## Abstract

This paper presents the development of a novel set of second-order hydrodynamic equations, designated as the BGK-Burnett equations for computing flows in the continuum-transition regime. The second-order distribution function that forms the basis of this formulation is obtained by the first three terms of the Chapman-Enskog expansion applied to the Boltzmann equation with Bhatnagar-Gross-Krook (BGK) approximation to the collision terms. Such a distribution function, however, does not readily satisfy the moment closure property. Hence, an exact closed form expression for the distribution function is obtained by enforcing moment closure and solving a system of algebraic equations to determine the closure coefficients. Through a series of conjectures, the closure coefficients are designed to move the resulting system of hydrodynamic equations towards an entropy consistent set. An important step in the formulation of the higher-order distribution functions is the proper representation of the material derivatives in terms of the spatial derivatives. While the material derivatives in the first-order distribution function are approximated by Euler Equations, proper representations of these derivatives in the second-order distribution function are determined by an entropy consistent relaxation technique. The BGK-Burnett equations, obtained by taking moments of the Boltzmann equation with the second-order distribution function, are shown to be stable to small wavelength disturbances and entropy consistent for a wide range of grid points and Mach numbers.

Original language | English |
---|---|

DOIs | |

State | Published - 2001 |

Event | 39th Aerospace Sciences Meeting and Exhibit 2001 - Reno, NV, United States Duration: Jan 8 2001 → Jan 11 2001 |

### Conference

Conference | 39th Aerospace Sciences Meeting and Exhibit 2001 |
---|---|

Country/Territory | United States |

City | Reno, NV |

Period | 01/8/01 → 01/11/01 |