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Small modification of gas-surface interaction parameters at high Knudsen numbers can generate large deviations of the macroscopic parameters of the flow [1], [2]. The reason for this behavior of the flow is that nonlinear iterative equations describing rarefied gas flows in long channels and nozzles have solutions becoming instable for certain values of the parameters of scattering function V of gas atoms on the walls. Calculated by Monte-Carlo simulation distributions of the number of gas atoms and of the angles of inclination of gas atom trajectories along the channel demonstrate that the flow becomes instable if the values of gas-surface interaction parameters are close to the points where analytical limit solution has singularity [1]. Near these points two flows with negligible small difference in corresponding parameters of the gas and of the surface have large difference between calculated characteristics. Raydiffuse model of scattering function on channel walls is considered, i.e. diffuse scattering is combined with ray model of reflection (velocity of reflected gas particles is unique determined as a function of the velocity of incident gas atoms).

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Direct statistical Monte-Carlo simulation of rarefied gas molecular flow near a rough surface is studied on the base of analytical approximation of scattering function V and of the momentum and energy exchange coefficients [1-3]. The computation time is reduced due to the expansion of the roughness operatorŜ [2-6], which is used to express the scattering function V on rough surface in the form V =Ŝ V 0. The representation of the roughness operator is derived that is convenient to use both in numerical DSMC methods and in analytical investigations.