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Scientific Seminar
"Problems of Continuum Mechanics"
The abstracts of the reports 1999

3 November 1999
Aganin A.A. Numerical simulation of gas bubble dynamics in liquid. An efficient method of computation of spherically symmetric dynamics of a bubble in liquid with account of heat-conductivity of both media is proposed. Efficiency of this method results from the use of gasdynamic equations to describe the motion of the gas and the liquid only in the bub-ble collapse stage which is relatively short in time but fast duration. In the rest part of the period which is relatively long in time but slow in duration some approximations to the gasdynamic equations rather than those equations themselves are employed to describe the motion of the gas and the liquid. Criteria of transition from the approximations to the full system of equations are given. Results of application of this method to investigation of influence of heat-conductivity on the air bubble collapse in water are presented for various excitation amplitudes with using differ-ent equations of state.

16 November 1999
Aganin A.A. Nonlinear gas oscillations in domains with moving boundaries. On materials of thesis for Doctor of Sciences Degree, speciality: 01.02.05 - Mechanics of liquid, gas and plasma. Reviwers: DrSc Gilmanov A.N., DrSc Zaripov R.G. A technique of numerical simulation of nonlinear gas oscillations in domains with moving boundaries has been developed on the basis of gasdynamic equations in the conservation form; a model of dynamics of a gas bubble in a liquid has been proposed, combining the gasdynamic equations and their approximations; features of influence of gas - heating by shock waves on the development of nonlinear oscillations of the gas column in the closed tube under periodic move-ment of the piston have been stated; features of nonlinear oscillations of the gas column in the closed tube under the non-periodic resonant excitation have been revealed; features of collapse of a spherical gas bubble in the course of its oscillations in the center of a spherical liquid volume have been investigated; numerical simulation of the mean flows and the waves near the exit ori-fice of volume resonators has been performed for the first time; numerical simulation of the gas pulsations in the external field of an open resonant tube has been made for the first time.

24 November 1999
Martynov S.I. Interaction of particles in suspensions. Mordov State University, Saransk. On materials of thesis for Doctor of Sciences Degree, special-ity: 01.02.05 - Mechanics of liquid, gas and plasma. Reviwer: DrSc Mazo A.B. Theoretical investigation of interaction of particles in suspensions and the affect of such interac-tion on the rheologycal properties of a continuum were discussed in the report. The author stud-ied two mechanisms of interaction of particles: an electric interaction and a hydrodynamic one. The first mechanism defines coagulation of particles and the aggregates creation in liquid. The second mechanism takes into account the liquid viscosity. It is responsible for aggregate break-ing. The author suggested a new analytical method of solving the problem of hydrodynamic in-teraction of hard particles as well as elastic ones. He obtained new equations for coagulation and breaking of aggregates, solved a number of practical problems of effective viscosity definition for various flow types.

1 December 1999
Zaripov R.G. , Davydov R.I., Sonin N.V. Nonlinear gas oscillations in the open tube. Longitudinal nonlinear gas oscillations have been studied experimentally, excited by harmoni-cally displacing plane piston in the open tube, in the neighbourhood of linear and nonlinear reso-nances. The results of experimental studies of an outer field of waves emitted out of the open end of the tube are reported. Maximum velocity amplitudes are found to occur in the near wall region close to the open end. The jet core in axial direction of the outer field of waves examined.

1 December 1999
Gimadiev R. Sh. About an algorithm of the plane statement problem of elasticity boundary element method. Static problem of deformation of linearly elastic body is considered on the ba-sis boundary element method (bondary integral method). Numerical modeling of deformation of body of various form: rectangle, triangle, wing homogenious profile are reported. Accuracy of numerical results is analysed. Further development of the model used is associated with algo-rithmization of the plane dynamic problem of elasticity. Fundamental solutions for displacement obtained by Eringen A.C. and Suhubi E.S. are the basis to derive stresses on the boundary and the values of the derivative of the displacement with respect to time present in the main boundary equation.

28 December 1999
Panova A.M. Investigation of supersonic viscous gas flow deceleration in a two-dimensional channel with separating boundary layer. On materials of thesis for Candidate of Sciences De-gree, speciality: 01.02.05 - Mechanics of liquid, gas and plasma. Reviwer: PhD Aganin A.A. The phenomenon of supersonic laminar flow deceleration in a two-dimensional channel is simu-lated. A method combining a second-order difference scheme and dynamically adaptive grids is used to solve the Navier-Stokes equations. A zone method based on the concept of viscous-inviscid interaction is presented.

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