Physics of Fluids -- December 1998 -- Volume 10, Issue 12, pp. 3214-3226

Moment realizability and the validity of the Navier–Stokes equations for rarefied gas dynamics

C. David Levermore
Department of Mathematics and Program in Applied Mathematics, University of Arizona, Tucson, Arizona 85721
William J. Morokoff
School of Mathematics, Institute of Advanced Study, Princeton, New Jersey 08540
B. T. Nadiga
Applied Theoretical and Computational Physics Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545

(Received 20 February 1998; accepted 26 August 1998)

We present criteria for monitoring the validity of the Navier–Stokes approximation during the simulation of a rarefied gas. Our approach is based on an underlying kinetic formulation through which one can construct nondimensional non-negative definite matrices from moments of the molecular distribution. We then identify one such 3 × 3 matrix that can be evaluated intrinsically in the Navier–Stokes approximation. Our criteria are based on deviations of the eigenvalues of this matrix from their equilibrium value of unity. Not being tied to a particular benchmark problem, the resulting criteria are portable and may be applied to any Navier–Stokes simulation. We study its utility here by comparing stationary planar shock profiles computed using the Navier–Stokes equations with those computed using Monte Carlo simulations. © 1998 American Institute of Physics.

PII: S1070-6631(98)01312-9
PACS: 47.45.-n, 47.10.+g, 47.11.+j      

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