基于自适应笛卡尔网格的可压缩黏性流动数值模拟

摘要

Navier-Stokes equations were solved with adaptively-refined Cartesian grid approach, grid was ac-cessed based on quad-tree data structure, and solid wall boundary was introduced by a ghost body cell method. The grid was automatically established and refined, and flow field was automatically solved with specified geometries. Supersonic flow around NACA0012 airfoil with shock wave and subsonic flow around double NACA0012 airfoils with recirculation region were numerical simulated, and then compared with published results which were based on stretched Cartesian grid and unstructured grid. The results show that, compressible viscous flows can be adequately simulated with adaptively-refined Cartesian grid, the number of cells is dramatically decreased compared with stretched Cartesian grid, but current approach is inefficient in the resolution of boundary layer when compared with unstructured grid, which needs further development.%基于自适应笛卡尔网格方法求解Navier-Stokes方程，网格以四叉树数据结构存储，固壁边界条件通过一种虚拟单元体方法引入。在几何外形确定的前提下自动完成网格生成、加密和流场的求解任务。对含有激波的NACA0012翼型的超音速绕流工况和含有回流区的双NACA0012翼型亚音速绕流工况进行了数值模拟，并与现有的非等距笛卡尔网格解和非结构网格解进行了对比。结果表明：基于自适应笛卡尔网格能够准确模拟可压缩黏性流动，同非等距笛卡尔网格相比，自适应技术的使用显著降低了网格量，但是同非结构网格相比，现有的自适应笛卡尔网格技术在边界层的分辨上效率较低，有待进一步发展。