##
**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 |

### Keywords:

phase space; second order upwind finite difference scheme; Runge-Kutta scheme; double ellipse
PDF
BibTeX
XML
Cite

\textit{N. Satofuka} et al., Comput. Mech. 11, No. 5--6, 452--464 (1993; Zbl 0771.76050)

Full Text:
DOI

### References:

[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 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.