Krylov子空间法在SIMPLER算法中的求解性能分析

ANALYSIS OF SOLUTION CHARACTERISTIC FOR KRYLOV SUBSPACE METHODS IN SIMPLER ALGORITHM

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。

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.