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Numerical solution of the kinetic model equations for hypersonic flows. (English) Zbl 0771.76050

Summary: A numerical method for solving the model kinetic equations for hypersonic flows has been developed. The model equations for the distribution function are discretized in phase space using a second order upwind finite difference scheme for the spatial derivatives. The resulting system of ordinary differential equations in time is integrated by using a rational Runge-Kutta scheme. Calculations were carried out for hypersonic flow around a double ellipse under various free stream conditions. Calculated results are compared with the Navier-Stokes solutions and the direct simulation Monte Carlo method for the corresponding case. The agreement is quite excellent in general.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
76K05 Hypersonic flows
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[1] Abe, T.; Oguchi, H. (1977): Rarefied gas dynamics. Progress in Astronautics and Aeronautics. 51, 2, 781
[2] Abe, T.; Oguchi, H. (1979): Rarefied gas dynamics. Comminssariat A L’energie Atomique. I, 177
[3] Bhatnager, P. L.; Gross, E. P.; Krook, M. (1954): Physical Review. 94, 511 · Zbl 0055.23609
[4] Bird, G. A. (1976). Molecular gas dynamics. Clarendon Press, Oxford. 113-115
[5] Desideri, J. A.; Glinsky, N.; Hettena, E. (1990): Hypersonic reactive flow computations. Computers and Fluids. 18, 2, 151-182
[6] Morinishi, K.; Oguchi, H. (1984): A computational method and its application to analyses of rarefied gas flows. Proceeding of the 14th Int. Symp. on Rarefied Gas Dynamics. Univ. of Tokyo Press. 1, 149-158
[7] Morinishi, K.; Satofuka, N. (1987): A numerical study of viscous transonic flows using RRK scheme. AIAA paper 87-0426
[8] Nanbu, K. (1990): Workshop on hypersonic flows for reentry problems. Co-organized by GAMNI-SMAI and INRIA. 1, 307-326
[9] Oguchi, H.; Morinishi, K.; Satofuka, N. (1985): Time-dependent approach to kinetic analyses of two-dimensional rarefied gas flows. Proceeding of the 13th Int. Symp. of Rarefied Gas Dynamics. Plenum Publishing Corp. I, 293-302
[10] Satofuka, N.; Morinishi, K.; Nishida, Y. (1987): Numerical solution of two-dimensional compressible Navier-Stokes equations using rational Runge-Kutta method. Note on Numerical Fluid Mechanics. 18, Vieweg, 201-218 · Zbl 0631.76067
[11] Thompson, J. F.; Thames, F. C.; Mastin, C. W. (1974): J. Comp. Phys. 15, 299 · Zbl 0283.76011
[12] Wambecq, A. (1978): Rational Runge-Kutta methods for solving system of equations. Computing. 20, 333-342 · Zbl 0395.65036
[13] Yee, H. C.; Klopfer, G. H.; Montagne, J. L. (1990): High-resolution shock-capturing schemes for invicid and viscous hypersonic flows. J. Comput. Physics 88, 36-61 · Zbl 0697.76079
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