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 [Kong, et al. Chin Phys B 29(10):100203, 2020], we explored a novel global-direction stencil and combined it with the face-area-weighted centroid on unstructured finite volume methods from differential form to realize the skewness reduction and a better reflection of flow anisotropy. Greatly inspired by the differential form, in this research, we demonstrate that it is also feasible to extend this novel method to the unstructured finite volume discretization from integral form on both second and third-order finite volume solver. 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 superiorities on both computational accuracy and convergence rate.

中文翻译：

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将具有“面部区域加权质心”的全局方向模具扩展为从整数形式进行的非结构化有限体积离散化

梯度重建极大地影响了非结构化有限体积离散化的准确性。对于常用的k精确重构方法，始终选择细胞质心作为参考点，以表述重构函数。但是在某些实际问题中，例如边界层，该区域中的单元始终设置为高宽比，以提高局部场分辨率，如果仍然使用几何质心进行空间离散化，则无法避免严重的网格偏斜，这不利于非结构化有限体积求解器的数值性能。在以前的工作中[Kong等。Chin Phys B 29（10）：100203，2020]，我们探索了一种新颖的全局方向模版，并将其与脸部加权质心在微分形式的非结构化有限体积方法上结合起来，以实现偏斜度的减小和流动各向异性的更好反映。受到微分形式的启发，在这项研究中，我们证明了将这种新方法扩展到二阶和三阶有限体积求解器上从积分形式到非结构化有限体积离散化的可行性。由线性对流，欧拉和拉普拉斯方程控制的数值示例被用来检验这种扩展的正确性和有效性。与传统的基于几何质心的顶点相邻和面相邻模板相比，带有面面积加权质心的全局方向模板几乎消除了网格偏斜，大大提高了计算精度以及收敛速度。结果，在从积分形式进行非结构化有限体积离散化时，该方法在计算精度和收敛速度上也具有优势。