Preconditioned Krylov subspace methods used in solving two-dimensional transient two-phase flows

Abstract

We investigate the performance of preconditioned Krylov subspace methods used in a previously presented two-fluid model developed for the simulation of separated and intermittent gas-liquid flows. The two-fluid model has momentum and mass balances for each phase. The equations comprising this model are solved numerically by applying a two-step semi-implicit time integration procedure. A finite difference numerical scheme with a staggered mesh is used. Previously, the resulting linear algebraic equations were solved by a Gaussian band solver. In this study, these algebraic equations are also solved using the generalized minimum residual (GMRES) and the biconjugate gradient stabilized (Bi-CGSTAB) Krylov subspace iterative methods preconditioned with incomplete LU factorization using the ILUT(p, r) algorithm. The decrease in the computational time using the iterative solvers instead of the Gaussian band solver is shown to be considerable