Well-posedness of one-dimensional transient, two-fluid models of two-phase flows

摘要

The existence of regions of the flow map for which the transient one-dimensional two fluid model for stratified flows is ill-posed is demonstrated in a series of numerical experiments. The extent of these regions, previously identified in theoretical analyses, is shown to depend on the models included for momentum transfer at the interface, and the results from the numerical experiments agreed well with the behaviour expected from these theoretical analyses. Both in viscid and frictional flows are studied, and the masking of ill-posedness by numerical diffusion is clearly demonstrated for each. The existence of a region of unstable flow in a well-posed problem for viscous flows is demon-strated, and the growth of instabilities in such a regime is well simulated by the model, provided adequate numerical resolution is ensured.