Mathematical simulation of acoustic wave refraction near a caustic

被引：0
|
作者：
A. V. Baev
机构：
[1] Moscow State University,Faculty of Computational Mathematics and Cybernetics
来源：
Computational Mathematics and Mathematical Physics | 2013年 / 53卷
关键词：
acoustic wave equation; caustic; Goursat problem; hypergeometric functions; Volterra equation; Green’s function; finite difference scheme; numerical simulation;
D O I：
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学科分类号：
摘要：
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.
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页码：947 / 961
页数：14
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