An improved global-direction stencil based on the face-area-weighted centroid for the gradient reconstruction of unstructured finite volume methods  

作　　者：Ling-Fa Kong Yi-Dao Dong Wei Liu Huai-Bao Zhang 孔令发;董义道;刘伟;张怀宝(College of Aerospace Science and Engineering,National University of Defense Technology,Changsha 410073,China;School of Physics,Sun Yat-sen University,Guangzhou 510275,China)

机构地区：[1]College of Aerospace Science and Engineering,National University of Defense Technology,Changsha 410073,China [2]School of Physics,Sun Yat-sen University,Guangzhou 510275,China

出　　处：《Chinese Physics B》2020年第10期109-130,共22页中国物理B（英文版）

基　　金：Project supported by the National Key Project, China (Grant No. GJXM92579).

摘　　要：The accuracy of unstructured finite volume methods is greatly influenced by the gradient reconstruction, for which the stencil selection plays a critical role. Compared with the commonly used face-neighbor and vertex-neighbor stencils, the global-direction stencil is independent of the mesh topology, and characteristics of the flow field can be well reflected by this novel stencil. However, for a high-aspect-ratio triangular grid, the grid skewness is evident, which is one of the most important grid-quality measures known to affect the accuracy and stability of finite volume solvers. On this basis and inspired by an approach of using face-area-weighted centroid to reduce the grid skewness, we explore a method by combining the global-direction stencil and face-area-weighted centroid on high-aspect-ratio triangular grids, so as to improve the computational accuracy. Four representative numerical cases are simulated on high-aspect-ratio triangular grids to examine the validity of the improved global-direction stencil. Results illustrate that errors of this improved methods are the lowest among all methods we tested, and in high-mach-number flow, with the increase of cell aspect ratio, the improved global-direction stencil always has a better stability than commonly used face-neighbor and vertex-neighbor stencils. Therefore, the computational accuracy as well as stability is greatly improved, and superiorities of this novel method are verified.

关 键 词：unstructured finite volume methods improved global-direction stencil grid skewness face-area-weighted centroid 

分 类 号：O35[理学—流体力学]