and Computational Methods

Rubric: "01.02.00 Mechanics"

doi: 10.18698/2309-3684-2016-2-5568

We suggest classification for dynamical problems of a space station motion near a precessing small planet. This classification is based on three signs. These signs are the model of the asteroid gravitational potential, the method of holding the space station near the small planet, the type of dynamical problem. Within the offered classification we review the results received earlier. In particular, we construct sets of the space station equilibria or stationary orbits if the asteroid gravitational potential is composed by potentials of two real or conjugate complex point masses on real or imaginary distance and if the station coast along the leier or it moves freely. (In our case the leier is a tether with ends fixed in the asteroid poles). Moreover, we establish some facts of stability for the found orbits and equilibria and note some integrable cases of the motion equations along the leier

Rodnikov A. Modeling of a space station dynamics in vicinity of an asteroid. Маthematical Modeling and Coтputational Methods, 2016, №2 (10), pp. 55-68

doi: 10.18698/2309-3684-2015-3-89100

This paper considers the problem of function estimating for times to failure translation from one mode to another. This problem arises, for example, when there is data on failures of products in vitro tests and you need to estimate the reliability of the same type products with actual test conditions. For simplicity, we consider the case where MTBF have linear relation. The proposed method is based on minimizing the Kolmogorov-Smirnov statistic, which is used to test the homogeneity of two progressively censored samples. A special feature of the proposed statisticis using the Kaplan-Meier estimates of the reliability function for each sample. Provided conjecture homogeneity of two samples, the distribution of statistics does not depend on the type of distribution of failures. This paper proposes a method for calculating the exact distributions of these statistics. Tables of exact distributions probabilities are presented for a wide range of possible values of the volumes of samples. By means of statistical modeling a table of acceleration factor values is calculated and its histograms are presented.

Keywords: non-parametric statistics, the Kolmogorov-Smirnov test, Kaplan-Meier estimate, progressive censoring.

Timonin V., Tyannikova N. Progressively censored sample comparison - numerical methods for homogeneity statistic distributions and study of communication parameters estimating by Monte Carlo method. Маthematical Modeling and Coтputational Methods, 2015, №3 (7), pp. 89-100

doi: 10.18698/2309-3684-2016-3-3352

Modification of Pohlhausen method is developed. It allows for quick and effective heat transfer distribution over the blunt body surfaces. Calculations were done. Their results are described in comparison with the numerical solution of a problem within the framework of Navier — Stokes equations.

Kotenev V., Bulgakov V., Ozhgibisova Y. Modification of Pohlhausen method for calculating heat transfer on blunt bodies. Маthematical Modeling and Coтputational Methods, 2016, №3 (11), pp. 33-52

doi: 10.18698/2309-3684-2015-4-7591

This article deals with the finite-element RKDG method (Runge-Kutta Discontinuous Galerkin) and its application for numerical integration of three-dimensional system of equations of ideal gas on unstructured grids. By means of the described algorithm we solved two test tasks. For each task we conducted the analysis and compared the task solution with well-known analytical solutions or with tabular data. We also give error assessment in the solution.

Dimitrienko Y., Koryakov M., Zakharov A. Application of RKDG method for computational solution of three-dimensional gas-dynamic equations with non-structured grids. Маthematical Modeling and Coтputational Methods, 2015, №4 (8), pp. 75-91

doi: 10.18698/2309-3684-2014-1-3656

The theory of thin constructive-orthotropic plates with a two-periodic structure was suggested. Examples of such structures are honeycomb sandwich panels and backed plates. The theory is based on equations of a three-dimensional elasticity theory with the help of asymptotic expansions in terms of a small parameter being the ratio of a plate thickness and a characteristic length without introducing any hypotheses on a distribution character for displacements and stresses through the thickness. Local problems were formulated for finding stresses in all structural elements of a plate. It was shown that the global (averaged by the certain rules) equations of the plate theory are similar to equations of the

Dimitrienko Y., Gubareva E., Sborschikov S. Asymptotic theory of constructive-orthotropic plates with two-periodic structures. Маthematical Modeling and Coтputational Methods, 2014, №1 (1), pp. 36-56

doi: 10.18698/2309-3684-2014-1-115130

The article shows theoretical bases of the methods and algorithms developed to analyze the stability and supercritical behavior of thin elastic shells. The author deals with the problem of numerical analysis of nonlinear deformation of the spherical dome loaded with uniform external pressure. An algorithm for the numerical analysis method based on the parameter continuation method combined with the method of the subspace change of control parameters. The author illustrates the effectiveness of the proposed algorithm by sample calculations.

Gavryushin S. Numerical simulation of nonlinear deformation of thin elastic shells. Маthematical Modeling and Coтputational Methods, 2014, №1 (1), pp. 115-130

doi: 10.18698/2309-3684-2014-2-4961

The paper presents comparison of asymptotic analysis of a composite plate lateral bending under the impact of surface load against classical theories of thin and thick plates. Layers of the plate are assumed to be homogeneous linear elastic orthotropic materials.

Sheshenin S., Skoptsov K. Theory of plates based on the method of asymptotic decompositions. Маthematical Modeling and Coтputational Methods, 2014, №2 (2), pp. 49-61

doi: 10.18698/2309-3684-2014-2-115126

During the last decades we are witnessing climate changes. Scientists assume global warming to be the result of man-generated increase of green house gases in the atmosphere, the most important one being СО2. The article deals with the problem and describes cutting-edge solutions for stabilising climate. The research makes use of a seasonal global combined threedimensional hydrodynamic model of climate. This model of climate includes model of the World Ocean with real depths and configuration of continents, model of evolution of sea ice and energy — moisture balance model of the atmosphere. The first stage covers estimation of climate change through 2100 following IPCC A2 СО2 increase scenario. The calculations yield rise of average annual surface temperature of the atmosphere by 3,5 С. A number of calculations have been made to estimate possibility of stabilising climate at the level of 2010 by means of controlled release of sulphate aerosol into stratosphere. The aerosol will reflect and disperse a part of the coming solar radiation. We have calculated concentration (albedo) of the aerosol from 2010 to 2100 which will enable us to stabilise the average annual temperature of the surface layer of atmosphere. We have shown that by this way it is impossible to achieve the seasonal uniform approximation to the existing climate, although it is possible to significantly reduce the greenhouse warming effect. Provided that the aerosol is distributed evenly in space in stratosphere, we can stabilize the average annual temperature of the atmosphere, herewith in middle and low latitudes the climate will be colder by 0,1…0,2 С and in high latitudes it will be warmer by 0,2…1,2 С. Besides, these differences are essentially seasonal in nature, they increase in winter. If we stop releasing the aerosol in 2080 the average annual global temperature of the atmosphere will rise, reaching the former value without the aerosol by the year 2100.

Parkhomenko V. Modelling global climate stabilisation by controlled emission of stratospheric aerosol. Маthematical Modeling and Coтputational Methods, 2014, №2 (2), pp. 115-126

doi: 10.18698/2309-3684-2014-2-6276

We have studied impact of near bottom flow ply boundaries waves’ forces on an underwater pipeline. We have performed numerical analysis of the obtained integral representation for the force of aqueous medium impact on the pipeline. We have revealed certain flow conditions with significant increase of hydrodynamic reactions.

Vladimirov I., Korchagin N., Savin A. Simulation of wave influence of a stratified current on an underwater pipeline. Маthematical Modeling and Coтputational Methods, 2014, №2 (2), pp. 62-76