Construction of boundary conditions for Navier-Stokes equations from the moment system

TL;DR

This paper develops boundary conditions for the Navier-Stokes equations derived from the linearized moment system of rarefied gases, incorporating second-order effects and validated through analysis and numerical tests.

Contribution

It introduces a novel method to construct boundary conditions for Navier-Stokes equations from the moment system, accounting for second-order effects.

Findings

The boundary conditions include second-order effects on velocity slip and temperature jump.

Error estimates confirm the validity of the constructed boundary conditions.

Numerical tests demonstrate the effectiveness of the proposed boundary conditions.

Abstract

This work concerns with boundary conditions (BCs) of the linearized moment system for rarefied gases. As the Knudsen number is sufficiently small, 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 propose a matching requirement and construct BCs for the Navier-Stokes equations. The obtained BCs contain the effect of second-order terms on the velocity slip and temperature jump. For the illustrative case of the Couette flow, we prove the validity of the constructed BCs through the error estimates. Meanwhile, numerical tests are presented to show the performance of the constructed BCs.