ИСТИНА

This study is devoted to the application of continuum approach to the numerical modeling of gas flows in transition regime. Regularized 13-moment set of equations (R13) ([1]) is used as mathematical model. The variant of explicit high resolution Godunov scheme with linear flow parameter reconstruction is chosen for numerical solution of the R13 ([2]). Five so-called kinetic boundary conditions are taken as a base of mathematical model of isothermal solid wall ([3]). The complete set of the wall boundary conditions is obtained by an approximation of the selected sub-set of the R13 bulk equations. The resulted set of nonlinear equations for the wall is solved with Newton’s numerical method on each time step ([2]). The application of the R13 to numerical modeling of supersonic gas flows has been discussed for example here [4-6]. This study is devoted to low-speed gas flows in transition regime and especially to micro-pump gas flows. This area attracts a lot of attention last time because of rapid development of Micro-Electro-Mechanical Systems (MEMS). So the growth of the interest to engineering calculations of such devises functioning is observed. Theoretically kinetic approach is the most universal method for any problem of gas flows in transition regime. At the same time it is the most demanding in sense of numerical resources. So continuum methods are steel interesting for such problems due to the absence of these requirements. The applicability of the R13 set of equations for mathematical modeling of transition gas flow regime in micro scale devices was confirmed due to comparison with kinetic model and other numerical results for Kn≤0.5 ([2,3]). R13 numerical results and comparison with other methods for several types of micro-compressors are presented in this study. This work was supported by the Russian Government under the grant “Measures to Attract Leading Scientists to Russian Educational Institutions” (Contract No. 14.Z50.31.0019) and by the Russian Foundation for Basic Research (Project No. 14-02-31079). REFERNCES 1. H. Struchtrup and M. Torrilhon “Regularization of Grad’s 13-moment-equations: Derivation and linear analysis”, Phys. Fluids, 2003, 15, pp. 2668–2680. 2. I.E. Ivanov, I.A. Kryukov, and M.Yu. Timokhin “Application of Moment Equations to the Mathematical Simulation of Gas Microflows”, Comp. Math. and Math. Phys., 2013, 53, 10, pp. 1534–1550. 3. H. Struchtrup and M. Torrilhon “Boundary conditions for regularized 13-moment-equations for micro-channel-flows”, J. Comput. Phys., 2008, 227, pp. 1982–2011. 4. M. Torrilhon and H. Struchtrup “Regularized 13-moment Equations: Shock Structure Calculations and Comparison to Burnett Models” // J. Fluid Mech., 2004, 513, pp. 171–198. 5. M.Yu Timokhin, Ye A. Bondar, A.A. Kokhanchik, M.S. Ivanov, I.E. Ivanov, and I.A. Kryukov “Study of the Shock Wave Structure by Regularized Grad’s Set of Equations” Phys. Fluids, 2015, 27, 037101. 6. I.A. Znamenskaya, I.E. Ivanov, I.A. Kryukov, I.V. Mursenkova, and M.Yu Timokhin “Shock-wave Structure Formation by Nanosecond Discharge in Helium” Technical Phys. Letters, 2014, 40, 6 pp. 533–536.