Variational Multiscale Moment Method for the Boltzmann Equation: An Entropy Stable Extension to the Navier-Stokes-Fourier Equations

We use the Variational Multicale Method [1] as a framework for deriving a closed set of conservation equations from the Boltzmann equation. The framework is general enough to encompass existing closure methods such as the Chapman-Enskog expansion while opening the door to novel closures. It also incorporates an analysis of the entropy of the resulting system of equations in a natural way.

We then use the framework to derive a novel entropy stable extension to the Navier-Stokes-Fourier equations for rarefied gas dynamics and present results that show that these equations represent an improvement upon the Navier-Stokes-Fourier equations for the transitional flow regime.

References.

[1] T.J.R. Hughes, G.R. Feijoo, 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.