模糊控制技术在SIMPLER算法中的应用及求解性能分析

Application of a Fuzzy Control Method in SIMPLER Algorithm and Its Solving Performance Analysis

为了提高SIMPLER算法在三维流动问题上的求解性能,引入模糊控制方法来自动调控速度亚松弛因子的大小.在数值计算过程中,将相邻两个迭代层次上的最大动量残差比值作为模糊控制输入量,速度亚松弛因子的变化量作为模糊控制输出量,基于最大动量残差的变化趋势可实现速度亚松弛因子的自动调控,从而达到加快收敛的目的.最后,通过3个经典的流动问题验证了模糊控制方法的优越性.研究表明：当初始亚松弛因子为最不利值时,模糊控制方法的收敛速度约是固定松弛因子方法的5~30倍;当初始亚松弛因子为最佳值时,模糊控制方法迭代次数与固定松弛因子方法迭代次数之比为0.7~2.0,收敛速度相差不大;采用模糊控制方法后,SIMPLER算法在不同初始亚松弛因子下均能得到高速收敛的解,同时健壮性也显著提高.研究工作将为大幅提升SIMPLER算法在三维流动问题上的求解性能起到重要作用.

In order to enhance the solving performance of the SIMPLER algorithm for threedimensional fluid flow problems,a fuzzy control method was introduced to automatically adjust the value of the velocity under-relaxation factor.The ratio of the maximum momentum residuals of two successive iteration levels is used as the input variable of the fuzzy control,and the variation of the velocity under-relaxation factor is taken as the output variable of the fuzzy control.Based on the changing trend of the maximum momentum residual,the velocity underrelaxation factor could be adjusted for accelerating the iteration convergence.Finally,the fuzzy control method was evaluated by solving three classic fluid flow problems.It could be concluded that when the initial under-relaxation factor is set at its most unfavorable value,the convergence rate of the fuzzy control method is about 5-30 times of the fixed relaxation factor method;however,when the initial under-relaxation factor is at its optimum value,the ratio of the iteration number of the fuzzy control method to the fixed relaxation factor method is 0.7-2.0andthere is a little difference for the convergence rates between the two methods.The SIMPLER algorithm using fuzzy control method could not only always get solutions with high convergence rate under different initial under-relaxation factors,but also possess much better robustness.Therefore,this research is of great significance in improving the solving performance of the SIMPLER algorithm for three-dimensional fluid flow problems.