We obtained augmented Burnett-equation solutions and conducted some preliminary studies on the extent to which the Burnett equations can be used in estimating the departure from the NavierStokes model for hypersonic flow over axisymmetric blunt bodies. The augmented Burnett equation solutions were restricted to the flow inside the bow shock in the stagnation region because of the uncertainty of...

A new closure for Grad’s 13 moment equations is presented that adds terms of SuperBurnett order to the balances of pressure deviator and heat flux vector. The additional terms are derived from equations for higher moments by means of the distribution function for 13 moments. The resulting system of equations contains the Burnett and Super-Burnett equations when expanded in a series in the Knuds...

Chapman-Enskog expansion is the orthodox approach to derive continuum flow models from Boltzmann’s kinetic equation for dilute gases. Beyond the Navier-Stokes-Fourier order, these models known as Burnett hydrodynamic-regime equations violate a number of fundamental mechanical and thermodynamic principles in their original forms. This has generated a widely investigated problem in the kinetic th...

In this paper, we construct a hierarchy of hybrid numerical methods for multi-scale kinetic equations based on moment realizability matrices, a concept introduced by Levermore, Morokoff and Nadiga in [15]. Following such a criterion, one can consider hybrid scheme where the hydrodynamic part is given either by the compressible Euler or Navier-Stokes equations, or even with more general models, ...

In [16] a visco-elastic relaxation system, called the relaxed Burnett system, was proposed by Jin and Slemrod as a moment approximation to the Boltzmann equation. The relaxed Burnett system is weakly parabolic, has a linearly hyperbolic convection part, and is endowed with a generalized entropy inequality. It agrees with the solution of the Boltzmann equation up to the Burnett order via the Cha...

Abstract. Our interest in the stability analysis of the high-order continuum (HOC) equations is motivated by the relevance to the development of a hybrid method combining such equations with the Direct Simulation Monte-Carlo (DSMC) technique for the computation of hypersonic flows in all regimes – continuum, transition, and rarefied. The hybrid approach allows the effects of thermophysics (ther...

Two recent works have shown that at small Knudsen number (K) the pressure and temperature profiles in plane Poiseuille flow exhibit a different qualitative behavior from the profiles obtained by the Navier-Stokes equations. Tij and Santos [J. Stat. Phys. 76, 1399 (1994)] used the Bhatnagar-Gross-Kook model to show that the temperature profile is bimodal and the pressure profile is nonconstant. ...