Martynovsky I.M., Serdjuchenko A.M. «Non-linear hydrodynamic modelling of the irregular wind generated water waves» КОНСОНАНС-2013. Акустический симпозиум (1–2 октября 2013 г.), с. 200-206 (2013)

The key aspects in the hydrodynamic modelling of wind-generated water waves including irregularity and non-linearity of the wave motion are presented in the report. On the first stage of the investigations the intensity and frequency structure of irregular surface wave field ware determined by using generalized 6th parametric double-peak Hassellman frequency spectrum. Irregular wave surface ware calculated in the frame of classical spectral theory on the so-called quasi-stationary temporal intervals, but irregular wave pressure field and fluid particle velocity field have been derived as a spectral solution of the specially formulated quasi linear boundary value problem for surface waves. On the second stage local group characteristic of wave surface realizations such as amplitude envelope, phase perturbations and corresponding local values of the wave numbers and frequencies ware derived by using Hilbert transform procedure. All these values are considered as input data for the non-linear generalization of the initial quasi linear wave model on the next stages. In the procedure of the non-linear generalization of the model first of all irregular wave surface must be “saturated” by high order bounded harmonics (up to 20th order) with special phase shift to obtain asymmetric surface profiles to be specific for wind generated waves. On the next stage fluid particle velocities on the wave surface ware calculated by using specially developed half-inverse solution of the fully non-linear boundary value problem. For the non-linear calculation of wave particle velocity and pressure fields in the fluid domain Cauchy integral formula (in 2D model) has been used. Testing and systematic numerical calculations and animated pictures displayed realistic results for irregular wave surface and hydrodynamic fields in the fluid domain.

Shimuk Y.D., Artyukh A.V. «Mathematical model of the wideband antenna with inhomogenetic surface properties excitation» Акустооптические и радиолокационные методы измерений и обработки информации. 4-я международная конференция, 20–22 сентября 2011 г., с. 39-42 (2011)

In this work the problems of single semitransparent and resistive cones with longitudinal slots excitation by a monochromatic radial dipole are considered. It is shown that the original electromagnetic problems can be reduced to the boundary problems of mathematical physics relatively to the scalar functions. Both numerical and analytical results of the scattering properties investigation for the considered structures are provided.

Artjukh A.V., Shimuk Yu.D. «Mathematical modeling of the electromagnetic waves scattering from an open conical reflector in time domain» Акустооптические и радиолокационные методы измерений и обработки информации. 4-я международная конференция, 20–22 сентября 2011 г., с. 36-39 (2011)

The rigorously stated model problem of electromagnetic waves scattering in time domain from an open conical reflector is investigated The solution method is based on the Meler–Fo integral transforms usage. The numerical experiment is made, and the fields distribution dependencies on the time and spatial parameters are studied.