Department of applied mathematical physics

(Head: Prof. A. Tolstykh)

Tel.:(095) 135 6280
Fax: (095) 135 6159


General activity

  1. Investigations in the areas of numerical analysis, the Monte-Carlo methods, the boundary value problems theory, the theory of functions of complex variables and functional spaces aimed at solving problems of applied mathematical physics.
  2. Development of high accuracy numerical & analytical methods for equations of mathematical physics including equations of fluid dynamics, magnetohydrodynamics, elasticity, electrodynamics etc.
  3. Solving applied problems concerning numerical simulation complicated physical and mechanical phenomena.

Subdepartment of applied hydrophysic

The main section activity concerns with development, justification and applications of high-order difference schemes based on compact non-centered (upwind) differencing (CUD) for hyperbolic parts of convection-diffusion equations, special emphasize being placed on incompressible and compressible Navier-Stokes and Reynolds equations.

The computational practice and comparisons with traditional schemes have shown that such an approach can provide increase of accuracy for fixed grid point numbers measured by order (or orders) of magnitude. As a rule, no monotonization devices are needed with applying CUD methods.

The recent ideas and their implementations include:


The developed techniques are applied (or planned to be applied) to CFD problems.

They are, in particular:


Applied problems which the division concerns with are:

Main recent publications

  1. A.I. Tolstykh, High Accuracy Non-centered Compact Difference Schemes for Fluid Dynamics Applications. World Scientific, p. 314, (1994).
  2. A.I. Tolstykh and D.A. Shirobokiv, Fifth order compact upwind method and its applications to three-dimensional compressible Navier-Stokes equations, Computational Fluid Dynamics Journal, N 5, pp. 425-438, (1997).
  3. A.I. Tolstykh, M.V. Lipavskii, On performance of methods with third- and fifth-order compact upwind differencing. J. Comput. Phys. N 140, pp. 205-232 (1998).
  4. A.D.Savel'ev, Implicit method for turbulent compressible flow c calculations, N 38 c. 522-533 (1998).
  5. V.N.Koterov, A.D.Savel'ev, A.I.Tolstykh’ Numerical simulation of aerooptics fields near open ports of airborne observatory (in Russian), Matematicheskoe modelirovanie, N 9,p. 27-39 (1997).
  6. A.I.Tolstykh, Two-Step fifth-order methods for evolutionary problems with positive operators. Positivity N 2, pp. 193-219 (1998).
  7. Yanitskii V.E., Serikov V.V. Multicomponent rarefied gas weighting algorithm for Monte Carlo simulation. In Proc. 2nd Japan-Soviet Union Joint CFD Symposium. Tsukuba, Japan. 1990. V. 2 P. 36-43.
  8. Yanitskii V.E. Operator approach to direct Monte Carlo simulation theory in rarefied gas dynamics. In Proc. 17th Int. RGD Symposium, Aachen,Germany, 1991, P. 770-777.
  9. Yanitskii V.E. Stochastic Model of a Boltzmann Gas and Its Numerical realization. In book: Modern Problems in Computational Aerohydrodynamics. Ed. A.A.Dorodnicyn and P.I.Chushkin. Mir Publishers, Moscow, 1992. P. 339-355.
  10. Yanitskii V.E., Ivanov S.A. Direct Monte Carlo simulation of free turbulence. In Proc. 5th Japan-Soviet Union Joint CFD Symposium. Sendai, Japan, 1993. V. 2. P. 385-390.
  11. Azarova O.A., Samsonov A.V., Shtemenko L.S., Shugaev F.V. and Yanitskii V.E. Motion of a shock wave through a gas with random inhomogeneities. Proc. of the Symp. on Shock waves. (March, 14-16, 1996. Tokyo, Japan) Tokyo University of Technology, 1996. P. 579-581.
  12. Azarova O.A. and Yanitskii V.E. Shock wave propagation in gases with random non-uniformities. Proc. of the 20th Int. RGD Symp. Beijing, China, Peking University Press, 1996.

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