The following report was presented at plenary Session of the Final Scientific Conference'2001 of the Kazan Science Center RAS on January 28, 2002:

Gubaidullin D.A. Some problems of wave dynamics of multiphase media. Some problems of dynamics of multiphase media are considered. It is marked, that the investigation of wave dynamics of gas-droplets and liquid-bubbles systems with using a continuum model has achieved the most successes to date. Propagation of weak waves in polydispersed fogs in plane, spherical and cylindrical cases were considered. Some results are presented from calculation of the nonsteady discharge of liquified hydrocarbons during accidental depressurization of pipelines. A comparison is made between the discharge of the hydrocarbons and water.

The following reports were presented at section Sessions (chaired by Director of IME KazSC RAS Dr. Phys. & Math. Sc. D.A.Gubaidullin) on January 30, 2002:

Aganin A.A., Kosolapova L.A., Malakhov V.G. Stability of spherical shape of the gas cavity in the liquid under strong compression. The work is devoted to the study of conditions of steady-spherical compression of the gas bubble in the liquid as well as to the influence of deviations from spherical shape on the degree of its compression. It is assumed that the gas in the bubble is ideal and the liquid surrounding the bubble in the proximity of the bubble area (near field) is noncompressible and has small viscosity. The linear acoustic is used in the far field of the liquid. It has been shown that when taking into account compressibility of the liquid in the far field and the viscosity of the liquid in the near field the spherical shape of the bubble becomes more stable.

Аgаnin A.A., Smirnova E.Т. The supercompression of the gas bubble by pulse-periodic excitation. In the present work a method to increase the degree of the compression of the gas bubble during the one-bubble sonoluminescence by the pulse-periodic excitation is presented. This method is the combination of the single excitation of the travelling wave with the repeating excitation of the standing wave. It makes sense because the possibility of the bubble compression by the pulse excitation is broader than in periodic excitation. The results of calculations illustrating potential efficiency of the method of the pulse-periodic excitation are given.

Zaripov R.G., Galiullin R.G., Galiullina E.R. Nonlinear oscillations of aerosol in a closed tube. Rezults of experimental investigation of nonlinear oscillations of aerosol contained in long cylindrical tube are presented. Oscillations were generated by a plane piston, light-penetrance of medium governing particle concentration were registered by photo-transducer attached to the quartz section of a tube.Dependences of aerosol particle concentration on time for several frequency values including subharmonic resonance were obtained and dependence of coagulation time versus frequency. It has been revealed that as we approach the resonance coagulation time decreases by nonlinear law.

Fedyaev V.L., Mazo A.B., Morenko I.V. On simulation of the admixture motion in the vertical filters for water rough cleaning. A filter-trap for cleaning water from large admixture has been suggested. Its main elements are the cone filtering gauze and the reservoir for admixture collection. The math models of water flow and of particles motion were studied. The Lavrentiev's potential-vortex scheme was used for calculation of hydrodynamics. The equation of the particle motion takes into account the force of gravitation, carrying capacity, as well as the hydrodynamic drag. The slop of the cone gauze and the particles density were varied in the numerical investigations. Robust quality of the suggested filter-trap was confirmed by math modeling.

Mazo A.B. Modelling of separate flows of incompressible fluid at moderate Reynolds number.

Taldykin M.V. The waves tasks models in hydro- and biomechanics. The traction force, the self-propulsion velocity and the flow around a thin flexible plate performing a relatively large amplitude undulating motion was investigated using force gauge, velocity measurement system and flow visualization techniques. This undulating motion is a base of a fish, snake and microorganism propulsion in fluid at a wide range of Reynolds number. Some technical devices (inventions) for reducing a drag of a objects by means of travelling waves are discussed.

Khairullin M.Kh. Shamsiyev M.N., Sadovnikov R.V., Morozov P.Ye. On interpretation of hydrodynamic researches of vertical and horizontal wells by the methods of regularization. The inverse coefficient problem of determination of flow parameters with account of their dependence on pressure is considered in this work. The results of hydrodynamic researches are used as an input data. Algorithm of numerical solution is based on the method of descriptive regularization, that allows one to use additional information about the structure of required parameter by construction of a quasi-solution on the set of allowable functions.

Gabidullina A.N., Elesin A.V., Kadyirova A.Sh., Mazurov P.A. Estimation of aquifer parameters with using the sensitivity analysis. The concept of the sensitivity store has been proposed. It characterises the potential possibility of the parameters to minimization of residual function. The parameter can have the largest sensitivity but in this case it can possess a small sensitivity store regarding to other parameters. The possibility is shown how to use the information about the sensitivity store distribution according to the parameters for analysing the existing algorithms and designing new minimization ones.

Mazurov P.A. Tsepaev A.V. Superposition method for solution flow equation of fluid in three dimensional confined aquifer with partially penetrating wells. At present time development of the efficient algorithms of the solution of three-dimensional problems with large number of wells remains actual. One of the developing directions of similar problems decision are methods of division of solution domain and methods of division of general system of equations on subsystems. New type of agreement of solutions in areas near the wells and solution beyond of such areas is offered in given algorithm with use of the superposition principle.

Nikiforov A.I. Numerical simulation of oil displacement by water with an active additive on a nonstructured grid. The main goal of this work was to report of a numerical methodology using an unstructured finite volume method for the solution of two-phase filtration of poorly compressible fluids in oil reservoirs. The numerical model of oil displacement from a porous medium by a solution of an active additive of small concentration is developed. The algorithm relies on the well-known construction of the Delaunay triangulation and the Voronoi diagram. The prognosis of waterflooding process on Nurkeev oil field was exemplifyed.

Gilmanov A.N., Khismatullina N.A. A method for solving of supersonic gas dynamics problems based on implicit TVD schemes and adaptive-embedded meshes. New effective method and program package for solving steady two-dimensional gas dynamics Euler problems with singularities in curvilinear boundary domain are suggested. It is shown, that the implementation of strategies of combining implicit and explicit calculations used in the method allows us to reach the solution with given accuracy 5-11 times faster than on calculations using only explicit schemes.

Gilmanov A.N., Guseva T.S. Supersonic gas flow deceleration in a 2d channel with heat admission.

The following reports were presented at section Session (chaired by Deputy Director of IME KazSC RAS Dr. Phys. & Math. Sc. R.G.Zaripov) on January 31, 2002:

Ganeeva M.S., Moiseeva V.E. Deformation of shells of revolution with negative and positive Gauss curvature under the action of nonaxisymmetric loading. Numerical results for the hyperboloid of revolution of one nappe and the ellipsoidal shell prolated along an axis of rotation under nonaxisymmetric normal pressure have been obtained. The stress concentration areas of the hyperboloidal shell depending on a series of boundary conditions and geometrical characteristics have been established. The ellipsoidal shell stress concentration around the central hole has been investigated with respect to the hole radius and boundary conditions at the edges of the hole. Means of reducing the stress concentration have been proposed.

Yakupov N.M., Galimov Sh.K, Khismatullin N.I. (Nizhnekamskneftekhim Company). From immovable clumps to thin-wall designs. The most relevant phases of birth both development of building members and power schemes of designs are marked. The invention of concrete in Ancient Rome has become a start of broad usage of arch patterns and cupolas. In the architecture Islam countries the arches and cupolas with a composite delineation of a contour have appeared. The corrugated and two-layer cupolas have appeared. In the Middle Ages in Europe cupolas were increased by powerful arches. At the end of XIX centuries the thin-wall covers from a reinforced concrete have appeared. Metallical, including metallical membrane covers and also covers from a glass and metal were realized. The role of composite materials in further development is marked.

Yakupov N.M., Galyaviev Sh.Sh. (Nizhnekamskneftekhim Company), Nurullin R.G., Serazutdinov M.N. (Kazan State Technological University). Reference system for strengthening of a body of a cooling tower. Cooling towers of a type СК-1200, working in high-gravity conditions and located in exploitation without big repair more than 27 years, are in a unsatisfactory state. With the aim of preventing destruction and prolongation of a service, the strengthening of cooling towers by the installation of a reference system is recommended. The reference system is designed as a kind of a truncated cone and consists of elements which are formed a triangular network. Some versions of strengthening are analyzed. One of versions satisfying strength, economical and operational communication requirements, is realized for a cooling tower with a rejected vertical axis.

Zakirov U.N. The new chapter of a relativistic mechanics of jet propulsion. The dilated five-measurement theory Kaluza-Klein-Wesson's is offered within the framework of a Riemannian geometry, taking into account change of a specific localized mass and change of mass of charged attractive Centre. Such model allows one, not leaving frameworks of dimensionality of dilated spall, to take into account all builders of jet acceleration, lacquer gasdynamics and electromagnetic. The availability of a Hamiltonian for such system simultaneously allows us to develop an analitical mechanics of relativistic jet propulsion, including the analysis of nonlinear effects and stability of orbital motion of a charget variable particle.

Yakupov N.M., Galimov N.K., Leontiev A.A., Nurgaliev A.R. Investigation of a representation forms of a shell cupola at construction of deforming curves of films. The spherical and parabolic representation of the form of a cupola in representation of deforming curves of film material is investigated by experimental and theoretical method. The round diaphragm as a specimen is restricted between a matrix and punch of the special plant by hydraulic press. The specimen in loading by air is swelt. Arresting given pressure and hoisting height of a diaphragm in its center and using ratio of a non-linear shell theory and the plasticities, curves of deforming are plotted.

The following report was presented at the Scientific Seminar "Problems of Continuum Mechanics" on December 19, 2001:

Khismatullina N.A. Increasing efficiency of numerical solution of gas dynamics equations. On materials of thesis for Candidate of Sciences Degree, speciality: 05.13.18 - Mathematical simulation, numerical methods and program packages. Reviewer: PhD (Phys.&Math.) Nikiforov A.I. An effective method of numerical solution of Euler equations using implicit finite-difference schemes on adaptive-embedded meshes is presented. A number of strategies for combination implicit and explicit methods are developed. This method is realized as a computer programs. Executed test computations confirm the efficiency of presented programs and method in comparison with explicit methods.