Abstract
In this paper a new set of equations, designated as the BGK-Burnett equations, are derived for computing hypersonic flow in the continuum transition regime. 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 BGK-Burnett equations are derived by taking moments of the BGK-Boltzmann equation with the collision invariant vector. These equations are entropy consistent and do not violate the second law of thermodynamics at all Knudsen numbers. 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 the shock tube and hypersonic shock structure problems.
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