Calculation of radial supersonic gas flow past sharp-nosed cones

The paper presents the results of numerical analysis of supersonic source flow of a gas past sharp-nosed cones. Axisymmetric and three-dimensional flows are considered. The flow geometry and the distributions of the gas-dynamic parameters in the shock layer are analyzed; their asymptotic properties are established. The numerical solutions are compared with solutions for uniform gas flow past a cone.Translated from Matematicheskie Modeli Estestvoznaniya, Published by Moscow University, Moscow, 1995, pp. 32–47.     

System of equations describing the flow of viscous liquid and gas in a wide range of reynolds numbers

A mathematical model is proposed for describing stationary and various self-exciting nonstationary (including turbulent) flows of viscous liquid and gas. The model does not assume that the stressed state at the points of the medium is described by a symmetric stress tensor. The model thus allows for internal moments of elementary viscous liquid and gas volumes relative to their centers of mass and for unsymmetric strains.Translated from Matematicheskie Modeli Estestvoznaniya, Published by Moscow University, Moscow, 1995, pp. 17–26.     

Some features of the thermodynamics of nonlinear classical systems

We derive the thermodynamic characteristics of an ideal gas of diatomic molecules with a nonlinear interatomic interaction, solving the problem for a wide class of potentials on the classical level, which is permissible for relatively high temperatures. The nonlinearity of the interaction can yield some characteristic properties of the gas. Moscow State Institute of Radio Engineering, Electronics, and Automatics (Moscow Technical University), Moscow, Russia Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 125, No. 2, pp. 315–325, November, 2000.     

Nonstationary interaction of supersonic inviscid gas flows

We consider the flow of supersonic homogeneous gas past a supersonic spherical source. This problem provides a gas-dynamic model of the interaction of interstellar wind with solar wind, and is thus also of independent interest. It is solved using an explicit through divergence scheme of third-order approximation. The analysis focuses on formation and stability of the structure of discontinuity surfaces and convergence to the stationary solution. The results are compared qualitatively and quantitatively with solutions obtained by other methods. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996, pp. 125–128.     

Compressible gas flow inside a cylindrical channel with a source on the channel axis

The article solves the problem of compressible nonviscous gas flow inside a cylindrical channel in the presence of a source on the channel axis. The cases considered include a supersonic spherically symmetrical source and a hypersonic source modeling jet flow. The numerical solution is obtained by two methods: one method treats the flow singularities (shocks, etc.) in explicit form, while the other uses the “through calculation” procedure. The solution is applied to analyze the physical flow pattern and the distribution of gasdynamic parameters in the shock layer, in particular on the channel walls. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 169–180.     

Using completely implicit methods to solve the direct problem of nozzle theory

An iterative method from the class of completely implicit methods (CIM) is proposed for solving the equation of the velocity potential of elliptical-hyperbolic type. The advantage of the proposed method compared to other CIM schemes is demonstrated in application to mixed perfect gas flows in a nozzle of a given shape. Accuracy issues, rate of convergence, and various techniques of ensuring stability in the hyperbolic region are discussed. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996, pp. 39–51.     

Supersonic longitudinal flow past a cylinder in the presence of a second coaxial cylinder in the wake

The compressible-gas complete Navier-Stokes equations are applied for a numerical analysis of the flow structure between two coaxial cylinders of equal radius set in tandem in a supersonic flow. The results for Re_∞=10⁴, M_∞=3 ω=0.75, Tw=1.08, when the distance between the coaxial cylinders is equal to two blunt-nose radii, show that the flow between the cylinders is subsonic and quasiperiodic. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 199–203.     

On a Control Problem for a Linear System with Measurements of a Part of Phase Coordinates

We consider a three-dimensional unsteady flow with a rotating detonation wave arising in an annular gap of an axially symmetric engine between two parallel planes perpendicular to its symmetry axis. The corresponding problem is formulated and studied. It is assumed that there is a reservoir with quiescent homogeneous propane–air combustible mixture with given stagnation parameters; the mixture flows from the reservoir into the annular gap through its external cylindrical surface toward the symmetry axis, and the parameters of the mixture are determined by the pressure in the reservoir and the static pressure in the gap. The detonation products flow out from the gap into a space bounded on one side by an impermeable wall that is an extension of a side of the gap. Through a hole on the other side of the gap and through a conical output section with a half-opening angle of 45°, the gas flows out from the engine into the external space. We formulate a model of detonation initiation by energy supply in which the direction of rotation of the detonation wave is defined by the position of the energy-release zone of the initiator with respect to the solid wall situated in a plane passing through the symmetry axis. After a while, this solid wall disappears (burns out). We obtain and analyze unsteady shock-wave structures that arise during the formation of a steady rotating detonation. The analysis is carried out within single-stage combustion kinetics by the numerical method based on the Godunov scheme with the use of an original software system developed for multiparameter calculations and visualization of flows. The calculations were carried out on the Lomonosov supercomputer at Moscow State University.     

Exact solution to the behavior of the electron plasma in a metal layer in an alternating electric field

Exact expressions are obtained for the first time for the response of the conduction electrons in a metal layer to an external alternating electric field. Case's well-known method of separation of the variables is modified, and the methods of singular integral equations and boundary-value problems of complex analysis are used. The solutions can be used to determined the screened field and also the absorption in a metal layer in a wide range of frequencies.N. K. Krupskaya Moscow Region Pedagogical Institute; Moscow Institute of Chemical Mechanical Engineering. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 90, No. 2, pp. 179–189, February, 1992.     

The probability function of a generalized poisson distribution and special polynomials

The probability function of a generalized Poisson distribution is written in terms of modified Hermite polynomials of 2nd kind in many variables. Their relationship is established with special polynomials previously derived for this purpose. The properties of the polynomials and the probability function are studied. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996. pp. 160–169.     

Investigation of the fiber packing density in a unidirectional composite

Recommendations are made for designing a unidirectional composite with an optimal arrangement of the fibers. The effect of the fiber diameter distribution law on the packing density is investigated.All-Union Scientific-Research Institute of Glass-Reinforced Plastics and Glass Fiber, Moscow. Moscow Institute of Electronic Machine-Building. Translated from Mekhanika Polimerov, No. 3, pp. 538–541, May–June, 1976.     

Simulation of oscillation modes in a supersonic unrated jet impinging on a cavity

The flow of a supersonic underexpanded jet past a cavity is analyzed numerically. Through difference schemes approximate to first, second, and third order are used. The focus is on oscillation modes and their effect on back-flow. Deceased. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 181–188.     

Nonlinear dynamical problem of a cyclinder with a slowly changing internal boundary

The problem of a hollow viscoelastic cylinder enclosed in an elastic shell is examined. The inside diameter varies. A nonlinear cubic theory is used to describe the relation between the stresses and strains in time. A vibration analysis is carried out for variable internal pressure.Moscow Institute of Electronic Machine Building. Translated from Mekhanika Polimerov, No. 2, pp. 274–280, March–April, 1973.     

An inverse problem for a system with a moving boundary

The problem of estimating the right-hand side of a nonlinear parabolic equation is considered. A finite-step algorithm based on the model positional control method and the finite element method is proposed. The algorithm is robust to informational noise and computational errors. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 23–33.     

Sudden buckling of the outer layer of a noncentrally compressed triple-layer rod

The stability of the outer nonmetallic layer of a triple-layer rod with foam core was studied both experimentally and theoretically by the energy balance method. The buckling of the outer layer occurs by a sudden transition to a nonadjacent equilibrium form and this process should be seen in regard to a set of deformational factors.Moscow State University for Ecology and Environmental Studies, Moscow, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 4, pp. 525–530, July–August, 1996.     

Axisymmetric excitation of a dielectric torus: Numerical solution

The article considers the mathematical model of a lens antenna in the shape of a homogeneous dielectric torus excited by an axial magnetic dipole. The boundary-value problem for an elliptical differential equation is posed and reduced by the fundamental solution method to an integral equation of 2nd kind over the torus section. A numerical algorithm is proposed, and the numerical results are compared with experimental findings. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 109–115.     

Initial stage of laser-induced crack development in polymethyl methacrylate

It is shown that the successive stages of development of the damage caused by a laser beam are the same in technically pure polymethyl methacrylate and the same material containing artificially introduced absorbing particles. The formation of the characteristic flat cracks from gas bubbles in the specimen is observed. The mechanism of fracture development in polymethyl methacrylate is further refined.Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 551–552, May–June, 1971.     

Development of integro-differential methods of parameter determination for a sum of exponential functions

We consider the problem of determination of decay decrements and amplitudes of exponential functions form observations with errors of the sum of these functions on a nonuniform grid. The integro-differential methods proposed by other authors lead to numerically unstable ill-posed problems, and make it impossible to estimate the errors in the results. New approaches are proposed that overcome these difficulties. The effectiveness of the proposed solutions is demonstrated. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University. Moscow, 1996, pp. 129–136.     

Development and analysis of a mathematical model of the Earth's upper atmosphere

Tomsk State University. Translated from Matematicheskoe Modelirovanie, Published by Moscow University, Moscow, 1993, pp. 122–138.     

Basis of a test procedure for anisotropic annular samples

The mixed boundary problem for an anisotropic ring loaded by semidiscs or semirings is discussed. A numerical analysis of the solution is given. The results can be used for evaluating results of tests on annular samples manufactured from anisotropic materials.Moscow Energy Institute. Translated from Mekhanika Polimerov, No. 1, pp. 171–175, January–February, 1972.