Extended Fluid Dynamic Model for Micron-Scale Flows Based on Gaussian Moment Closure

terms having an elliptic nature. The extended model can be achieved by taking a Chapman-Enskog-type expansion about either the Gaussian moment equations of the kinetic equation and both methods are presented here. The elliptic nature of the additional generalized heat-flux terms lead to fully dispersed shock wave solutions, unlike the partially dispersed solutions provided by the Gaussian closure as the Mach number increases. Using a Godunov-type finite-volume scheme with block based adaptive-mesh refinement (AMR) on body-fitted multi-block meshes, the proposed equations are applied to several canonical continuum and micron-scale flow situations such as shock structure, Couette flow, and flow past a circular cylinder, as well as for transonic flow past a micro airfoil. Comparisons with analytic, experimental, and direct-simulation Monte Carlo (DSMC) results are made and demonstrate the capabilities of the proposed non-equilibrium model.