中文摘要：

以二维高雷诺数可压缩粘性流动问题为背景，提出了一种全新的笛卡尔网格虚拟单元方法。基于壁面函数基本假设，构造了壁面函数-虚拟单元方法（WF-GCM），用于定义湍流壁面边界条件。引入参考点的概念计算虚拟单元上的基本变量与湍流变量值，定义了“非贴体”笛卡尔网格下的湍流壁面边界条件，并通过壁面函数模型修正近壁面单元与界面单元。基于自适应笛卡尔网格体系，采用发展的具有二阶精度的格心格式有限体积求解器，数值模拟了跨音速 RAE2822翼型绕流问题与超音速圆柱绕流问题，计算结果与实验值吻合良好，显示了 WF-GCM 对高雷诺数可压缩粘性问题是有效的。

英文摘要：

This work presents a new Cartesian-based ghost cell method for two-dimensional high Reyn-olds number compressible viscous flows.Based on the six fundamental assumptions used in the law-of-the-wall,a wall function-ghost cell method （WF-GCM）is developed to treat turbulent wall boundary conditions. Reference points are employed to compute primitive variables and turbulent properties at ghost cells.Mean-while,the turbulent variables at the near wall cells and boundary cells are modified by using the wall func-tion model.The turbulent boundary conditions are incorporated into a Reynolds average Navier-Stokes （RANS）finite volume solver that includes the SST k-ω turbulence model.Finally,the transonic flow past a RAE2822 airfoil and supersonic flow past a circle cylinder are simulated with adaptive Cartesian grid.Good agreement with the experimental datas shows the accuracy and efficiency of the presented WF-GCM.