Preconditioned Krylov subspace methods for solving nonsymmetric matrices from CFD applications Original Research Article

We conduct an experimental study on the behavior of several preconditioned iterative methods to solve nonsymmetric matrices arising from computational fluid dynamics (CFD) applications. The preconditioned iterative methods consist of Krylov subspace accelerators and a powerful general purpose multilevel block ILU (BILUM) preconditioner. The BILUM preconditioner and an enhanced version of it are slightly modified versions of the originally proposed preconditioners. They will be used in combination with different Krylov subspace methods. We choose to test three popular transpose-free Krylov subspace methods: BiCGSTAB, GMRES and TFQMR. Numerical experiments, using several sets of test matrices arising from various relevant CFD applications, are reported.