Comparison of convergence rate and analysis of robustness by using different algebraic equation solution methods

The alterative direct iterative (ADI), strong implicit procedure (SIP), preconditioning transpose-free variant of quasi-minimum residual method (TFQMR) and biconjugate gradient stabilized method (Bi-CGSTAB) of the Krylov subspace methods were implemented in SIMPLER algorithm to solve the algebraic equations. The convergence rate and the robustness comparisons were conducted for the solution procedure using the above-mentioned different iterative solution methods. It is found that the solution methods for the algebraic equations can affect the robustness of SIMPLER algorithm. By using different algebraic equation solution methods and the related parameters, the robustness of SIMPLER algorithm can be controlled to a certain degree. Through analysis of specific examples, it is found that the convergence rate of SIP method can be about 30% to 50% higher than that of ADI with high offset factor a, while the related robustness of SIMPLER is somewhat weakened. In contrast, decreasing a makes its convergence rate more or less the same as that of ADI, and the robustness is much better than that of ADI. The average convergence rate of ILU(0) preconditioning Bi-CGSTAB method is about 15% to 40% higher than that of ADI, which can be easily reached by SIP method with an appropriate value of offset factor a, but the robustness of SIP is worse than that of Bi-CGSTAB. The convergence rate of preconditioning TFQMR is the smallest, but the robustness is the best.