A two-fluid model is discretized with the FCT method to simulate two-phase flows in gas pipelines.
Hyperbolicty is lost over a range of the Taitel and Dukler's diagram for stratified-flow pattern.
Eigenvalues alternate signs at boundaries with implications on how to impose the boundary conditions.
Accuracy analysis is conducted to show that the FCT is up to second-order in space.
The model is validated against numerical simulations carried out with a commercial software.