Resolving Knudsen layer by high-order moment expansion

We model the Knudsen layer in Kramers’ problem by the linearized high-order hyperbolic moment system. Thanks to the hyperbolicity of the moment system, its boundary conditions are properly reduced from the kinetic boundary condition. For the Kramers’ problem, we present the analytical solutions of the linearized moment systems. The velocity profile in the Knudsen layer is captured with improved accuracy for a wide range of accommodation coefficients. With the order of the moment system increasing, the velocity profile approaches to that of the linearized Boltzmann–BGK equation.