递归投影方法(RPM)及其在流场数值模拟中的加速收敛性能研究  

The RPM method and the investigation of its accelerating convergence for flow simulations

作　　者：李孝伟[1] 王正裕[1] 

机构地区：[1]上海大学,上海市应用数学和力学研究所,上海200072

出　　处：《空气动力学学报》2010年第1期17-22,共6页Acta Aerodynamica Sinica

基　　金：国家自然科学基金资助项目(10672097,10772103)

摘　　要：随着计算流体力学中的物理模型的日益复杂和数据运算量的增大,人们越来越重视提高数值方法的计算效率。本文在研究RPM方法的基础上,提出了一种更易于保证实施精度的具有良好加速收敛性能的改型的RPM方法。一方面,通过构造的一维迭代格式研究了几个控制参数如Krylov接受比、Krylov向量维数等对RPM方法的加速收敛性能的影响。另一方面,研究了在流场数值模拟中即使采用了常规的加速收敛措施如当地时间步长和隐式残值光顺以后,改型的RPM方法的加速收敛性能;结果表明,此时,RPM方法仍然能使总体上的收敛速度提高近1/3。As models of CFD become more and more complex and amounts of algebraic operations become much greater,it is more and more important to improve the efficiency of numerical simulations.Based on the study of the RPM method,a modified RPM which is easier to keep accuracy of the basis and has good accelerating convergence is proposed in this paper.Several RPM control parameters,Krylov acceptance ratio,Krylov vector dimension,etc.,which can effect on the acceleration performance of RPM,are studied through constructed one-dimensional iteration schemes.On the other hand,after the general accelerating methods such as the local time step and implicit residual smoothing are used in the simulation algorithm for fluid flow,the RPM is implemented in order to investgate the accelerating efficiency of RPM,and the results show that even so the RPM can improve the convergence velocity up to 1/3.

关 键 词：RPM方法 不变子空间 当地时间步长 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程]