Gradient Divergence of Fluid-Dynamic Quantities in Rarefied Gases on Smooth Boundaries

Abstract

The behavior of fluid-dynamic (or macroscopic) quantities of rarefied gases is studied, with a special interest in its non-analytic feature near boundaries. It is shown that their gradients normal to the boundary diverge even if the boundary is smooth, irrespective of the value of the (nonzero) Knudsen number. The boundary geometry determines the diverging rate. On a planar or concave boundary, the logarithmic divergence lns should be observed, where s is the normal distance from the boundary. In other cases, the diverging rate is enhanced to be the inverse-power s[−1/n], where n(≥2) is the degree of the dominant terms of the polynomial which locally represents the boundary. Some numerical demonstrations are given as well.