. .
Main page
Personal pages

Professor Anvar N. Gil'manov

Brief description and some results of the numerical method intended for simulation of viscous gas flows is given here. This method enables one to solve internal and external gas dynamics problems at supersonic and subsonic regimes of an inviscid or viscous gas flow.

The method represents a combination of a second order of accuracy scheme with geometrically and dynamically adaptive grids. Geometrically adaptive grids are curvilinear grids adjusted to the curvilinear internal or external boundaries of computational domain (fig. gg). In non-stationary problems the geometrically adaptive grids are usually moving. Depending on the problem the dynamically adaptive grids can be adaptive-moving (fig.gm) and/or adaptive-embedded (fig.ge). The adaptive-moving grids consist of a fixed number of cells, which are redistributed from their initial position to collect in zones of large gradients of gas dynamic variables. The disadvantages of methods of moving grids consist in fact that in a series of cases there appear large distortions of the grids in some zones. This leads to the loss of accuracy of the solution in those zones. Unlike the methods of moving grids the methods of embedded grids are much more complicated from the viewpoint of algorithm and programming since their structure is not homogeneous. Computations on adaptive-embedded grids need special organization of the data structure (fig.str).

To check the efficiency of the technique the following test problems were solved: interaction of a shock wave with a contact discontinuity and with a rigid wall; collision of two shock waves of equal intensity; interaction of explosive waves of different intensity; a behavior of a fixed shock wave on a moving grid; nonlinear gas oscillations in a pipe. Solutions obtained to all listed problems are in gratifying agreement with those known in literature.

Thus the method of solution of internal and external gas dynamic problems is based on:

  • The TVD difference scheme of the second order of accuracy on smooth solutions;

  • Geometrically adaptive grids (fig.gg);

  • Dynamically adaptive-moving (fig.gm) or/and adaptive-embedded grids (fig.ge).

  • Three examples of solution of challenges of gas dynamics are presented below.

    1. Deceleration of supersonic viscous gas flow in a model inlet. The complicated structure of the flow with separations of boundary layer in inlet found in this problem is shown in the fig.in_m-in_r.

    2. Boundary layer separation by action of an oblique shock. Comparison with experimental data confirms the high accuracy and reliability of numerical data obtained on the basis of the presented technique. The lines of equal density are shown on fig.owr.

    3. Deceleration of supersonic viscous gas flow in the flat channel ("pseudo-shock") (fig.psch). It was found that in dependence of the outlet pressure the flow can be supersonic or subsonic.



    CV of Professor Anvar N. Gil'manov

    Date of Birth:

    · November 19, 1948


    · Doctor of Sciences (Application of computers, mathematical simulation and mathematical methods to scientific research problems in physical and mathematical sciences), Institute of Applied Mathematics of the Russian Academy of Sciences (RAS), Moscow, 1996

    · Candidate of Sciences (Ph.D.) (Mechanics of Liquid, Gas and Plasma), Institute of Theoretical and Applied Mechanics, RAS, Siberian Branch, Novosibirsk, 1982

    · Student at the Moscow State University, Department of Physics, Moscow, USSR, 1967-1973


    · Professor, Faculty of Theoretical Foundation of Heat Power Engineering, Kazan Energy Power Institute, Kazan, RUSSIA, 1996-1999.

    · Head of Laboratory, Inst. of Mechanics and Engineering, Kazan Scientific Center, the Russian Academy of Sciences (IME KSC RAS), Kazan, RUSSIA, 1989-1996.

    · Senior Researcher, IME KSC RAS, Kazan, RUSSIA, 1981-1989.

    · Junior Researcher, IME KSC RAS, Kazan, RUSSIA, 1975-1981.


    · Principal investigator, Grant (N 96-01-00483) of the Russian Foundation of Basic Research for group of 5 researchers, 1997-1998.

    · Principal investigator, Grant (N 98-01-00257) of the Russian Foundation of Basic Research for group of 5 researchers, 1998-2000.

    Research Experience:

    · Mathematical simulation; Computational Fluid Dynamics; Numerical Methods; Laminar and Turbulent Flows; Finite Difference Schemes; Adaptive Grids

    Experience of Reading of the Lectures:

    · Mechanics of Liquid and Gas, 1996-1999.

    · Computational Gas Dynamics, 1998-1999.

    Recent & Relevant Publications:

    1. Deceleration of a supersonic laminar gas flow in a pseudo-shock, (coauthor A.M.Panova). Russian Journal of Mechanics of Liquid and Gas, 1999, (in press).
    2. The locally - characteristic approach in the difference scheme of the increased order of approximation. Russian Journal of Computational Mathematics and Mathematical Physics, 1999, (in press).
    3. Application of dynamically adaptive grids to a research of separation flows. Russian Journal of Computational Mathematics and Mathematical Physics, 1999, (in press).
    4. Numerical simulation of gas flow with separation at high Reynolds numbers. Numerical Modelling in Continuum Mechanics. The third Summer Conference, Prague. Part II. 8-11 September 1997. P.298-305.
    5. Numerical simulation of a viscous gas flow in a supersonic inlet. Proceedings the Second International Conference on Hydrodynamics, Hong Kong, 1996, P.601-606.
    6. Numerical simulation of deceleration of a gas flow in a supersonic inlet, (coauthor N.A. Kulachkova), Aviation techniques, Kazan, 1996, N4, pp.26-32 (in Russian), This Journal is translated into English as Russian Aeronautics, Allerton Press, USA.
    7. A numerical research of two-dimensional gas flow with shocks by a TVD method on physically adaptive grids, (coauthor N.A.Kulachkova), Journal of Mathematical simulation, 1995, Vol.7, N.3, pp.97 - 106 (in Russian).
    8. TVD method and adaptive-embedded grids in the problems of supersonic gas dynamics, (coauthor N.A.Kulachkova), Issues of Atomic Science and Engineering. Mathematical Simulation of Physical Processes, 1995, Vol.1-2, pp.72-79 (in Russian).
    9. Numerical investigation of supersonic flows by TVD method on adaptive grids (coauthor N.A.Kulachkova), Abstracts of the International Conference "Advanced Mathematics, Computations and Applications", Novosibirsk, Russia, 20-24 June 1995, p.124.
    10. On an approach to calculating hypersonic inlets, (coauthor N.A.Kulachkova), Abstracts of TsAGI's Workshop-school "Research in Hypersonic Flows and Hypersonic Technologies". Zhukovsky, Russia. 19- 21 September 1994, Section 5, pp.6-8.
    11. Investigation of strong viscous/inviscid shock-boundary layer interaction in a hypersonic inlet, (coauthor N.A.Kulachkova.), Abstracts of the International Conference "Fundamental Research in Aerospace Science". Zhukovsky, Russia. 22-24 September 1994, Section 4, pp.18-20.
    12. A research of a separation of a supersonic gas flow at a flow around cylinder (coauthor A.A.Il'ushin), Journal of Simulation in Mechanics, Novosibirsk, 1988, Vol.2, N1, pp.26-34 (in Russian).
    13. Numerical simulation of interaction of gas flow with moving bodies of variable geometry, (coauthor A.A.Aganin and V.B.Kuznetsov), Numerical Methods of a Mechanics of a Continuous Medium. Novosibirsk, 1986, Vol.17, N 6, pp.3-11 (in Russian).
    14. An Arbitrary Lagrangian - Eulerian method in the nonlinear problems of interaction of elastic bodies with a gas flow, (coauthor J.M.Sakhabutdinov). "Interaction of envelopes with fluid". Proceedings of seminar, Kazan Phys.-Technical Inst., 1981, N 14, pp.127-145 (in Russian).
    15. Dynamics of impact interaction of a soft spherical shell with a wall. "Nonlinear problems in aeroelasticity". Proceedings of seminar, Kazan Phys.-Technical Inst., 1979, N 11, pp.98-114 (in Russian).


    | Presidium RAS | Kazan Science Center RAS | ??????.???????