Neumann Boundary-Value Problem for a Singularly Perturbed Heat Equation with Pulse Action

We propose an algorithm for the construction of an asymptotic solution of the Neumann boundary-value problem for a singularly perturbed heat equation with pulse action at fixed times. A theorem on the order with which the asymptotic solution satisfies the original problem is proved.__________Translated from Neliniini Kolyvannya, Vol. 8, No. 1, pp. 89–122, January–March, 2005.     

Gas-dynamic calculation of pulsating flow in pipelines

A numerical solution is examined for a system of equations of one-dimensional isothermal flow of a perfect gas in a horizontal pipe with a periodically varying function of the flow rate at the boundary. The numerical solution is compared with the solution of the linearized problem. The results can be used to calculate the pulsating motion of gas in the pipeline systems of piston compressors [1].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 85–88, July–August, 1972.     

Application of potential theory to a problem of the limiting configuration of the stagnant zones in the displacement of viscoplastic oil by water

A solution of the problem of determining the limiting-equilibrium portions of residual viscoplastic oil in connection with the displacement of oil by water from a porous formation in a multiwell system is constructed by the methods of potential theory and analyzed. The results of a comparison with a standard exact solution are presented for certain asymptotic cases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 182–185, January–February, 1989.     

Flow and heat transfer of a viscous fluid when there is a phase transition

A study is made of the problem of the flow and heat transfer of a fluid formed by the phase transition (melting or sublimation) when the end of a rod touches a heated surface. Problems of this kind arise, in particular, when a heated surface is cooled by means of the heats of the phase transitions of materials with an energy content. A solution is obtained to a simplified system of heat and mass transfer equations obtained by estimating the order of magnitude of the various terms in the Navier-Stokes equations in a manner similar to that in [1–3]. The parameters that govern the process are identified, and an approximate analytic solution is found for the quasi-stationary case. The analytic solution is compared with a numerical solution obtained iteratively.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 128–131, May–June, 1931.     

Nonlinear steady-state motion of an elastic plate floating on the surface of a liquid of infinite depth

The nonlinear problem of steady-state waves in an ideal fluid of infinite depth with a thin elastic plate floating on its surface is considered. The solution is found by a perturbation method. Three approximations are obtained. A case of branching of the solution is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 119–123, March–April, 1987.     

Numerical simulation of the unstable motion of a slug of polymer solution in a porous medium

The numerical solution to the problem of unstable motion of a slug of polymer solution in a porous medium is considered. The influence of various factors on the simulated flows is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 88–93, September–October, 1981.     

Nonlinear far field in the case of transonic flow past a nonlifting profile

A new analytic solution is constructed for the nonlinear transonic equations describing the irrotational far flow field (with two symmetry axes) in the case of transonic flow past a nonlifting profile. With increasing distance from the profile, the nonlinear field goes over continuously into the field of the linear theory. The solution is expressed in terms of an elliptic Weierstrass function.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 171–173, Novembe–December,1982.     

Integral approach to the solution of problems of free interaction

An integral approach to the solution of free-interaction problems that uses integral moment relations for the viscous sublayer is proposed. The method is tested on the solution of a laminar separation problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 99–104, January–February, 1984.     

Dispersion of a gas cloud with de-excitation. Self-similar solution

A solution of the problem of cloud dispersion in a vacuum with de-excitation is obtained by the method of separation of variables in a Lagrange coordinate system. The energy equation corresponds to the de-excitation of an optically thin volume with a power-law dependence of the radiativity on the density and temperature. The self-similar solution is examined.Translated from Izvestiya Akademii Nauk SSSR, Mekhani'ka Zhidkosti i Gaza, No. 6, pp. 128–131, November–December, 1971.     

Flow of rarefied gas past a sphere in the presence of blowing from its surface

Flow of a rarefied gas past a sphere with various conditions of blowing on the surface is considered. The investigation is based on numerical solution of model kinetic equations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 182–185, September–October, 1982.     

Hurling of shells by hollow charges

Results of the numerical solution of the problem of one-dimensional hurling of shells by hollow explosive charges are elucidated. The results of the numerical solution are compared with asymptotic formulas. Numerous domestic and foreign papers have been devoted to the question of hurling shells by explosive charges. A numerical solution of the problem of convergence of a ring to the center under the effect of detonation products is presented in [1–3]. The problem of hurling a shell by a hollow explosive charge with an internal lining is considered in [4]; the solution of the problem of hurling a shell by a hollow explosive charge without the cavity lining is presented in [5] on the basis of the energy-balance equations; however, the complete picture of the processes occurring in the detonation products is not considered.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 161–166, May–June, 1976.     

Heat and mass transfer with natural convection at a vertical porous surface,with blowing of carbon dioxide into air

This paper gives the results of a numerical calculation of a laminar boundary layer with the free convection of a binary mixture of carbon dioxide and air at a vertical heated surface. It compares the numerical solution with an approximate analytical solution and with experiment.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 122–125, November–December, 1971.     

Solution of the inverse problem of thermal conductivity for a melting slab with entrainment

This article proposes an approximate solution to the inverse problem of the Stefan type for a finite region with arbitrary boundary and initial conditions. A comparison with exact solutions is made.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 132–137, May–June, 1973.     

Solution to problem of strong evaporation of a monatomic gas by the Monte Carlo method

The Monte Carlo method has been used to obtain a numerical solution to the problem of strong evaporation of a monatomic gas in which the molecules are modeled by pseudo-Maxwellian and hard spheres. A comparison with the results of other authors is made. The results agree well with the solution of the problem obtained on the basis of the model Bhatnagar—Gross—Krook kinetic equation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 185–188, January–February, 1984.I should like to thank M. N. Kogan for discussing the results.     

Plane problem of uniform flow of a two-layer fluid past a circular cylinder

An explicit solution is found for the problem of uniform horizontal flow of a two-layer fluid of infinite depth past a circular cylinder. The cylinder axis is perpendicular to the flow. The problem is solved within a linear formulation. The solution of the problem is expressed in the form of rapidly converging series with coefficients determined from a recurrence relation. The first seven terms of the series yield the values of the hydrodynamic loads with a relative accuracy of 10^–6. The results are in good agreement with the known values for similar problems in a homogeneous fluid. Tables of the lift and wave drag are given for homogeneous and two-layer fluids.Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 91–97, January–February, 1996.     

Some plane adiabatic ideal gas flows containing shocks

We obtain the solution describing adiabatic flows of an ideal gas characterized by the two parameters a and b such that [a]=L ^m+1 T ^–1, [b]=ML ^–2–2m where m is arbitrary (m > 0).h This solution permits the construction of flows containing shocks.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 10, No. 3, pp. 71–73, May–June, 1969.     

Investigation of the transitional process of the startup of a gas bearing

In this article we derive equations for transitional conditions of a gas lubricant under nonisothermal conditions. A numerical solution of the Reynolds equation is described for the problem of the pulsed startup of a radial bearing with a fixed geometry, and the results of this solution are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 156–160, September–October, 1977.     

Nonlinear problems of the thermal conductivity equation

The asymptotic behavior of solutions of parabolic equations at infinite times has been investigated for various cases [1–6]. Two initial boundary-value problems are considered in this paper. The solution of the thermal conductivity equation with a nonlinear right-hand side is found, including also nonlinear boundary conditions. It is shown that the solution of the corresponding problem tends either to a stable, steady-state solution, or to a periodic solution, depending on the initial values of the functions and constants appearing in the conditions of the problem. Other papers [7, 8] are devoted to finding the periodic solutions of these two problems encountered in hydrodynamics (diffusion, underground hydrodynamics), and to studying the asymptotic behavior of the corresponding initial boundary problems.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 123–128, May–June, 1972.     

Structure of weak shock waves with phase transitions of the first kind

An analytic solution is found to the problem of the structure of weak shock waves with phase transitions of the first kind; it is based on the use of the Mandel ' shtam—Leontovich—D ' yakov concept of second viscosity. The kinetic and thermodynamic characteristics of the problem are investigated, and also the condition of applicability of the second viscosity concept. It is shown that the obtained solution simplifies considerably if the vapor phase is regarded as a perfect gas. The results of calculations for the water—water vapor system are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 55–62, July–August, 1980.     

Quasi-three-dimensional calculation of flow in blade passages of turbines

The flow in turbomachines is currently calculated either on the basis of a single successive solution of an axisymmetric problem (see, for example, [1-A]) and the problem of flow past cascades of blades in a layer of variable thickness [1, 5], or by solution of a quasi-three-dimensional problem [6–8], or on the basis of three-dimensional models of the motion [9–11]. In this paper, we derive equations of a three-dimensional model of the flow of an ideal incompressible fluid for an arbitrary curvilinear system of coordinates based on averaging the equations of motion in the Gromek–Lamb form in the azimuthal direction; the pulsation terms are taken into account in the equations of the quasi-three-dimensional motion. An algorithm for numerical solution of the problem is described. The results of calculations are given and compared with experimental data for flows in the blade passages of an axial pump and a rotating-blade turbine. The obtained results are analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 69–76, March–April, 1991.I thank A. I. Kuzin and A. V. Gol'din for supplying the results of the experimental investigations.