A novel set of second-order hydrodynamic equations for flows in continuum-transition regime

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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 languageEnglish
StatePublished - 2001
Event39th Aerospace Sciences Meeting and Exhibit 2001 - Reno, NV, United States
Duration: Jan 8 2001Jan 11 2001


Conference39th Aerospace Sciences Meeting and Exhibit 2001
Country/TerritoryUnited States
CityReno, NV


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