An approximate grossly determined solution to a simplified BGK equation

In this paper, we consider a simplified BGK equation admitting grossly determined solution, as introduced by Truesdell and Muncaster. This assumption enables the formulation of an iterative system, from which we derive an expansion for the molecular density. We then compare this approach with the Chapman–Enskog perturbation method, showing that the Chapman–Enskog solution belongs to the class of grossly determined solutions. The derived expansion is subsequently applied to the Rayleigh’s problem. Specifically, the velocity slip and the temporal evolution of the gas velocity in the vicinity of the solid boundary are examined.