Simulation of rarefied gas flows on the basis of the Boltzmann kinetic equation solved by applying a conservative projection method. (English. Russian original) Zbl 1381.76321
Comput. Math. Math. Phys. 56, No. 6, 996-1011 (2016); translation from Zh. Vychisl. Mat. Mat. Fiz. 56, No. 6, 1008-1024 (2016).
Summary: Flows of a simple rarefied gas and gas mixtures are computed on the basis of the Boltzmann kinetic equation, which is solved by applying various versions of the conservative projection method, namely, a two-point method for a simple gas and gas mixtures with a small difference between the molecular masses and a multipoint method in the case of a large mass difference. Examples of steady and unsteady flows are computed in a wide range of Mach and Knudsen numbers.
MSC:
| 76P05 | Rarefied gas flows, Boltzmann equation in fluid mechanics |
| 82C40 | Kinetic theory of gases in time-dependent statistical mechanics |
Keywords:
rarefied gas; gas mixture; Boltzmann equation; conservative projection method; numerical simulationReferences:
| [1] | O. M. Belotserkovskii and V. E. Yanitskii, “The statistical particles-in-cells method for solving rarefied gas dynamics problems,” USSR Comput. Math. Math. Phys. 15 (5), 101-114 (1975). · Zbl 0338.76044 · doi:10.1016/0041-5553(75)90108-1 |
| [2] | A. Nordsieck and B. L. Hicks, “Monte Carlo evaluation of the Boltzmann collision integral,” Rarefied Gas Dyn. 1, 695-710 (1967). |
| [3] | V. V. Aristov and F. G. Cheremisin, “The conservative splitting method for solving Boltzmann’s equation,” USSR Comput. Math. Math. Phys. 20 (1), 208-225 (1980). · Zbl 0458.76061 · doi:10.1016/0041-5553(80)90074-9 |
| [4] | Tcheremissine, F. G., Conservative discrete ordinates method for solving Boltzmann kinetic equation (1996), Moscow |
| [5] | F. G. Cheremisin, “Conservative method of calculating the Boltzmann collision integral,” Phys. Dokl. 42 (1), 607-610 (1997). · Zbl 0921.76148 |
| [6] | F. G. Cheremisin, “Solving the Boltzmann equation in the case of passing to the hydrodynamic flow regime,” Phys. Dokl. 45 (8), 401-404 (2000). · doi:10.1134/1.1310733 |
| [7] | F. G. Tcheremissine, “Solution to the Boltzmann kinetic equation for high-speed flows,” Comput. Math. Math. Phys. 46 (2), 315-329 (2006). · Zbl 1210.76149 · doi:10.1134/S0965542506020138 |
| [8] | A. A. Raines, “A method for solving Boltzmann’s equation for a gas mixture in the case of cylindrical symmetry in the velocity space,” Comput. Math. Math. Phys. 42 (8), 1212-1223 (2002). · Zbl 1056.35117 |
| [9] | Dodulad, O. I.; Tcheremissine, F. G., Multipoint conservative projection method for computing the Boltzmann collision integral for gas mixtures, 302-309 (2012) |
| [10] | F. G. Tcheremissine, “Method for solving the Boltzmann kinetic equation for polyatomic gases,” Comput. Math. Math. Phys. 52 (2), 252-268 (2012). · Zbl 1249.82002 · doi:10.1134/S0965542512020054 |
| [11] | Yu. A. Anikin and O. I. Dodulad, “Solution of a kinetic equation for diatomic gas with the use of differential scattering cross sections computed by the method of classical trajectories,” Comput. Math. Math. Phys. 53 (7), 1026-1043 (2013). · Zbl 1299.82005 · doi:10.1134/S096554251307004X |
| [12] | V. V. Aristov and F. G. Cheremisin, “Splitting the inhomogeneous kinetic operator of the Boltzmann equation,” Dokl. Akad. Nauk SSSR 231 (1), 49-52 (1976). · Zbl 0364.76071 |
| [13] | A. V. Bobylev and T. Ohwada, “On the generalization of Strang’s splitting scheme,” Riv. Math. Univ. Parma 6 (2), 235-243 (1999). · Zbl 0959.65073 |
| [14] | N. M. Korobov, Number-Theoretic Methods in Approximate Analysis (Fizmatgiz, Moscow, 1963) [in Russian]. · Zbl 0115.11703 |
| [15] | Y. A. Anikin, O. I. Dodulad, Y. Y. Kloss, D. V. Martynov, P. V. Shuvalov, and F. G. Tcheremissine, “Development of applied software for analysis of gas flows in vacuum devices,” Vacuum 86 (11), 1770-1777 (2012). · Zbl 1268.54021 · doi:10.1016/j.vacuum.2012.02.024 |
| [16] | Bazhenov, I. I.; Dodulad, O. I.; Ivanova, I. D.; Kloss, Y. Y.; Rjabchenkov, V. V.; Shuvalov, P. V.; Tcheremissine, F. G., Problem solving environment for gas flow simulation in micro structures on the basis of the Boltzmann equation, 246-257 (2013) |
| [17] | Yu. Yu. Kloss, N. I. Khokhlov, F. G. Tcheremissine, and B. A. Shurygin, “Development of numerical schemes for solving kinetic equations in cluster environments on the basis of MPI technology,” Inf. Protsessy 7 (4), 425-431 (2007). |
| [18] | Yu. Yu. Kloss, P. V. Shuvalov, and F. G. Tcheremissine, “Solving Boltzmann equation on GPU,” Proc. Computer Sci. ICCS 1 (1), 1077-1085 (2010). · Zbl 1201.76238 |
| [19] | O. I. Dodulad and F. G. Tcheremissine, “Computation of a shock wave structure in monatomic gas with accuracy control,” Comput. Math. Math. Phys. 53 (6), 827-844 (2013). · Zbl 1299.76123 · doi:10.1134/S0965542513060055 |
| [20] | H. Alsmeyer, “Density profiles in argon and nitrogen shock waves measured by the absorption of an electron beam,” J. Fluid Mech. 74, 497-513 (1976). · doi:10.1017/S0022112076001912 |
| [21] | W. Garen, R. Synofzik, and A. Frohn, “Shock tube for generation of weak shock waves,” AIAA J. 12, 1132-1134 (1974). · doi:10.2514/3.49425 |
| [22] | V. Yu. Velikodnyi, A. V. Emel’yanov, and A. V. Eremin, “Diabatic excitation of iodine molecules in the translational nonequilibrium zone of a shock wave,” Tech. Phys. 44 (10), 1150-1158 (1999). · doi:10.1134/1.1259489 |
| [23] | O. I. Dodulad, Yu. Yu. Kloss, and F. G. Tcheremissine, “Computation of shock wave structure in a gas mixture by solving the Boltzmann equation,” Fiz.-Khim. Kinetika Gaz. Din. 14 (1), 1-18 (2013). |
| [24] | Gmurczyk, A. S.; Tarczynski, M.; Walenta, Z. A., Shock wave structure in the binary mixtures of gases with disparate molecular masses, 333-341 (1978) |
| [25] | C. Chung, K. J. D. Wittt, D. Jeng, and P. F. Penko, “Internal structure of shock waves in disparate mass mixture,” J. Thermophys. 7 (4), 742-744 (1993). · doi:10.2514/3.490 |
| [26] | Miyoshi, N.; etal., Development of ultra small shock tube for high energy molecular beam source, 557-562 (2009) |
| [27] | Yu. Yu. Kloss, F. G. Tcheremissine, and P. V. Shuvalov, “Solution of the Boltzmann equation for unsteady flows with shock waves in narrow channels,” Comput. Math. Math. Phys. 50 (6), 1093-1103 (2010). · Zbl 1224.76092 · doi:10.1134/S096554251006014X |
| [28] | J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1954; Inostrannaya Literatura, Moscow, 1961). · Zbl 0057.23402 |
| [29] | S. Takata, H. Sugimoto, and S. Kosuge, “Gas separation by means of the Knudsen compressor,” Eur. J. Mech. 26 (2), 155-181 (2007). · Zbl 1124.76048 · doi:10.1016/j.euromechflu.2006.05.002 |
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