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 heatconductivity 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 bubble 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 heatconductivity on the air bubble collapse in water are presented for various excitation amplitudes with using different 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 movement of the piston have been stated; features of nonlinear oscillations of the gas column in the closed tube under the nonperiodic 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 orifice 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, speciality: 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 interaction on the rheologycal properties of a continuum were discussed in the report. The author studied 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 breaking. The author suggested a new analytical method of solving the problem of hydrodynamic interaction 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 harmonically displacing plane piston in the open tube, in the neighbourhood of linear and nonlinear resonances. 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 basis 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 algorithmization 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 twodimensional channel with separating boundary layer. On materials of thesis for Candidate of Sciences Degree, speciality: 01.02.05  Mechanics of liquid, gas and plasma. Reviwer: PhD Aganin A.A.
The phenomenon of supersonic laminar flow deceleration in a twodimensional channel is simulated. A method combining a secondorder difference scheme and dynamically adaptive grids is used to solve the NavierStokes equations. A zone method based on the concept of viscousinviscid interaction is presented.
 Scientific Seminar 
Potential participants are kindly invited for the presentation of their results at the Seminar.
2001
