Numerical Investigations of Slip Effects on Rarefied Gas Flows by First and Second-Order Slip Boundaries

Abstract

This paper discusses comparisons of first and second-order slip boundary conditions on the range of Knudsen numbers of some typical MEMS as O(10-3)<Kn<O(10-1) by numerical simulations using the continuum model based on the Navier-Stokes (N-S) equations. Slip flows are solved by the Constrained Interpolation Profile (CIP) method. A numerical method for a simple but general form of a slip boundary condition on a simple planar wall is also introduced. Numerical solutions are in very good agreement with exact solutions of the N-S equations with slip boundaries in two-dimensional Poiseuille flows in the hard sphere (HS) model. The present numerical method is next applied to two and three-dimensional rid-driven cavity flows, employing slip coefficients for the Bhatnagar-Gross-Krook (BGK) model. The results indicate differences of slip effects near walls between the first and second-order slip boundary can also affect whole streamlines and velocity distributions in a closed region with increasing the Knudsen number.

Keywords

• cip method
• navier-stokes
• slip flows
• rarefied gas
• micro-fluids