## Abstract

In this paper a kinetic theory based upwind algorithm for the BGK-Burnett equations is presented. The Boltzmann equation, with Bhatnagar-Gross-Krook (BGK) approximation for the collision integral, describes the spatial and temporal variations of the second-order distribution function which forms the basis of this formulation. The second order distribution function is derived by considering the first three terms in the Chapman-Enskog expansion and using the Navier-Stokes equations to express the material derivatives, present in the second-order terms, in terms of the spatial derivatives. The Burnett equations are derived by taking moments of the BGK-Boltzmann equation with the collision invariant vector. A Kinetic Wave/Particle Split scheme for the BGK-Burnett equations is derived by taking moments of the upwind discretized Boltzmann equation. This algorithm is applied to a 1-D shock tube problem and a hypersonic shock structure problem. This is the first time that a kinetic-theory based method has been developed for solving the Burnett equations.

Original language | English |
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DOIs | |

State | Published - 1996 |

Event | 34th Aerospace Sciences Meeting and Exhibit, 1996 - Reno, United States Duration: Jan 15 1996 → Jan 18 1996 |

### Conference

Conference | 34th Aerospace Sciences Meeting and Exhibit, 1996 |
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Country/Territory | United States |

City | Reno |

Period | 01/15/96 → 01/18/96 |