气体动理论BGK格式的网格自适应方法

为了提高气体动理论BGK（Bhatnagr-Gross-Krook）格式在超声速流动问题计算时激波捕捉的准确性与计算效率，提出了一种适用于气体动理论BGK格式的网格自适应加密方法。该方法采用基于四边形的链表技术来描述网格的拓扑结构，在物理量重构过程中，使用了在四边形网格中表现优异的van Leer限制器，以保证粗细网格过渡处物理量重构的精度。用跨声速翼型绕流（马赫数Ma=0.85）、超声速前台阶流（Ma=3）和高超声速圆柱绕流（Ma=8.03）等多个典型算例验证了BGK自适应网格方法。计算结果表明，自适应网格BGK方法在保证数值精度的前提下，可大幅度提高计算效率。这为该方法用于高效地解决复杂问题提供了一种选择。

Adaptive Mesh Refinement for Gas-kinetic BGK Scheme

An adaptive mesh refinement method based on the gas-kinetic BGK (Bhatnagr-Gross-Kroor) scheme is proposed in this paper to improve the accuracy and computational efficiency of gas-kinetic BGK schemes for shock capturing. In the present work, a linked list based on a quadrilateral is applied to describe the topology of the meshes. In the reconstruction stage, the van Leer limiter is introduced to ensure the accuracy of physical quantities reconstruction at the interface between the coarse meshes and the refined meshes. Some cases from transonic airfoil flow (Mach number Ma=0.85), supersonic flow over forward-facing step (Ma=3) to hypersonic flow around a cylinder (Ma=8.03) are presented to verify the adaptive mesh method for the BGK scheme. It is found that the proposed method can greatly improve the computational efficiency without reducing accuracy. The approach provides a numerical technique for the BGK scheme to compute complex flows efficiently.