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孔令发, 董义道, 刘伟. 全局方向模板对非结构有限体积梯度与高阶导数重构的影响[J]. 力学学报, 2020, 52(5): 1334-1349. DOI: 10.6052/0459-1879-20-093
引用本文: 孔令发, 董义道, 刘伟. 全局方向模板对非结构有限体积梯度与高阶导数重构的影响[J]. 力学学报, 2020, 52(5): 1334-1349. DOI: 10.6052/0459-1879-20-093
Kong Lingfa, Dong Yidao, Liu Wei. THE INFLUENCE OF GLOBAL-DIRECTION STENCIL ON GRADIENT AND HIGH-ORDER DERIVATIVES RECONSTRUCTION OF UNSTRUCTURED FINITE VOLUME METHODS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1334-1349. DOI: 10.6052/0459-1879-20-093
Citation: Kong Lingfa, Dong Yidao, Liu Wei. THE INFLUENCE OF GLOBAL-DIRECTION STENCIL ON GRADIENT AND HIGH-ORDER DERIVATIVES RECONSTRUCTION OF UNSTRUCTURED FINITE VOLUME METHODS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1334-1349. DOI: 10.6052/0459-1879-20-093

全局方向模板对非结构有限体积梯度与高阶导数重构的影响

THE INFLUENCE OF GLOBAL-DIRECTION STENCIL ON GRADIENT AND HIGH-ORDER DERIVATIVES RECONSTRUCTION OF UNSTRUCTURED FINITE VOLUME METHODS

  • 摘要: 模板选择方式对非结构有限体积方法的计算准确性会产生显著影响. 在之前的工作中, 基于局部方向模板存在的问题, 我们探索了一种更加简单有效的全局方向模板选择方法, 并将其应用于二阶精度非结构有限体积求解器. 基于该方法找到的模板单元均沿着壁面法向与流向, 可有效捕捉流场变化, 反映流动的各向异性, 并且模板选择过程脱离了对网格拓扑的依赖, 避免了局部方向模板选择方法中复杂的阵面推进与方向判断过程, 克服了在大压缩比三角形网格上模板单元偏离壁面法向的现象, 同时在二阶精度求解器上得到了较高的计算精度与计算准确性. 为了进一步验证全局方向模板在高阶精度非结构有限体积方法中应用的可行性, 本文初步测试了该模板对变量梯度及高阶导数重构的影响. 经检验, 在不同类型的网格上, 采用全局方向模板得到的变量梯度与高阶导数误差明显低于局部方向模板, 同时也低于共点模板的计算误差. 此外, 在高斯积分点处由全局方向模板得到的变量点值与导数误差同样在三种模板中最低. 因此该模板选择方法在非结构有限体积梯度与高阶导数重构方面具有较好的数值表现, 具备在高阶精度非结构有限体积求解器中应用并推广的可行性.

     

    Abstract: The accuracy of unstructured finite volume methods is greatly influenced by different stencils. In previous work, based on the existing problems of local-direction stencil, we explored a more concise global-direction stencil selection method for the second-order unstructured finite volume solver, and stencil cells selected by this novel stencil selection method are always along the boundary normal and circumferential directions even on grids with high aspect ratio. As a result, the variation of flowfield is effectively captured, and flow anisotropy are well reflected. In addition, the novel method is topology-independent, since global directions are determined by the flowfield, while the local directions are strongly coupled with the grid. Therefore, the complex process of advancing front as well as local directions estimation are completely avoided in the novel stencil selection method, and the phenomenon that stencil cells deviate from the boundary normal vector is effectively eliminated on high-aspect-ratio triangular grids. What's more, a better computational accuracy and lower truncation errors on the second-order accurate finite volume solver are obtained by the employment of global-direction stencil. In order to further test the effectiveness of global-direction stencil on high-order unstructured finite volume methods, we will preliminarily utilize this stencil to test the effect of gradient and high-order derivatives reconstruction. After verification, computational errors of global-direction stencil are lower than that of local-direction stencil, and also lower than that of commonly used vertex-neighbor stencil on different grid types. Besides, errors of variable and derivatives at the Gauss point obtained by global-direction stencil are also the lowest among three methods we tested. Therefore, the global-direction stencil is well performed on gradient as well as high-order derivatives reconstruction, and it is feasible to extend this novel stencil selection method to high-order unstructured finite volume methods.

     

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