Unified analysis of higher-order finite volume methods for parabolic problems on quadrilateral meshes

2015 ◽  
Vol 36 (2) ◽  
pp. 872-896 ◽  
Author(s):  
Min Yang ◽  
Jiangguo Liu ◽  
Qingsong Zou
Keyword(s):  
Finite Volume ◽  
Finite Volume Methods ◽  
Higher Order ◽  
Parabolic Problems ◽  
Quadrilateral Meshes

scholarly journals Extending the global-direction stencil with "face-area-weighted centroid" to unstructured finite volume discretization from integral form

2020 ◽  
Author(s):  
Lingfa Kong ◽  
Yidao Dong ◽  
Wei Liu ◽  
Huaibao Zhang
Keyword(s):  
Finite Volume ◽  
Differential Form ◽  
Integral Form ◽  
Finite Volume Methods ◽  
Higher Order ◽  
Reconstruction Method ◽  
Computational Accuracy ◽  
Face Area ◽  
Finite Volume Discretization ◽  
Numerical Performance

Abstract Accuracy of unstructured finite volume discretization is greatly influenced by the gradient reconstruction. For the commonly used k-exact reconstruction method, the cell centroid is always chosen as the reference point to formulate the reconstructed function. But in some practical problems, such as the boundary layer, cells in this area are always set with high aspect ratio to improve the local field resolution, and if geometric centroid is still utilized for the spatial discretization, the severe grid skewness cannot be avoided, which is adverse to the numerical performance of unstructured finite volume solver. In previous work, we explored a novel global-direction stencil and combine it with face-area-weighted centroid on unstructured finite volume methods from differential form to realize the skewness reduction and a better reflection of flow anisotropy. Note, however, that the differential form is hard to achieve higher-order accuracy, and in order to set stage for the method promotion on higher-order numerical simulation, in this research, we demonstrate that it is also feasible to extend this novel method to the unstructured finite volume discretization in integral form. Numerical examples governed by linear convective, Euler and Laplacian equations are utilized to examine the correctness as well as effectiveness of this extension. Compared with traditional vertex-neighbor and face-neighbor stencils based on the geometric centroid, the grid skewness is almost eliminated and computational accuracy as well as convergence rate is greatly improved by the global-direction stencil with face-area-weighted centroid. As a result, on unstructured finite volume discretization from integral form, the method also has a better numerical performance.

scholarly journals Higher-order finite volume methods II: Inf–sup condition and uniform local ellipticity

2014 ◽  
Vol 265 ◽  
pp. 96-109 ◽  
Author(s):  
Zhongying Chen ◽  
Yuesheng Xu ◽  
Yuanyuan Zhang
Keyword(s):  
Finite Volume ◽  
Finite Volume Methods ◽  
Higher Order
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