Krylov子空间法在SIMPLER算法中的求解性能分析

本文开发了Krylov子空间法中的Bi-CGSTAB、GMRES(m)、CGS、TFQMR及QMR方法的计算程序,并将其实施于SIMPLER算法作为其内迭代方法,针对CFD/NHT领域的问题,研究了它们的求解特性;发现:Bi-CGSTAB方法有着高效的收敛速度和良好的稳定性;N-S方程求解中不同方程不同m值的协调选取是GMRES(m)方法在CFD/NHT领域推广应用的关键;CGS和QMR方法易于中断;TFQMR方法收敛速度慢于其他方法,但能适用于更广泛问题的求解.

ANALYSIS OF SOLUTION CHARACTERISTIC FOR KRYLOV SUBSPACE METHODS IN SIMPLER ALGORITHM

In this paper,the programs of Krylov subspace methods,namely Bi-CGSTAB,GMRES(m), TFQMR,CGS and QMR methods,were developed and implemented in SIMPLER algorithm as the inner iteration method.Analyzing the specific examples,we can find that,Bi-CGSTAB method behaves more efficient in CPU time and higher robustness than other methods;it is a key to GMRES(m) method to choose the different m value to different equations of N-S equation in order to enlarge the application in CFD/NHT;CGS and QMR methods are easily broken off;the CPU time of TFQMR method is the slowest among other methods,but this method is easier to solve wider problems of CFD/NHT.