On Short-Wave Diffraction by an Elongated Body. Numerical Experiments
- Authors: Kirpichnikova N.Y.1, Popov M.M.1, Semtchenok N.M.1
-
Affiliations:
- St. Petersburg Department of the Steklov Mathematical Institute
- Issue: Vol 226, No 6 (2017)
- Pages: 734-743
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/240059
- DOI: https://doi.org/10.1007/s10958-017-3563-5
- ID: 240059
Cite item
Abstract
The paper is a continuation of previous papers of the authors dealing with the exploration of shortwave diffraction by smooth and strictly convex bodies of revolution (the axisymmetric case). In these problems, the boundary layer method contains two large parameters: one is the Fock parameter M and the second is Λ that characterizes the oblongness of the scatterer. This naturally gives the possibility of using the two-scaled asymptotic expansion, where both M and Λ are regarded as independent. The approximate formulas for the wave field in this situation depend on the mutual strength between the large parameters and may vary. In the paper, we carry out numerical experiments with our formulas, in the case where the Fock analytical solution is in good coincidence with the exact solution of a model problem, in order to examine the influence of the parameter Λ 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 parabolic equation does not meet mathematical difficulties.
About the authors
N. Ya. Kirpichnikova
St. Petersburg Department of the Steklov Mathematical Institute
Author for correspondence.
Email: nkirp@pdmi.ras.ru
Russian Federation, St. Petersburg
M. M. Popov
St. Petersburg Department of the Steklov Mathematical Institute
Email: nkirp@pdmi.ras.ru
Russian Federation, St. Petersburg
N. M. Semtchenok
St. Petersburg Department of the Steklov Mathematical Institute
Email: nkirp@pdmi.ras.ru
Russian Federation, St. Petersburg