Linear stability analysis of the discretized one-Dimensional two-Fluid model equations for slug capturing in vertical flow

In this paper, a Von Neumann analysis of the discretized form of the 1D two-fluid model is presented for slug flow in vertical pipes in order to study the effect of the discretization scheme on the ill-posedness of the system. The resulting growth rate is compared to that obtained from a stability analysis of the parent system of differential equations. It is shown that the discretization of the equations introduces a cutoff limit for short wavelengths, below which all the perturbations are damped. This is equivalent to rendering the system numerically well posed. It is suggested here that this effect, for practical sizes of the mesh, is sufficient to stabilize the system and to yield valid solutions that lead to the prediction of the initiation of slugs in vertical configurations, and hence the computations for intermittent vertical flow using the two-fluid model. Those computations have been validated in a companion paper against experimental data. © 2015 by Begell House, Inc.