Study on the Stability and Boundedness of Discrete Schemes for Convection Term Based on Finite Volume Method

YU Bo; JIAO Kaituo; CHEN Yujie; LI Jingfa; DENG Yajun; WANG Peng; SUN Dongliang

doi:10.7652/xjtuxb202304012

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Study on the Stability and Boundedness of Discrete Schemes for Convection Term Based on Finite Volume Method

更新时间：2025-07-09

- Study on the Stability and Boundedness of Discrete Schemes for Convection Term Based on Finite Volume Method
- Vol. 57, Issue 4, Pages: 107-121(2023)
- 作者机构：
  
  1. 北京石油化工学院机械工程学院,北京,102617
  2. 西安交通大学动力工程多相流国家重点实验室,西安,710049
- 作者简介：
- 基金信息：
- DOI：10.7652/xjtuxb202304012
  CLC： TK14
- Online First：10 April 2023，
  
  Published：2023
- 稿件说明：
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YU Bo, JIAO Kaituo, CHEN Yujie, et al. Study on the Stability and Boundedness of Discrete Schemes for Convection Term Based on Finite Volume Method[J]. 2023, 57(4): 107-121.
DOI：

YU Bo, JIAO Kaituo, CHEN Yujie, et al. Study on the Stability and Boundedness of Discrete Schemes for Convection Term Based on Finite Volume Method[J]. 2023, 57(4): 107-121. DOI： 10.7652/xjtuxb202304012.

摘要

对于流动传热问题

控制方程对流项处理不当会导致模拟结果出现无物理意义的振荡或越界现象。针对有限容积法对流项离散格式的稳定性和有界性开展深入研究

并提出了一种新的高阶有界格式。在对流项离散格式稳定性方面

指出在均分网格条件下

边界相邻节点的对流稳定性条件与内部节点不同

并给出了边界相邻节点处常见对流项离散格式的稳定性条件; 指出绝对稳定的SGSD格式权重系数计算方法不唯一

并给出了两种适合于强对流问题的权重系数表达式。在对流项离散格式有界性方面

提出了高阶有界格式的通用分段线性形式——GHB格式(general high-order bounded scheme)

可提高程序的通用性; 高阶有界格式计算精度、收敛速率和健壮性等性能互相制约

根据规正变量图中不同区域线型对这些性能的影响

提出了含有两个可调参数的性能可控的高阶有界格式——AHB格式(adjustable high-order bounded scheme); 在此基础上

通过优化参数得到了计算精度、有界性、收敛速率和健壮性兼顾的ABC格式(accuracy

boundedness and convergence rate-balanced scheme)

并通过多个典型算例验证了该格式计算性能。

Abstract

For the flow and heat transfer problems

improper discretization of the convection term in the governing equation may cause the simulation results to be out of bounds or oscillate unphysically. In this paper

the stability and boundedness of discrete schemes for the convection term based on the finite volume method were studied

and a new high-order bounded scheme was proposed. For the stability of discrete schemes for the convection term

the convection stability conditions of nodes adjacent to boundary differ from those of internal nodes based on the uniform grid

and the stable range is presented for the common discrete schemes. Besides

the calculation method of the weight coefficient of the absolutely stable SGSD scheme is not unique. To this end

two calculation expressions of the weight coefficient suitable for the strong convection problem were provided. Regarding the boundedness of discrete schemes for the convection term

a general piecewise linear form of the high-order bounded scheme named GHB scheme(general high-order bounded scheme)was proposed

favoring improving the universality of the program. Besides

based on the idea that the computational accuracy

convergence rate

and robustness of the higher-order bounded scheme are mutually restricted and related to the line segment trends in the normalized variable diagram

an adjustable high-order bounded scheme(AHB scheme)with two adjustable parameters was proposed. Furthermore

an ABC scheme(accuracy

boundedness

and convergence rate-balanced scheme)balancing accuracy

boundedness

convergence rate

and robustness is obtained by optimizing the parameters in the AHB scheme

and its computational performance is proven by solving some classical problems.

关键词

Keywords

references

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