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- Title
Mathematical simulation of acoustic wave refraction near a caustic.
- Authors
Baev, A.
- Abstract
Issues related to the computation of wave fields in an acoustic medium near caustics are considered. A boundary condition on a caustic is established, and the Green's function of a boundary value problem for the general case of a varying speed of sound is constructed. For this purpose, an auxiliary Goursat problem is considered and a system of its particular solutions is constructed using hyper-geometric functions. A Volterra integral equation for the Green's function is obtained, and an algorithm for its expansion with respect to smoothness is described. A finite difference scheme approximating the solution of the differential problem with an unbounded coefficient is proposed. Numerical results are presented.
- Subjects
CAUSTICS (Optics); SOUND wave refraction; GREEN'S functions; GOURSAT problem; VOLTERRA equations
- Publication
Computational Mathematics & Mathematical Physics, 2013, Vol 53, Issue 7, p947
- ISSN
0965-5425
- Publication type
Article
- DOI
10.1134/S0965542513070051