Mathematical simulation of acoustic wave refraction near a caustic
A. V. Baev
M. V. Lomonosov Moscow State University, Faculty of Physics
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 GreenТs 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 GreenТs 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.
acoustic wave equation, caustic, Goursat problem, hypergeometric functions, Volterra equation, GreenТs function, finite difference scheme, numerical simulation.
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Computational Mathematics and Mathematical Physics, 2013, 53:7, 947–961
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
Citation in format AMSBIB
\paper Mathematical simulation of acoustic wave refraction near a caustic
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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