Resolving Knudsen Layer by High Order Moment Expansion
This work provides a more accurate analytical method for resolving the Knudsen layer in rarefied gas dynamics, which is important for microfluidics and vacuum technology.
The authors model the Knudsen layer in Kramers' problem using high-order hyperbolic moment systems, deriving analytical solutions that converge to the linearized BGK kinetic solution as order increases, achieving improved accuracy in velocity profiles across a wide range of accommodation coefficients.
We model the Knudsen layer in Kramers' problem by linearized high order hyperbolic moment system. Due to the hyperbolicity, the boundary conditions of the moment system is properly reduced from the kinetic boundary condition. For Kramers' problem, we give the analytical solutions of moment systems. With the order increasing of the moment model, the solutions are approaching to the solution of the linearized BGK kinetic equation. The velocity profile in the Knudsen layer is captured with improved accuracy for a wide range of accommodation coefficients.