ИСТИНА

This study is devoted to the investigation of linear and four nonlinear variants of regularized thirteen moment set of equations (R13) obtained for Maxwell molecules [1]. The difference between the sets of R13 equations is in definition of higher order moments. The work continues the analysis [2-4] of the R13 equations based on numerical results for shock-wave structure problem for monatomic Maxwell gas. The goal of the present study is to get the answer to assess the boundaries of the applicability of the R13 variants to numerical modelling of supersonic nonequilibrium flows in terms of the shock-wave Mach number and the local Knudsen number defined in several different ways. In this work the local Knudsen number is based on gradients of density, temperature, heat flux and stress tensor components ([5]). R13 numerical results have been compared and analyzed with DSMC results obtained with SMILE software system [6]. The shock-wave structure has been obtained in a wide Mach number range (from M=1.0 to M=10.0). The detailed analysis of gas macro-parameters’ profiles inside the shock will be presented in the full-length paper. ACKNOWLEDGEMENTS 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). REFFERENCES [1] H. Struchtrup, M. Torrilhon, Phys. Fluids, 15, 2668-2680 (2003) [2] M. Torrilhon, H. Struchtrup, J. Fluid Mech., 513, 171–198 (2004) [3] I.E. Ivanov, I.A. Kryukov, M.Yu. Timokhin, Ye.A. Bondar, A.A. Kokhanchik, M.S. Ivanov, in Proc. of 28th Int. Symp. on RGD, Melville, New York, 2012, pp. 215-222 [4] M. Yu. Timokhin, Ye A. Bondar, A. A. Kokhanchik, M. S. Ivanov, I. E. Ivanov, I. A. Kryukov, Phys. Fluids, 27, 037101, (2015) [5] D.A. Lockerby, J.M. Reese, H. Struchtrup, Proc. R. Soc. A, 465, 1581-1598 (2009) [6] M.S. Ivanov, A.V. Kashkovsky, S.F. Gimelshein, G.N. Markelov, A.A. Alexeenko, Ye.A. Bondar, G.A. Zhukova, S.B. Nikiforov, and P.V. Vashenkov, in Proc. of 25th Int. Symp. on RGD, Publishing House of the SB RAS, Novosibirsk, 2007, pp. 539-544