流场特性驱动的亚松弛因子自动获取方法

康杰; 樊桦; 吴东垠

doi:10.7652/xjtuxb202504004

您当前的位置：

首页 >

文章列表页 >

流场特性驱动的亚松弛因子自动获取方法

—————————————————————— | 更新时间：2026-01-06

- 流场特性驱动的亚松弛因子自动获取方法
- Flow Field Characteristics-Driven Automatic Under-Relaxation Factor Acquisition Method
- 西安交通大学学报 2025年59卷第4期页码：40-49
- 作者机构：
  
  西安交通大学能源与动力工程学院， 710049，西安
- 作者简介：
  
  康杰（1998—），男，硕士生；
  吴东垠（通信作者），男，教授，博士生导师。
- 基金信息：
  
  陕西省秦创原“科学家+工程师”队伍建设项目(2023KXJ-218)
- DOI：10.7652/xjtuxb202504004
  中图分类号： TK124
- 收稿：2024-10-12，
  
  网络首发：2024-12-04，
  
  纸质出版：2025-04-10
- 稿件说明：
移动端阅览
康杰, 樊桦, 吴东垠. 流场特性驱动的亚松弛因子自动获取方法[J]. 西安交通大学学报, 2025,59(4):40-49.

KANG Jie, FAN Hua, WU Dongyin. Flow Field Characteristics-Driven Automatic Under-Relaxation Factor Acquisition Method[J]. Journal of Xi’an Jiaotong University, 2025, 59(4): 40-49.
康杰, 樊桦, 吴东垠. 流场特性驱动的亚松弛因子自动获取方法[J]. 西安交通大学学报, 2025,59(4):40-49. DOI： 10.7652/xjtuxb202504004.

KANG Jie, FAN Hua, WU Dongyin. Flow Field Characteristics-Driven Automatic Under-Relaxation Factor Acquisition Method[J]. Journal of Xi’an Jiaotong University, 2025, 59(4): 40-49. DOI： 10.7652/xjtuxb202504004.

摘要

为解决传统亚松弛因子选取过度依赖计算经验并且没有考虑流场本身特性的问题，提出了一种流场特性驱动的亚松弛因子自动获取方法。针对压力耦合方程组的半隐式方法（SIMPLE）系列算法，基于流场速度梯度给出了用于表征速度分布的表征量，在此基础上利用非线性函数对该表征量进行转化，导出了速度亚松弛因子的计算表达式，

并且在顶盖驱动流、后台阶流和水箱流3个经典算例下对比分析了固定亚松弛因子与自动获取方法在一阶迎风格式、对流项二阶迎风插值（QUICK）格式和保证隐定性的二阶插分格式下的计算表现。结果表明：所提自动获取方法在各算例和离散格式中的计算时间均与固定亚松弛因子下的最短计算时间相当，有些工况下甚至小于固定亚松弛因子的最短计算时间；当后台阶流算例采用30×180和30×210的网格，QUICK格式下固定亚松弛因子为0.1、0.5、0.9时，计算均不收敛，改用所提自动获取方法后计算收敛；采用自动获取方法的计算残差最终可以达到10

－14

量级，与收敛情况下的固定亚松弛因子量级相同。研究为进一步优化亚松弛因子自动获取方法提供了参考。

Abstract

To address the issue of traditional under-relaxation factor selection overly reliant on computational experience and overlooking inherent flow field characteristics

a method for automatically acquiring under-relaxation factors driven by flow field characteristics is proposed. For the semi-implicit method for pressure-linked equations (SIMPLE) series algorithm

a quantity representing the velocity distribution based on the velocity gradient of the flow field is provided. Utilizing a nonlinear function to transform this quantity

an expression for calculating the velocity under-relaxation factor is derived. Comparative analyses of fixed under-relaxation factors and the automatic acquisition method are conducted in three classic cases of lid-driven flow

backward-facing step flow

and tank flow under first-order upwind

quadratic upwind interpolation of convective kinematics (QUICK)

and stability-guaranteed second-order difference schemes. The results show that the proposed automatic acquisition method yields computation times comparable to the shortest computation times under fixed under-relaxation factors in all cases and discretization schemes

and in some scenarios

even shorter than the shortest computation time under fixed under-relaxation factors. In the case of the backward-facing step flow with grid sizes of 30×180 and 30×210 under the QUICK scheme

computations do not converge with fixed under-relaxation factors set at 0.1

0.5

and 0.9

but converge when using the proposed automatic acquisition method. The residual values obtained using the automatic acquisition method can reach the order of 10

－14

equiv

alent to the order of fixed under-relaxation factors under convergence conditions. This research provides a reference for further optimizing automatic under-relaxation factor acquisition methods.

关键词

Keywords

references

宣领宽 , 龚京风 , 张文平 , 等 . 用于非均质复合材料应力分析的交错网格有限体积法 [J ] . 西安交通大学学报 , 2014 , 48 ( 3 ): 121 - 127 .

XUAN Lingkuan , GONG Jingfeng , ZHANG Wenping , et al . Staggered cell-vertex finite volume method for analyzing stress in heterogeneous composite materials [J ] . Journal of Xi'an Jiaotong University , 2014 , 48 ( 3 ): 121 - 127 .

VAN DOORMAAL J P , RAITHBY G D . Enhancements of the simple method for predicting incompressible fluid flows [J ] . Numerical Heat Transfer , 1984 , 7 ( 2 ): 147 - 163 .

PATANKAR S V , SPALDING D B . A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows [J ] . International Journal of Heat and Mass Transfer , 1972 , 15 ( 10 ): 1787 - 1806 .

王锋 , 孙中国 , 刘启新 , 等 . Y型微混合器内流流场移动粒子半隐式法数值分析 [J ] . 西安交通大学学报 , 2021 , 55 ( 5 ): 162 - 170 .

WANG Feng , SUN Zhongguo , LIU Qixin , et al . Numerical analysis of the flow field in a Y-type micromixer using moving particle semi-implicit method [J ] . Journal of Xi'an Jiaotong University , 2021 , 55 ( 5 ): 162 - 170 .

李冬 , 柳云钊 , 陈鑫 , 等 . 酚醛树脂基复合材料传热-热解模型构建与试验研究 [J ] . 西安交通大学学报 , 2024 , 58 ( 8 ): 49 - 59 .

LI Dong , LIU Yunzhao , CHEN Xin , et al . Research on construction and experimental verification of heat transfer-pyrolysis model for phenolic resin-based composite materials [J ] . Journal of Xi'an Jiaotong University , 2024 , 58 ( 8 ): 49 - 59 .

王长安 , 侯育杰 , 刘成昌 , 等 . 燃煤链条炉掺烧半焦NO x 生成特性及配风优化数值模拟研究 [J ] . 西安交通大学学报 , 2022 , 56 ( 4 ): 1 - 12 .

WANG Changan , HOU Yujie , LIU Chengchang , et al . Numerical simulation study on NO x emission characteristics and the optimization of air induction of coal-fired chain boiler blended with semi-coke [J ] . Journal of Xi'an Jiaotong University , 2022 , 56 ( 4 ): 1 - 12 .

邓雅军 , 张琳 , 孙东亮 , 等 . IDEAL算法在OpenFOAM界面两相流求解器中的实现与性能分析 [J ] . 西安交通大学学报 , 2020 , 54 ( 12 ): 147 - 157 .

DENG Yajun , ZHANG Lin , SUN Dongliang , et al . Implementation and performance analysis of IDEAL algorithm for unsteady two-phase flow problems in OpenFOAM [J ] . Journal of Xi'an Jiaotong University , 2020 , 54 ( 12 ): 147 - 157 .

PATANKAR S V . Numerical heat transfer and fluid flow [M ] . Boca Raton, FL, USA : CRC Press , 1980 .

BARRON R M , SALEHI NEYSHABOURI A A . Effects of under-relaxation factors on turbulent flow simulations [J ] . International Journal for Numerical Methods in Fluids , 2003 , 42 ( 8 ): 923 - 928 .

MAREK R , STRAUB J . Hybrid relaxation: a technique to enhance the rate of convergence of iterative algorithms [J ] . Numerical Heat Transfer: Part B Fundamentals , 1993 , 23 ( 4 ): 483 - 497 .

GOPINATH R , GANESAN V . Orthogonal arrays: An introduction and their application in optimizing underrelaxation factors in ‘simple’-based algorithm [J ] . International Journal for Numerical Methods in Fluids , 1992 , 14 ( 6 ): 665 - 680 .

CHATWANI AV , TURAN A . Technical note improved pressure-velocity coupling algorithm based on minimization of global residual norm [J ] . Numerical Heat Transfer: Part B Fundamentals , 1991 , 20 ( 1 ): 115 - 123 .

范晓伟 , 阴建民 , 陈钟颀 . SIMPLE算法中压力松驰因子的自动生成 [J ] . 郑州纺织工学院学报 , 1997 , 8 ( 3 ): 7 - 12 .

FAN Xiaowei , YIN Jianmin , CHEN Zhongqi . The auto production of pressure relaxation factor in simple algorithm [J ] . Journal of Zhengzhou Textile Institute , 1997 , 8 ( 3 ): 7 - 12 .

LIU Xunliang , TAO Wenquan , ZHENG Ping , et al . Control of convergence in a computational fluid dynamic simulation using fuzzy logic [J ] . Science in China: Series E Technological Science , 2002 , 45 ( 5 ): 495 - 502 .

王艳宁 , 孙东亮 , 苗政 , 等 . 模糊控制技术在SIMPLER算法中的应用及求解性能分析 [J ] . 西安交通大学学报 , 2016 , 50 ( 1 ): 78 - 84 .

WANG Yanning , SUN Dongliang , MIAO Zheng , et al . Application of a fuzzy control method in SIMPLER algorithm and its solving performance analysis [J ] . Journal of Xi'an Jiaotong University , 2016 , 50 ( 1 ): 78 - 84 .

MORII T , VIEROW K . The soar method for automatically optimizing simple relaxation factors [J ] . Numerical Heat Transfer: Part B Fundamentals , 2000 , 38 ( 3 ): 309 - 332 .

马淼 , 李春光 , 景何仿 . 确定SIMPLE算法中压力松弛因子的自适应方法 [J ] . 甘肃科学学报 , 2011 , 23 ( 4 ): 102 - 105 .

MA Miao , LI Chunguang , JING Hefang . The adaptive method for fixing the pressure relaxation factor of SIMPLE algorithm [J ] . Journal of Gansu Sciences , 2011 , 23 ( 4 ): 102 - 105 .

YOU Wei , LI Zengyao , TAO Wenquan . A general self-adaptive under-relaxation strategy for fast and robust convergence of iterative calculation of incompressible flow [J ] . Numerical Heat Transfer: Part B Fundamentals , 2020 , 77 ( 4 ): 299 - 310 .

宇波 , 焦开拓 , 陈宇杰 , 等 . 有限容积法对流项离散格式的稳定性与有界性研究 [J ] . 西安交通大学学报 , 2023 , 57 ( 4 ): 107 - 121 .

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 ] . Journal of Xi'an Jiaotong University , 2023 , 57 ( 4 ): 107 - 121 .

陶文铨 . 数值传热学 [M ] . 2版 . 西安 : 西安交通大学出版社 , 2001 .

王福军 . 计算流体动力学分析 [M ] . 北京 : 清华大学出版社 , 2004 .

NI Mingjiu , TAO Wenquan , WANG Shangjin . Stability-controllable second-order difference scheme for convection term [J ] . Journal of Thermal Science , 1998 , 7 ( 2 ): 119 - 130 .

LI Z Y , TAO W Q . A new stability-guaranteed second-order difference scheme [J ] . Numerical Heat Transfer: Part B Fundamentals , 2002 , 42 ( 4 ): 349 - 365 .

ERTURK E . Numerical solutions of 2-D steady incompressible flow over a backward-facing step: part I high Reynolds number solutions [J ] . Computers & Fluids , 2008 , 37 ( 6 ): 633 - 655 .

GHIA U , GHIA K N , SHIN C T . High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method [J ] . Journal of Computational Physics , 1982 , 48 ( 3 ): 387 - 411 .

MAZHAR Z . A procedure for the treatment of the velocity-pressure coupling problem in incompressible fluid flow [J ] . Numerical Heat Transfer: Part B Fundamentals , 2001 , 39 ( 1 ): 91 - 100 .

浏览量

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

布西内斯克近似下速度-压力全耦合求解的伪瞬态延拓方法

有限体积法与LBM分区耦合模拟方腔自然对流

用于非均质复合材料应力分析的交错网格有限体积法

采用有限体积法的自然对流换热拓扑优化数值方法

语义区分和子图整合驱动的知识图谱表示学习方法