An improved global-direction stencil based on the face-area-weighted centroid for the gradient reconstruction of unstructured finite volume methodsProject supported by the National Key Project, China (Grant No. GJXM92579)

• Published in: Chinese physics B Vol. 29; no. 10
• Main Authors: Kong, Ling-Fa, Dong, Yi-Dao, Liu, Wei, Zhang, Huai-Bao
• Format: Journal Article
• Language: English
• Published: Chinese Physical Society and IOP Publishing Ltd 01.10.2020
• Subjects: face-areaweighted centroid; grid skewness; improved global-direction stencil; unstructured finite volume methods
• DOI: 10.1088/1674-1056/aba2da
• ISSN: 1674-1056

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.