Numerical wavefront propagation through inhomogeneous media

Gholam-Ali Zakeri

doi:10.1117/12.49616

11 November 1991 Numerical wavefront propagation through inhomogeneous media

Gholam-Ali Zakeri

Proceedings Volume 1558, Wave Propagation and Scattering in Varied Media II; (1991) https://doi.org/10.1117/12.49616
Event: San Diego, '91, 1991, San Diego, CA, United States

Abstract

An efficient simple numerical procedure is used to produce the motion of shockfront with small amplitude through inhomogeneous media. The mathematical model uses an intrinsic coordinate system and is based on Whitham's (1974) theory of geometrical shock dynamics. By using this model, the motion of the wavefront can be determined without explicitly calculating the flowfield quantities behind the wavefront. The model is given by a system of four partial differential equations (PDEs) which for small amplitude wavefront does not produce caustic in the wavefront. The small variations in sound speed and the corresponding distortion of the rays due to nonlinearity are included in the system of PDEs. Rays are given as the orthogonal trajectories to the wavefront and, because of the nonlinearity effects of the media, rays are not straight lines. We represent the wavefront by a discrete set of points, and then we propagate each point along orthogonal trajectories with sound speed determined by a discretized set of two PDEs relating Mach number and area of the ray tube. The numerical results obtained using the above procedure is compared with exact numerical solutions and experimental data given by other authors.

Citation Download Citation

Gholam-Ali Zakeri "Numerical wavefront propagation through inhomogeneous media", Proc. SPIE 1558, Wave Propagation and Scattering in Varied Media II, (11 November 1991); https://doi.org/10.1117/12.49616

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