Abstract: Methods and apparatus for investigating and predicting slug flow in complex pipes are disclosed. More particularly, the techniques provide a model of multiphase flow in a complex pipeline and its solution acquired using the Jacobian-Free Newton-Krylov (JFNK) method by way of non-limiting example. The fully implicit formulation framework described in this work enables to efficiently solve governing fluid flow equations. The framework can reduce the multiphase flow model in zones or cells of the pipe that exhibit phase disappearance based on the phase state distributions over the cells. The model of multiphase flow can include a model for single-phase cells that is different from a model for multiphase cells, and the proper model can be selected (or switched) as the phase characteristics of the multiphase flow of the cells change over time. A transient two-fluid model can be used to verify and validate the proposed algorithm for conditions of terrain-induced slug flow regime.