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

作　　者：康杰 樊桦 吴东垠[1] KANG Jie;FAN Hua;WU Dongyin(School of Energy and Power Engineering,Xi’an Jiaotong University,Xi’an 710049,China)

机构地区：[1]西安交通大学能源与动力工程学院,710049西安

出　　处：《西安交通大学学报》2025年第4期40-49,共10页Journal of Xi'an Jiaotong University

基　　金：陕西省秦创原“科学家+工程师”队伍建设项目(2023KXJ-218)。

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)格式和保证稳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。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),equivalent 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：SIMPLE算法 有限体积法 高精度格式 亚松弛因子 

分 类 号：TK124[动力工程及工程热物理—工程热物理]