Stability of two-phase flow calculation using two-fluid models

Abstract Two-fluid modeling of two-phase flow may yield a system of partial differential equations having complex characteristics; this results in a mathematically ill-posed initial-value problem. Despite the fact that no finite-difference method for solving such a problem can be stable in the usual sense, finite-difference solution of two-fluid models is in widespread use. We investigate the numerical behavior of one such set of difference equations, derive conditions under which solutions appear to be well behaved, and offer a physical interpretation.