Multiscale discrete Maxwell boundary condition for the discrete unified gas kinetic scheme for all Knudsen number flows

TL;DR

This paper introduces a multiscale boundary condition for the DUGKS that accurately models gas flows across all regimes, overcoming previous limitations and ensuring correct boundary behavior in simulations.

Contribution

It develops a multiscale DMBC that eliminates spurious slip and jump effects, enabling accurate all-regime flow simulations with fixed discretization.

Findings

Achieves non-slip and non-jump conditions in the continuum limit

Accurately captures non-equilibrium phenomena across all Knudsen numbers

Works with fixed spatial and temporal discretization without Knudsen layer limitations

Abstract

In this paper, a multiscale boundary condition for the discrete unified gas kinetic scheme (DUGKS) is developed for gas flows in all flow regimes. Based on the discrete Maxwell boundary condition (DMBC), this study addresses the limitations of the original DMBC used in DUGKS. Specifically, it is found that the DMBC produces spurious velocity slip and temperature jump, which are proportional to the mesh size and the momentum accommodation coefficient. The proposed multiscale DMBC is implemented by ensuring that the reflected original distribution function excludes collision effects. Theoretical analyses and numerous numerical tests show that the multiscale DMBC can achieve exactly the non-slip and non-jump conditions in the continuum limit and accurately captures non-equilibrium phenomena across a wide range of Knudsen numbers. The results demonstrate that the DUGKS with the multiscale DMBC can work properly for wall boundary conditions in all flow regimes with a fixed discretization in both space and time, without limitations on the thickness of the Knudsen layer and relaxation time.