Sibirskii Zhurnal Industrial'noi Matematiki
2017, vol. 20, No 4 (72)Contents
UDC 517.988.68
DOI 10.17377/sibjim.2017.20.401Ageev A. L., Antonova T. V.
A discrete algorithm for the localization of lines of discontinuity of a two-variable functionWe consider an illposed problem for the localization of lines of discontinuity. It is assumed that, instead of the exact function $f$, we know the values at the points of the uniform grid of the mean squares of the disturbed function $f^{\delta}$, $\|f-f^{\delta}\|_{L_2(\Bbb{R}^2)}\le\delta$, and the level of the error $\delta$. We construct an algorithm for the localization of lines of discontiuity, prove its convergence with approximation accuracy estimates whose order coincides with that of the estimates obtained earlier by the authors for the case when the function itself is given instead of the mean values of $f^{\delta}$. We also justify estimates for an important characteristic of the algorithm, separability threshold.
Key words: illposed problem, regularization method, line of discontinuity, discretization, separability threshold.
Pp. 3-12.
Ageev Alexander Leonidovich
Antonova Tatyana Vladimirovna
Institute of Mathematics and Mechanics Ural Branch of Russian Academy of Sciences
S. Kovalevskaya str., 16
620990 Ekaterinburg
E-mail: ageev@imm.uran.ru; tvantonova@imm.uran.ru
UDC 519.634
DOI 10.17377/sibjim.2017.20.402Blokhin A. M., Rudometova A. S.
Stationary currents of a weakly conducting incompressible polymeric fluid between coaxial cylindersWe study stationary solutions to a mathematical model describing nonisothermal electroconvection of a weakly conducting polymeric fluid in the channel between two coaxial cylinders.
Key words: incompressible polymeric fluid, nonisothermic flow, stationary flows of a polymeric fluid.
Pp. 13-21.
Blokhin Alexander Mikhajlovich
Rudometova Anna Sergeevna
Sobolev Institute of Mathematics SB RAS
Akad. Koptyug ave., 4
Novosibirsk State University
Pirogova str., 2
630090 Novosibirsk
E-mail: blokhin@math.nsc.ru; bush@math.nsc.ru
UDC 519.711.3
DOI 10.17377/sibjim.2017.20.403Buzdov B. K.
A numerical study of a two-dimensional mathematical model with a variable heat transfer coefficient arising in cryosurgeryA two-dimensional boundary value problem of Stefan type with nonlinear heat sources of a special type and a variable heat transfer coefficient is posed and solved numerically. The model arises in cryosurgery when a living biological tissue is frozen by a cylindrical cryoinstrument located on its surface. The model takes into account the actually observed effect of spatial heat localization. Some results of computer calculations are given.
Key words: mathematical models in cryosurgery, Stefan type problems, spatial heat localization.
Pp. 22-28.
Buzdov Beslan Karal'bievich
Institute of Computer Science and Problems of Regional Managemnet of KBSC RAS
I. Armand str., 37a
360000 Nalchik
E-mail: beslan2801@yandex.ru
UDC 539.3
DOI 10.17377/sibjim.2017.20.404Gordienko V. M.
Invariant operators and separation of residual stressesWe consider the equations of linear elasticity in stresses for the three-dimensional space. Solutions are decomposed into sums of stationary solutions not satisfying the compatibility condition (residual stresses) and nonstationary solutions satisfying the compatibility condition and hence representable through the displacements. The construction of this decomposition is reduced to solving a series of Poisson equations.
Key words: elasticity theory, strain tensor, stress tensor, deviator, residual stresses, Saint-Venant compatibility conditions.
Pp. 29-34.
Gordienko Valerii Mikhailovich
Sobolev Institute of Mathematics SB RAS
Akad. Koptyug ave., 4
Novosibirsk State University
Pirogova str., 2
630090 Novosibirsk
E-mail: gordienk@math.nsc.ru
UDC 519.63
DOI 10.17377/sibjim.2017.20.405Karchevsky A. L.
Determination the possibility of a rock burst in a coal seamThe paper presents an algorithm for computing the value serving as a criterion for the decision about a possible rock burst in a coal seam. This value is proposed to be sought for in the two step.: The first step solves an inverse problem for finding the necessary quantities, and the second step solves a boundary value problem for the biharmonic equation. The inverse problem can be solved by minimizing the objective functional. Its strong convexity is shown.
Key words: rock burst, coal seam, plane problem of the theory of elasticity, biharmonic equation.
Pp. 35-43.
Karchevsky Andrey Leonidovich
Institute of Comprehensive Exploitation of Mineral Resources RAS
Kryukovsky dumb, 4
111020 Moscow
E-mail: karchevs@math.nsc.ru
UDC 539.3
DOI 10.17377/sibjim.2017.20.406Klochkov Yu. V., Nikolaev A. P., Vakhnina O. V., Kiseleva T. A.
The use of Lagrange multipliers in the triangular element of a nonplanar shell under variable interpolation of displacementsWe expose an algorithm for calculating thin arbitrary shells on usig a triangular discretization element with correction Lagrange multipliers. The rigidity matrix of the triangular element is formed using the methods for approximating displacements as scalar and vector quantities.
Key words: shell, triangular discretization element, Lagrange multipliers, scalar approximation, vector approximation.
Pp. 44-54.
Klochkov Yuriy Vasil'evich
Nikolaev Anatoliy Petrovich
Vakhnina Ol'ga Vladimirovna
Kiseleva Tat'yana Alekseevna
Volgograd State Agrarian University
University ave., 26
400002 Volgograd
E-mail: Klotchkov@bk.ru; anpetr40@yandex.ru; OVahnina@bk.ru; moonway13@rambler.ru
UDC 621.224.35
DOI 10.17377/sibjim.2017.20.407Skorospelov V. A., Turuk P. A.
Geometric support of the optimization of the surface of the suction tube of a hydroturbine on the basis of a numerical simulation of a flowMethods are proposed for generating the set of surfaces of the smooth suction tube of a hydroturbine depending on nine geometric parameters and for constructing grids in the domain of the suction tube for subsequent optimization of its shape basing on a numerical simulation of flows.
Key words: hydraulic turbine, suction pipe, surface variation, finite-element grid, optimization.
Pp. 55-60.
Skorospelov Vladimir Anatol'evich
Turuk Polina Aleksandrovna
Sobolev Institute of Mathematics SB RAS
Akad. Koptyug ave., 4
630090 Novosibirsk
E-mail: vskrsp@math.nsc.ru; turuk@math.nsc.ru
UDC 534.112
DOI 10.17377/sibjim.2017.20.408Tomilin A. K., Kurilskaya N. F.
Vibrations of a conductive string in a nonstationary magnetic field with account taken of two nonlinear factorsWe consider vibations of a conductive string with fixed ends in a magnetic field whose induction is a given function of time. Two nonlinear factors are taken into account simultaneously: the variation of the tension of the string depending on the displacement and the magnetostrictive effect. It is shown that, in the case of a periodically changing magnetic field, the nonlinear factors can compensate each other, and the problem is reduced to the study of linearized parametric vibrations.
Key words: conductive string, nonstationary magnetic field, transverse magnetostriction, parametric vibrations.
Pp. 61-66.
Tomilin Alexander Konstantinovich
National Research Tomsk Polytechnic University
Lenin ave., 30
634050 Tomsk
Kurilskaya Natalya Fedorovna
Novosibirsk State University of Architecture and Civil Engineering (Sibstrin)
Leningradskaya str., 113
630008 Novosibirsk
E-mail: aktomilin@tpu.ru; dream60@mail.ru
UDC 536.46:534.222:517.5
DOI 10.17377/sibjim.2017.20.409Trilis A. V., Sukhinin S. V., Vasiliev A. A.
Stability of a cylindrical flame front in an annular combustion chamberWithin the framework of the phenomenological theory of combustion of mixtures, we investigate the stability of the cylindrical front of deflagration combustion in an annular combustion chamber with the use of small perturbations. The front of the flame is described by a discontinuity of the gas-dynamical parameters. We find that the flame front remains unstable for some types of small perturbations of the main flow of the fuel mixture and the flame front. Using numerical-analytical methods, we study the mechanics of instability. Some examples are given of the development of instabilities rotating in an annular channel.
Key words: continuous spinning detonation, normal flame velocity, deflagration combustion, stability of combustion front, acoustic vibration, quasi-natural frequency.
Pp. 67-79.
Trilis Artyom Valerievich
Sukhinin Sergey Viktorovich
Vasiliev Anatoly Aleksandrovich
Lavrentyev Institute of Hydrodynamics SB RAS
Akad. Lavrentyev ave., 15
630090 Novosibirsk
E-mail: trilisartie@yandex.ru; sukhinin@hydro.nsc.ru; gasdet@hydro.nsc.ru
UDC 550.362
DOI 10.17377/sibjim.2017.20.410Fadeeva I. I., Duchkov A. A.
Determination of the thermophysical properties of media with the help of a needle probeNeedle probes with linear heater inside are often used for determining the thermophysical characteristics of loose rocks. The main issue of contact methods of the measurements of the thermal characteristics of different media consists in the establishment of a thermal contact resistance at the boundary (line) between the source and the medium. This contact resistance should be taken into account while measuring the thermal diffusivity of the medium. The paper describes a mathematical model of the heating of a long needle probe in the medium under study that takes into account the size and thermal characteristics of the needle probe and an imperfect thermal contact between the probe and the studied medium. On the basis of this model, we pose and solve the inverse problem of finding the thermal diffusivity of the medium and the thermal contact resistance at the boundary between the probe and the medium. The aim of this research is to develop a new method for determining the thermal properties of various media in the field.
Key words: thermal conductivity, thermal diffusivity, thermal contact resistance, needle probe, inverse problem.
Pp. 80-89.
Fadeeva Irina Igorevna
N.A. Chinacal Institute of Mining of SB RAS
Krasnyi ave., 54
630091 Novosibirsk
A. A. Trofimuk Institute of Petroleum Geology and Geophysics SB RAS
Akad. Koptyug ave., 3
630090 Novosibirsk
Duchkov Anton Albertovich
A. A. Trofimuk Institute of Petroleum Geology and Geophysics SB RAS
Novosibirsk State Technical University
K. Marks ave., 20
630073 Novosibirsk
E-mail: FadeevaII@ipgg.sbras.ru; DuchkovAA@ipgg.sbras.ru
UDC 531.01:531.552
DOI 10.17377/sibjim.2017.20.411Shamolin M. V.
Auto-oscillations under the braking of a rigid body in a resisting mediumWe carry out a qualitative analysis of the rectilinear and spatial problems of the motion of rigid bodies in a resisting media. We contruct a nonlinear model of the impact of the medium on the rigid body taking into account the dependence of the arm of force on the reduced angular velocity of the body. In this case, the moment of the force is also a function of the angle of the attack. As was shown by processing the experimental data on the motion of homogeneous circular cylinders in water, these circumstances should be taken into account in the simulation. The analysis of the plane and space models of the interaction of a rigid body with a medium reveal sufficient conditions for the stability of the key motion regime, i.e., of the translational rectilinear braking. We show that, under certain conditions, the presence of a stable or unstable auto-oscillating regime in the system is possible.
Pp. 90-102.
Shamolin Maksim Vladimirovich
Institute of Mechanics, Lomonosov Moscow State University
Michurinskii ave., 1
119192 Moscow
E-mail:shamolin@rambler.ru