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

doi:10.1088/1674-1056/aba2da

摘要/Abstract

Abstract:

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.

Key words: unstructured finite volume methods, improved global-direction stencil, grid skewness, face-areaweighted centroid

中图分类号: (Numerical simulation; solution of equations)

02.60.Cb

47.11.-j (Computational methods in fluid dynamics) 47.11.Df (Finite volume methods)

Ling-Fa Kong(孔令发), Yi-Dao Dong(董义道), Wei Liu(刘伟), Huai-Bao Zhang(张怀宝). [J]. 中国物理B, 2020, 29(10): 100203-.

Ling-Fa Kong(孔令发), Yi-Dao Dong(董义道)†, Wei Liu(刘伟), and Huai-Bao Zhang(张怀宝). An improved global-direction stencil based on the face-area-weighted centroid for the gradient reconstruction of unstructured finite volume methods[J]. Chin. Phys. B, 2020, 29(10): 100203-.

图/表 54

参考文献 36

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Full name	Abbreviation
Vertex-neighbor stencil	V-stencil
Face-neighbor stencil	F-stencil
Global-direction stencil with geometric centroid (i.e., p = 0)	G-stencil (p = 0)
Global-direction stencil with the face-area-weighted centroid and p = 1	G-stencil (p = 1)
Global-direction stencil with the face-area-weighted centroid and p = 2	G-stencil (p = 2)

Grid name	Distribution in x and y directions (x,y ∈ [0, 1] × [0, 0.001]
Grid name	AR = 10²	AR = 5 × 10²	AR = 10³
vcoa	50 × 5	20 × 10	15 × 15
coa	100 × 10	40 × 20	30 × 30
med	150 × 15	60 × 30	45 × 45
fin	200 × 20	80 × 40	60 × 60
vfin	300 × 30	120 × 60	90 × 90

Different stencils	L₂ norm of pressure errors	L_∞ norm of pressure errors
V-stencil	0.000517445	0.00192892
F-stencil	0.000470333	0.00166419
G-stencil (p = 0)	0.000446073	0.00146549
G-stencil (p = 1)	0.000237936	0.000923927
G-stencil (p = 2)	0.000234345	0.000917014

Grid name	Distribution in x and x directions (x,y ∈ [0, 1] × [0, 0.001]
Grid name	AR = 10²	AR = 10³	AR = 10⁴	AR = 10⁵
vcoa	120 × 10	60 × 20	20 × 30	30 × 30
coa	180 × 15	90 × 30	30 × 45	45 × 45
med	240 × 20	120 × 40	40 × 60	60 × 60
fin	360 × 30	180 × 60	60 × 90	90 × 90
vfin	480 × 40	240 × 80	80 × 120	120 × 120

Different stencils	L₂ norm of solution errors	L_∞ norm of solution errors
V-stencil	0.000170044	0.00202639
F-stencil	0.00015098	0.00205056
G-stencil (p = 0)	0.00014244	0.00195697
G-stencil (p = 1)	0.0000746072	0.00140981
G-stencil (p = 2)	0.0000734274	0.00143022