Construction of Boundary Conditions for Navier–Stokes Equations from the Moment System

This work concerns with boundary conditions (BCs) of the linearized moment system for rarefied gases. Under the acoustic scaling, we analyze the boundary-layer behaviors of the moment system by resorting to a three-scale asymptotic expansion. The asymptotic analysis casts the flows into the outer solution, the viscous layer, and the Knudsen layer. Starting from the BCs of the moment system, we construct BCs for the Navier–Stokes equations by a matching requirement. The obtained BCs contain the effect of second-order terms on the velocity slip and temperature jump. For the illustrative case of the Rayleigh problem, we prove the validity of the constructed BCs through error estimates. Meanwhile, numerical tests are presented to show the performance of the constructed BCs.