Abstract

This paper is concerned with boundary treatments of a discrete kinetic approximation proposed in Guo et al. (J Sci Comput 16(4):569–585, 2001) for the Navier–Stokes equations. For this approximation we find that the widely used bounce-back scheme does not have second-order accuracy even the boundary is located at the middle of two neighbouring grid points. To remedy this, a new boundary scheme is proposed. It is shown with the Maxwell iteration that the new scheme is second-order accurate if the boundary is located at the middle of two neighbouring grid points, and is first-order accurate otherwise. In this regard, the present boundary scheme is a natural extension of the bounce-back scheme to the discrete kinetic approximation. Numerical experiments are conducted to validate the accuracy of the scheme and show its utility for both straight and curved boundaries.

中文翻译：

---

Navier-Stokes方程离散动力学逼近的边界方案

摘要

本文涉及郭等人提出的离散动力学逼近的边界处理。（J Sci Comput 16（4）：569–585，2001），用于Navier–Stokes方程。对于这种近似，我们发现，即使边界位于两个相邻网格点的中间，广泛使用的反跳方案也不具有二阶精度。为了解决这个问题，提出了一种新的边界方案。用麦克斯韦迭代法表明，如果边界位于两个相邻网格点的中间，则新方案是二阶准确的，否则是一阶准确的。在这方面，当前的边界方案是反跳方案到离散动力学近似的自然扩展。