The Boltzmann transport equation yields conservation equations for mass, momentum and energy from its first five moments. These equations require closure relations for the deviatoric stress and heat flux so as to balance the number of unknowns with the number of equations. The most storied closure method is the Chapman-Enskog expansion[1] which yields a sequence of closures in orders of Knudsen number: Euler’s and Navier-Stokes-Fourier equations at zeroth and first order, Burnett equations at second order and so on. Unfortunately, the Burnett equations are known to be unstable[2]. In this presentation, we propose a new framework for deriving closure relations based on the Variational Multiscale (VMS) method[3], which was originally created to derive stabilized Galerkin formulations to advective PDEs. Our VMS closure process subsumes the Chapman-Enskog expansion while opening the door to novel closures. It also provides a criterion based off the entropy production inequality of the Boltzmann equation for assessing the quality of a given closure. Focusing on the linearized Boltzmann equation, we will describe the VMS framework and use it to introduce an alternative to the Burnett equations that possesses an entropy inequality. We will then present results on the application of these alternative equations to the stationary heat transfer problem and the Poisseuille channel problem. In both setups, the alternative equations give solutions that are accurate far beyond the early transition regime of rarefied gas flow that they are designed for. REFERENCES [1] S. Chapman, T.G. Cowling, The Mathematical Theory of Non-Uniform Gases, 3rd Edition, Cambridge Mathematical Library, 1991. [2] A. V. Bobylev, The chapman-enskog and grad methods for solving the boltz- mann equation, Akademiia Nauk SSSR Doklady 262 (1), 71–75, 1982. [3] T.J.R. Hughes, G.R. Feij ́oo, L. Mazzei & J.B. Quincy, The variational multiscale method—a paradigm for computational mechanics, Computer Methods in Applied Mechanics and Engineering 166(1-2), pp. 3-24, 1998.