(in Russian)

• Development of physical models in kinetics, statistical physics, rarefied gas dynamics and investigation of non-equilibrium flows
• Development of modern & efficient numerical methods for the Boltzmann kinetic equation and other kinetic equations
• Numerical methods for evolution equations in general
• Development & implementation of numerical methods for hyperbolic conservation laws
• Development & implementation of efficient parallel algorithm for computational mechanics on high-performance machines with shared and distributed memory as well as graphical accelerators.

       The sector has ongoing collaboration with a number of universities and industrial companies from Russia, Italy, the UK, Germany and the USA.

• Professor, V. V. Aristov, Head of the Subdepartment
• Dr. S. A. Zabelok, senior researcher
• O. V. Ilyin, junior researcher
• Dr. I. N. Larina, senior researcher
• Dsc, Dr.  S. P. Popov, leading researcher
• Dr. V. A. Rykov, leading researcher
• Dr. V. A. Titarev, leading researcher
• Dsc, Dr. F. G. Tcheremissine, principle researcher

• Professor A. M. Bishaev
• Dr. E. F. Limar
• Dsc, Dr. A. A. Nikolskiy
• Professor E. M. Shakhov

• E. M. Shakhov. Method of investigation of rarefied gas flows. M.: Nauka, 1974, 207 p. (in Russian).
• V. V. Aristov, F. G. Tcheremisine. Direct numerical solution of the Boltzmann kinetic equation, Computing Center, Moscow, 1992, 192 p.
• V. V. Aristov. Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows. Kluwer Academic Publishers. Dordrecht / Boston / London, 2001, 294 pages.
• V. A. Aristov, Z. A. Zabelok. Application of direct solution method of the Boltzmann equation for modeling of non-equilibrium gas effects. Computing Center of RAS, Moscow, 2010. 144 pages.

1. Yu.Yu. Kloss, D.V.Martynov, and F.G. Cheremisin (2012). Computer Simulation and Analysis of the Holweck Pump, Technical Physics, 2012, Vol.57, N.4, pp. 451-456, Pleiades Publishing, Ltd.
2. F.G. Tcheremissine (2012). Method for Solving the Boltzmann Kinetic Equation for Polyatomic Gases. Comp. Math. and Math. Physics. pp.252-268, Pleiades Publishing, Ltd, 2012.
3. V. A. Titarev and E. M. Shakhov (2012). Computational study of a rarefied gas flow through a long circular pipe into vacuum. Vacuum, Special Issue ``Vacuum Gas Dynamics'', in press.
4. V. A. Titarev and E. M. Shakhov (2012). Efficient method of solution of a problem of rarefied gas flow in a planar channel of large finite length. Computational Mathematics and Mathematical Physics. V. 52, , N 2 pp. 269-284.
5. V. A. Titarev (2012). Implicit high-order method for calculating rarefied gas flow in a planar microchannel. Journal of Computational Physics, V. 231, pp. 109-134.
6. V. A. Titarev (2012). Efficient deterministic modelling of three-dimensional rarefied gas flows, Communications in Computational Physics, V. 12, , N 1 pp. 162-192.

1. V.V.Aristov., A.V.Stroganov. A method of formalizing computer operations for solving nonlinear differential equations // Applied Mathematics and Computation. 2011 (in press)
2. O. V. Ilyin. Steady solutions of the Broadwell kinetic model (accepted)
3. O. V. Ilyin. The analytical solutions of 2D stationary Broadwell kinetic model, J. Stat. Phys. (in press).
4. O. V. Ilyin. A new exact solution for a discrete kinetic model. Theoretical and mathematical physics (in press).
5. V. V. Aristov, O. I. Rovenskaya (2011) Application of the Boltzmann kinetic equation to the eddy problem. Computers & Fluids, V. 50, pp. 189-198.
6. V. V. Aristov, A. A. Frolova, S. A. Zabelok (2011) Supersonic flows with nontraditional transport described by kinetic methods. Communications in Computational Physics (in press).
7. Yu. Yu. Kloss, V. V. Ryabchenkov, F. G. Tcheremissine, P. V. Shuvalov (2011). Interaction of shock wave with a boundary layer inside a micro channel. Mathematical modeling, V. 23, N. 4, p. 131-140.
8. V. A. Rykov, V. A. Titarev and E. M. Shakhov (2011). Rarefied Poiseuille flow in elliptical and rectangular tubes. Fluid Dynamics, V. 6, N. 3, pp. 456-466.
9. V. A. Titarev and D. Drikakis (2011). Uniformly high-order schemes on arbitrary unstructured meshes for advection-diffusion equations. Computers & Fluids. V. 46, N. 1, pp. 467-471.
10. V. V. Aristov and M. V. Panyashkin (2011) Study of spatial relaxation by means of solving a kinetic equation. Computational Mathematics and Mathematical Physics, V. 51, N 1, pp. 122-132.
11. V. V. Aristov. (2011). The gravitational interaction and Riemannian geometry based on the relational statistical space-time concept. Gravitation & Cosmology. V. 17, N 2, pp. 166-169.

1. I. N. Larina and V. A. Rykov (2010). Kinetic model of the Boltzmann equation for a power-law intermolecular interaction potential. Computational Mathematics and Mathematical Physics, V. 50, N. 3, pp. 519-530.
2. I. N. Larina and V. A. Rykov (2010). Kinetic model of the Boltzmann equation for a diatomic gas with rotational degrees of freedom. Computational Mathematics and Mathematical Physics. V.  50, N. 12, pp. 2118-2130.
3. Anikin Yu. A., Derbakova E. P., Dodulad O. I., Kloss Yu. Yu., Martynov D. V., Rogozin O. A., Shuvalov P. V., Tcheremissine F. G. (2010) Computing of gas flows in micro- and nanoscale channels on the base of the Boltzmann Kinetic equation. Procedia Computer Science, N. 1, P. 735–744.
4. O. I. Dodulad, Yu. Yu. Kloss and F. G. Tcheremissin. (2010) Shock wave falling on a flat barrier that contains micro shells. Physico-chemical kinetics in gas dynamics. N. 10. p. 18.
5. Yu. Yu. Kloss, D. V. Martynov, F. G. Tcheremissin (2010). The Development of the Methods of Computer Simulation and Analysis of a Knudsen Micropump. Information Technologies, N. 10, pp. 30-35.
6. Yu. Yu. Kloss and F. G. Cheremisin and P. V. Shuvalov (2010). Solution of the Boltzmann equation for unsteady flows with shock waves in narrow channels, Computational Mathematics and Mathematical Physics, V.  50, N.  6, pp. 1093–1103.
7. Yu. A. Anikin and Yu. Yu. Kloss and D. V. Martynov and F. G. Tcheremissine (2010). Computer simulation and analysis of the Knudsen experiment of the 1910 year. Journal of nano and microsystem technique. N.  8, pp. 6-14..
8. P. Tsoutsanis, V. A. Titarev and D. Drikakis (2010). WENO schemes on arbitrary mixed-element unstructured meshes in three space dimensions. Journal of Computational Physics, V. 230, P. 1585 – 1601.
9. V. A. Titarev and E. M. Shakhov (2010). Non-isothermal flow in a long channel on the basis of S-model kinetic equation. Computational Mathematics and Mathematical Physics. V. 50, N. 12. P. 2131-2144.
10. V. A. Titarev (2010). Implicit numerical method for computing three-dimensional rarefied gas flows using unstructured meshes (2010). Computational Mathematics and Mathematical Physics. V. 50, N. 10, pp. 1719–1733.
11. V. A. Titarev and E. M. Shakhov (2010). Kinetic analysis of the isothermal flow in a long rectangular microchannel. Computational Mathematics and Mathematical Physics. V. 50, N. 7, pp. 1221–1237.
12. V. A. Titarev, P. Tsoutsanis and D. Drikakis (2010). WENO schemes for mixed-element unstructured meshes. Communications in Computational Physics, Vol. 8, No. 3, pp. 585-609.
13. V. A. Titarev (2010). Implicit unstructured-mesh method for calculating Poiseuille flows of rarefied gas. Communications in Computational Physics, V. 8, N 2, pp. 427-444.
14. V. A. Titarev and E. M. Shakhov. (2010). High-order accurate conservative method for computing the Poiseuille rarefied gas flow in a channel of arbitrary cross section. Computational Mathematics and Mathematical Physics, V. 50, No. 3, pp. 537--548.
15. V. V. Aristov, O. V. Ilyin (2010) Kinetic model of the spatio-temporal turbulence. Physics Letters A, V. 374, pp. 4381-4384.
16. V. V. Aristov and A. V. Stroganov. Construction of Solutions to Differential Equations by the Method of Computer Analogy. Doklady Mathematics, 2010, Vol. 82, No. 2, pp. 709–715.
17. S. P. Popov (2010). Application of the quasi-spectral fourier method to soliton equations. Computational Mathematics and Mathematical Physics, V. 50. N. 12 pp. 2064-2070.