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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2013, Volume 53, Number 7, Pages 1124–1138
DOI: https://doi.org/10.7868/S0044466913070053 (Mi zvmmf9826) 		 
Mathematical simulation of acoustic wave refraction near a caustic

A. V. Baev

M. V. Lomonosov Moscow State University, Faculty of Physics
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DOI: https://doi.org/10.7868/S0044466913070053
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 hypergeometric 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.
Key words: acoustic wave equation, caustic, Goursat problem, hypergeometric functions, Volterra equation, Green’s function, finite difference scheme, numerical simulation.
Received: 09.09.2011
English version:
Computational Mathematics and Mathematical Physics, 2013, Volume 53, Issue 7, Pages 947–961
DOI: https://doi.org/10.1134/S0965542513070051
Bibliographic databases:
Document Type: Article
UDC: 519.63, 517.958:533.77
Language: Russian
Citation: A. V. Baev, “Mathematical simulation of acoustic wave refraction near a caustic”, Zh. Vychisl. Mat. Mat. Fiz., 53:7 (2013), 1124–1138; Comput. Math. Math. Phys., 53:7 (2013), 947–961
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