An Analysis of Why Single Pressure Two-Fluid Two-Phase Unequal Velocity Model Equations Are Not Globally Hyperbolic

The characteristics for the slowly varying one-dimensional, single-phase flow equations with rigid and elastic walls are analyzed. The analysis of the characteristics for a single fluid in an elastic tube is extended to a set of analogous one-dimensional, two-phase flow equations having a common pressure. It is found that if the area available for flow for each phase is taken to be a function of a single pressure complex characteristics can arise. This analysis may explain part of the reason why two-phase flow equations having equal phase pressures are generally not globally hyperbolic.