and Computational Methods

#### 621.311.61:621.3.014.2 Mathematical modeling of coaxial electrogenerating elements

**Loshkarev A. I. (Bauman Moscow State Technical University), Oblakova T. V. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2015-1-316

The article presents a developed mathematical model of electric describing the coaxial electrogenerating elements (EGE) with isothermal cathode and a variety of ways for current collecting. To analyze their internal state and output parameters in the arc mode we used a two-parameter local linear current-voltage characteristic (CVC). It was shown that in the case of one-sided current collection maximum power of EGE and generated magnetic field asymptotically approach to their maximum values as the length of the electrodes goes into infinity. In the case of versatile current collection maximum values of these parameters can be achieved at the final length of the electrodes. In both methods of the current collection the acceptable value of EGE electrical power loss of 25% due to electrode non-equipotentionality was achieved at their universal critical length. The calculation of which is presented.

Loshkarev A., Oblakova T. Mathematical modeling of coaxial electrogenerating elements. Маthematical Modeling and Coтputational Methods, 2015, №1 (5), pp. 3-16

#### 5 Problem solution of aerodynamic design using multiprocessor computers

**Bratchev A. V. (JSC MIC NPO Mashinostroyenia), Dubrovina A. Y. (JSC MIC NPO Mashinostroyenia), Kotenev V. P. (Bauman Moscow State Technical University/JSC MIC NPO Mashinostroyenia), Maksimov F. A. (Institute for Computer Aided Design of the Russian Academy of Sciences), Shevelev Y. D. (Institute for Computer Aided Design of the Russian Academy of Sciences)**

doi: 10.18698/2309-3684-2015-1-1730

The article discusses a method for constructing an aircraft geometric shape for computing the parameters of aerogasdynamic flow as well as a method of meshing near the model to simulate the flow within the Navier–Stokes equations in the thin layer approximation. The results of the flow simulation are given. The calculations were performed on a multiprocessor computer system.

Bratchev A., Dubrovina A., Kotenev V., Maksimov F., Shevelev Y. Problem solution of aerodynamic design using multiprocessor computers. Маthematical Modeling and Coтputational Methods, 2015, №1 (5), pp. 17-30

#### 533.6:51-71 Investigation of the energy and mass transfer influence on the wake flow of supersonic conical models

**Sidnyaev N. I. (Bauman Moscow State Technical University), Gordeeva N. M. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2015-1-3149

We studied the dynamics of motion and energy transfer in supersonic flow in the base region. It is shown in the article that the current in the base region largely depends on the boundary layer structure in the area between the trailing edge and the sticking point on the centerline, where the boundary layer cut out from the rear edge converges. The study of the effect of gas mass injection into the base region from the body surface and the bottom as well as heat transfer in the bottom region is included. The resulting solution of the problem of the middle wake for axisymmetric body without considering recirculation at a limited distance from the stern has been obtained.

Sidnyaev N., Gordeeva N. Investigation of the energy and mass transfer influence on the wake flow of supersonic conical models. Маthematical Modeling and Coтputational Methods, 2015, №1 (5), pp. 31-49

#### 539.3 A short wave asymptotic analysis of the dispersion relation for a symmetric three-layered elastic plate

**Lashab M. I. (1Faculty of Science, Alasmarya University), Rogerson G. A. (Keele University), Sandiford K. J. (The University of Salford)**

doi: 10.18698/2309-3684-2015-1-5066

The dispersion relation for a symmetric 3-layered elastic plate is derived and analysed, both numerically and asymptotically. Each layer is assumed to be composed of a linear isotropic elastic material. Numerical solutions of the relation are first presented. After presentation of these numerical solutions, particular focus is applied to the short wave regime, within which appropriate asymptotic approximations are established. These are shown to provide excellent agreement with the numerical solution over a surprisingly larger than might be expected wave number regime. It is envisaged that these solutions might offer some potential for estimation of truncation error for wave number integrals and thereby enable the development of hybrid numerical-asymptotic methods to determine transient structural response to impact.

Lashab M., Rogerson G., Sandiford K. A short wave asymptotic analysis of the dispersion relation for a symmetric three-layered elastic plate. Маthematical Modeling and Coтputational Methods, 2015, №1 (5), pp. 50-66

#### 539.3 Computational modeling and experimental investigation of elastic-plastic plates deforming under crushing

**Dimitrienko Y. I. (Bauman Moscow State Technical University), Gubareva E. A. (Bauman Moscow State Technical University), Sborschikov S. V. (Bauman Moscow State Technical University), Erasov V. S. (Federal State Unitary Enterprise “All-Russian Scientific Research Institute of Aviation Materials”), Yakovlev N. O. (Federal State Unitary Enterprise “All-Russian Scientific Research Institute of Aviation Materials”)**

doi: 10.18698/2309-3684-2015-1-6782

The article presents a suggested method of numerical finite-element solving the ‘hole ovalization’ problem. This method can be applied for experimental development of advanced aviation materials with the aim of determining structure element resistance against deforming with stress concentrators, mainly, connectors. The method is based on three-dimensional finite element solution of the problem of lastoplastic deformation of plates with a hole under crushing. It is appropriate for reduction of xperimental studies and replacing them by the numerical experiments. The Ilyushin model of small lastoplastic deformations has been used. The results of numerical simulation of a threedimensional stress-strain state of elastoplastic plates under crushing are presented as well as results of experimental nvestigations of deforming plates of Al-alloy 163. It is shown that the results of numerical and experimental modeling for deforming plates under crushing agree quite well.

Dimitrienko Y., Gubareva E., Sborschikov S., Erasov V., Yakovlev N. Computational modeling and experimental investigation of elastic-plastic plates deforming under crushing. Маthematical Modeling and Coтputational Methods, 2015, №1 (5), pp. 67-82

#### 521.2:521.3:521.61 Evolution of the orbit of a passive fragment with a large area of surface in high Earth orbit

**Bazey A. A. (Scientific Research Institute “Astronomical Observatory” of Odessa Mechnikov National University), Bazey N. V. (Scientific Research Institute “Astronomical Observatory” of Odessa Mechnikov National University), Borovin G. K. (Keldysh Institute of Applied Mathematics of the Russian Academy of Scienсes), Zolotov V. E. (Keldysh Institute of Applied Mathematics of the Russian Academy of Scienсes), Kashuba V. I. (Scientific Research Institute “Astronomical Observatory” of Odessa Mechnikov National University), Kashuba S. G. (Scientific Research Institute “Astronomical Observatory” of Odessa Mechnikov National University), Kupriyanov V. V. (The Central Astronomical Observatory of the Russian Academy of Sciences at Pulkovo), Molotov I. E. (Keldysh Institute of Applied Mathematics of the Russian Academy of Scienсes)**

doi: 10.18698/2309-3684-2015-1-8393

We have analysed and presented observations of artificial celestial body 43096. We obtained the observations in 2006–2012 within the project “Scientific Network of Optic Instruments for Astrometric and Photometric Observations” (ISON). We have determined the Kepler orbit elements and state vector as of 1 hour 55 minutes 50,76 seconds, November 24, 2006 UTC (1:55:50,76 November 24,2006 UTC). We have performed numerical integration of the motion equations, taking into account the perturbations from the polar compression of the Earth, the Moon, the Sun and the solar radiation pressure. We propose a method for deorbiting artificial celestial bodies in high altitude orbits. The method is based on a numerical model of motion in circumterrestrial space, which takes into account only the largest perturbations. For the first time ever we have obtained such a great amount of data on objects with a large area of surface to mass ratio over long time spans. The data allowed us to study the objects and reveal their peculiar properties.

Bazey A., Bazey N., Borovin G., Zolotov V., Kashuba V., Kashuba S., Kupriyanov V., Molotov I. Evolution of the orbit of a passive fragment with a large area of surface in high Earth orbit. Маthematical Modeling and Coтputational Methods, 2015, №1 (5), pp. 83-93

#### 551.509.313.41 Global climate model including description of thermohaline circulation of the World Ocean

**Parkhomenko V. P. (Bauman Moscow State Technical University/Computing Centre of RAS)**

doi: 10.18698/2309-3684-2015-1-94108

The article considers a model of the climate, including interacting blocks of the ocean, atmosphere and sea ice. The model describes the deep thermohaline circulation of the oceans and the main characteristics of the other elements of the climate system. The paper presents model operating in the mode of the seasonal variations of solar radiation. The changes in atmospheric temperature in XXI century for different scenarios of CO2 concentration variations are calculated.

Parkhomenko V. Global climate model including description of thermohaline circulation of the World Ocean. Маthematical Modeling and Coтputational Methods, 2015, №1 (5), pp. 94-108

#### 533.6.07 Supersonic flow in axisymmetric channel

**Maksimov F. A. (Institute for Computer Aided Design of the Russian Academy of Sciences)**

doi: 10.18698/2309-3684-2015-1-109120

The supersonic flows are implemented in an axisymmetric channel in many technical devices. These flows are in an expanding part of the nozzle or in the working part of supersonic wind tunnel. The method of supersonic flow calculation in an axisymmetric channel is developed. The method is based on the construction of multi-block axisymmetric grid and linearization of boundary conditions on the aerodynamic surfaces. Testing the method has showed good agreement with known experimental data. The method allows predicting the aerodynamic properties of the aerodynamic form, depending on its location in the channel, as well as the effect of the aerodynamic form on the channel walls in the channel.

Maksimov F. Supersonic flow in axisymmetric channel. Маthematical Modeling and Coтputational Methods, 2015, №1 (5), pp. 109-120