On the use of continuous finite-elements for two-phase flow simulations in horizontal and nearly horizontal pipes

The one-dimensional two-fluid model, employed for simulating two-phase flows in long pipes, is conditionally well-posed and discretized with lower-order space and time schemes. This work investigates the capability of continuous finite-element methods of describing wave growth and potential flow pattern transitions, with stratified smooth flow as an initial condition, using the FEniCS computing platform. The effects of initial conditions, mesh configuration, order of basis functions, and pipe inclination on the stability were investigated through eigenspectra and flow pattern maps of the differential and discrete equations. The numerical model proposed describes potential wave growth, which serves as a baseline for simulating flow pattern transitions in oil and gas systems.