全局方向模板在高阶精度非结构有限体积方法中的推广

孔令发; 刘伟; 董义道

doi:10.7638/kqdlxxb-2020.0080

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全局方向模板在高阶精度非结构有限体积方法中的推广

研究论文 | 更新时间：2026-05-28

- 全局方向模板在高阶精度非结构有限体积方法中的推广
- Extension of the global-direction stencil on high-order unstructured finite volume methods
- 空气动力学学报 2021年39卷第4期页码：39-50
- 作者机构：
  
  国防科技大学空天科学学院,长沙,410073
- 作者简介：
  
  孔令发（1996-），男，甘肃兰州人，博士研究生，研究方向：计算流体力学与应用. E-mail：lfkong_nudt@163.com
  董义道*（1991-），讲师，研究方向：计算流体力学与应用. E-mail：tianyatingxiao@163.com
- 基金信息：
  
  国家重大项目（GJXM92579）
- DOI：10.7638/kqdlxxb-2020.0080
  中图分类号： V211.3
- 纸质出版：2021
- 稿件说明：
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孔令发, 刘伟, 董义道. 全局方向模板在高阶精度非结构有限体积方法中的推广[J]. 空气动力学学报, 2021, 39(4): 39−50.

KONG Lingfa, LIU Wei, DONG Yidao. Extension of the global-direction stencil on high-order unstructured finite volume methods[J]. 2021, 39(4): 39-50.
孔令发, 刘伟, 董义道. 全局方向模板在高阶精度非结构有限体积方法中的推广[J]. 空气动力学学报, 2021, 39(4): 39−50. DOI： 10.7638/kqdlxxb-2020.0080

KONG Lingfa, LIU Wei, DONG Yidao. Extension of the global-direction stencil on high-order unstructured finite volume methods[J]. 2021, 39(4): 39-50. DOI： 10.7638/kqdlxxb-2020.0080.

摘要

梯度与高阶导数重构是影响高阶精度非结构有限体积（Finite Volume

FV）格式计算效果的主要过程，其中，不同的模板选择方式发挥了重要作用。传统的模板选择方式往往依赖于固定的网格拓扑关系，无法有效反映流动变化特征，并且随着求解精度的提高，模板单元的数量上升明显，导致找到的模板单元包含过多冗余信息的同时，显著增大计算量，降低求解效率。基于此现状，文章将基于二阶精度FV格式发展的全局方向模板推广至高阶精度FV方法，以充分发挥模板的空间延展性优势，并减少冗余的模板单元数量。此外，文章通过基于制造解的流动与真实超声速涡流两个数值算例，测试了全局方向模板的数值表现。经检验，全局方向模板的使用可有效减少重构过程所需的模板单元数量，并且计算误差相比传统基于网格拓扑的共点、共面模板更低，计算稳定性优于局部方向模板。因此，全局方向模板选择方法在三阶精度非结构有限体积方法中具有较好的数值表现，具备进一步推广与应用的可行性。

Abstract

Gradients and high-order derivatives reconstruction is an important process for high-order unstructured finite volume (FV) methods

in which the stencil selection plays a critical role. Commonly used stencil selection methods depend on the fixed topology relationship among grid cells

thus the characteristics of flow fields cannot be well captured. Besides

with the improvement of the computational accuracy

the stencil size increases dramatically

yielding redundant stencil cells and low computational efficiency. On this basis

the global-direction stencil developed from the second-order numerical simulations is extended into high-order unstructured finite volume methods to make full use of the spatial extendability and to reduce redundant stencil cells. The effectiveness of this novel stencil is verified by a flow with manufactured solutions and a supersonic vortex flow. Compared with commonly used face-neighbor and vertex-neighbor stencils

the stencil size is considerably reduced

and the computational accuracy is greatly improved. In addition

the stability of this novel stencil is superior to local-direction stencils. As a result

the global-direction stencil has a better numerical performance in the third-order unstructured finite volume methods

and it is feasible to further apply it in high-order numerical simulations.

关键词

Keywords

references

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