A new numerical method for solution of boiling flow using combination of SIMPLE and Jacobian-free Newton-Krylov algorithms

In this paper, an efficient and stable numerical approach is developed in which a different combination of Jacobian-free Newton-Krylov (JFNK) and SIMPLE methods are introduced for solution of two-phase flow in both steady state and transient conditions. It is shown that, combination of Krylov subspace methods and SIMPLE type preconditioner give a fast convergence in the solution of the Drift Flux Model (DFM). It is demonstrated that the stability problem with SIMPLE approach, for two-phase flow problems, can be avoided by combining with JFNK. RELAP5 code and experimental data are considered for verification study. For all benchmarks, the proposed methods predictions are in good agreement with experiment and RELAP5 results. The accuracy of the proposed schemes were studied and compared with the classical SIMPLE method. It was found that the present approach to two-phase flow simulation predicts accurate results over a wide pressure range; whereas the classical SIMPLE algorithm underestimated the void fraction at low pressures. Finally, a typical power transient is considered to demonstrate how the problem fastest time scale can change during the course of a transient. The present assessment of the numerical method showed that the time step control is not based on a stability time step restriction, like the material Courant limit.