A New Boundary Scheme for BGK Model

TL;DR

This paper introduces a new boundary condition scheme for the BGK model that achieves second order accuracy, improves numerical results, and can be extended to higher accuracy levels.

Contribution

The authors develop a novel boundary scheme for the BGK model with second order accuracy, surpassing previous extrapolation methods in numerical precision.

Findings

Numerical solutions align well with analytical solutions.

The new scheme outperforms previous extrapolation schemes at small grid sizes.

The scheme can be extended to higher accuracy levels.

Abstract

In this paper, we proposed a new boundary condition scheme for the BGK model which has second order accuracy and can be developed to higher accuracy. Numerical tests show that the numerical solutions of the BGK model applied to the new boundary scheme have great agreement with analytical solutions. It is also found that the numerical accuracy of the present schemes is much better than that of the original extrapolation schemes proposed by Guo et al at small grid.