三维直角叉树切割网格Euler方程自适应算法

A 3D adaptive algorithm of Cartesian grid for Euler equations

基于叉树数据结构,实现了一种用于三维直角叉树切割网格的自适应算法,包括对几何外形,以及对流场计算的自适应网格加密技术。在初始网格的生成过程中,根据相邻网格的物面法向向量间的差值,进行针对外形的自适应网格加密;在流场计算中,根据相邻网格间选定物理量梯度的变化,进行针对流场的自适应网格加密。详细地描述了三维直角叉树切割网格的生成过程,以及对任意网格的切割细分算法。在自适应过程中,分别采用了八叉树和全叉树的数据结构,八叉树是基本的数据结构,而全叉树的采用,使网格具有了各向异性的特征,从而大大的减少了自适应网格的数量。采用中心有限体积法,求解Euler方程,并运用上述方法,完成了对外形和流场的自适应网格加密算法,获得了较好的数值计算结果,证明了自适应算法的正确性,体现了直角叉树切割网格自适应技术的有效性和实用性。

The paper presents an adaptive refinement method of the Cartesina grid for the Euler equations.Given the definition of body configuration,geometrybased refinement of Cartesian grids is generated automatically through cellcutting algorithm.Solutionbased grid adaptations are carried out after converged solutions are obtained on a given grid.In the course of initial grid generation,a twostep raycasting algorithm to excluded cells inside the body and a cellmerging technique to avoid numerical insability are described.An Octree and Omnitree data structure has beed to store the data,which respectively support isotropic and anisotropic grid refinement.For the sake of flow calculation,four separate data entities are defined.A flow solver of the Euler equations is performed by a conventional algorithms,including finite volume method and RungeKutta tinestepping scheme.The flow solver supports arbitrary control volume.Based on the above approach,the numerical analysis of flows around ONERA M6 wing and the wing/body configuration is finished.The numerical results presented show flexibility and accuracy of this approach.