On shortwave diffraction by elongated body. Numerical experiments

N. Ya. Kirpichnikova ; M. M. Popov ; N. M. Semtchenok

Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 46, Tome 451 (2016), pp. 65-78

Résumé

The paper is a continuation of previous works of the authors dealing with the exploration of shortwave diffraction by smooth and strictly convex bodies of revolution (axisymmetric case). In these problems the boundary layer method contains two large parameters: one is the Fock parameter $M$ and the second one $\Lambda$ which characterizes the oblongness of the scatterer. It naturally generates a possibility to use the two scaled asymptotic expansion where both $M$ and $\Lambda$ are regarded as independent. The approximate formulae for the wave field in this situation depend on mutual strength between the large parameters and may vary. In the paper we carry out numerical experiments with our formulae, in the case when Fock analytical solution is in good coincidence with exact solution of a model problem, in order to examine influence of the parameter $\Lambda$ on the wave field. It follows from our numerical experiments that the influence of the oblongness of the scatterer on the wave field is really insignificant if the method of Leontovich–Fock parabolick equation does not meet mathematical problems.