Hyperbolic set of equations for transient one-dimensional two-phase flow

Transient, one-dimensional, two-phase flow models are widely used in reactor safety analysis. The models are based on rather complex sets of differential equations and constitutive relations. Many studies pointed out that such sets may have complex characteristic roots (nonhyperbolic). According to well-known mathematical theorems, hyperbolic systems with complex characteristics are ill-posed as initial-value problems. They can produce numerical instabilities that are clearly nonphysical in nature. On the other hand, there are stable numerical methods to solve hyperbolic systems with proper initial and boundary data. The purpose of this paper is (1) to find out the principal cause of the existence of complex roots and to modify the initial system in such a manner as to render the system hyperbolic (2) to compare the initial and modified systems by the use of characteristics analysis.