It is well known that the basic single pressure, two fluid mode for two phase flow has complex characteristics and is dynamically unstable. Nevertheless, common nuclear reactor thermal-hydraulics codes use variants of this model for reactor safety calculations. In these codes, the non-physical instabilities of the model may be damped by the numerical method and/or additional momentum interchange terms. Both of these effects are investigated using the linearized Von Neumann stability analysis. The stability of the semi-implicit method is of primary concern, because of its computational efficiency and popularity.; It is shown that there is likely no completely stable numerical method, including fully implicit methods, for the basic single pressure model. Additionally, the momentum inter-change terms commonly added to the basic single pressure model do not result in stable numerical methods for all the physically interesting reference conditions. Although practical stable approximations may be realized on a coarse computational grid, it is concluded that the assumption of instantaneously equilibrated phasic pressures must be relaxed in order to develop a generally stable numerical solution of a two fluid model.; The numerical stability of the semi-implicit discretization of the true two pressure models of Ransom and Hicks, and Holm and Kupershmidt is analyzed. The semi-implicit discretization of these models, which possess real characteristics, are found to be numerically stable as long as certain convective limits are satisfied. Based on the form of these models, the general form of a numerically stable, basic two pressure model is proposed. The evolution equation required for closure is a volume fraction transport equation, which may possibly be determined based on void wave propagation considerations.
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