Comparison of numerical methods for slug capturing with the two-fluid model

In this paper the capability of the two-fluid model to describe the transition from stratified to slug flow is investigated, by employing three different numerical discretization techniques: classical finite volume, discontinuous Galerkin, and a Lagrangian finite volume approach. It is shown that stratified wavy flow can transition from well-posed to ill-posed following the KelvinHelmholtz instability mechanism. In the ill-posed regime grid convergence cannot be obtained. However, with low order discretization methods, or coarse grids and time steps, well-posed numerical solutions can still be obtained. Such solutions should however be critically assessed because they seem to be physical while in fact they are meaningless. The conditional well-posedness of the two-fluid model therefore requires a careful discretization in order to use it for slug capturing.