding author.
Email: skazuya@earth.kumst.kyoto-u.ac.jp (K. Shiraishi), matsuoka@earth.kumst.kyoto-u.ac.jp (T. Matsuoka)
 

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