Flow Field Characteristics-Driven Automatic Under-Relaxation Factor Acquisition Method

KANG Jie; FAN Hua; WU Dongyin

doi:10.7652/xjtuxb202504004

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Flow Field Characteristics-Driven Automatic Under-Relaxation Factor Acquisition Method

更新时间：2026-01-06

- Flow Field Characteristics-Driven Automatic Under-Relaxation Factor Acquisition Method
- Journal of Xi’an Jiaotong University Vol. 59, Issue 4, Pages: 40-49(2025)
- 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：
- 基金信息：
- DOI：10.7652/xjtuxb202504004
  CLC： TK124
- Received：12 October 2024，
  
  Online First：04 December 2024，
  
  Published：10 April 2025
- 稿件说明：
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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：

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.

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references

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