Numerical Modeling of Micron-Scale Flows Using the Gaussian Moment Closure

The application of the Gaussian moment closure to micron-scale flows is considered. The mathematical formulation of the closure is reviewed as well as an extension to allow for diatomic gases and treatment for solid wall boundaries. A parallel upwind finite-volume scheme with adaptive mesh refinement (AMR) using Roe and HLLE-type flux functions is described for solving the hyperbolic system of partial dierential equations arising from this closure. Comparisons are made between numerical solutions of the Gaussian model and analytical solutions for several test problems, including Couette, boundary layer and cylinder flow, over a range of Knudsen numbers. Agreement between analytical and numeric solutions for these problems are very encouraging.

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