Numerical Stability of the Six-Equation, Single-Pressure Model with Viscous Terms

A standard model for describing time-dependent two-phase flows is the so-called six-equation or two-fluid model, where mass, energy, and momentum equations are considered for each phase. It is well known that the single-pressure form of this model can contain complex characteristics and is therefore ill posed. This ill-posedness has been blamed for numerical instabilities that have at times been observed when finite difference solutions of these equations have been attempted. One method to render the characteristics real is to include viscous terms. The numerical implications of adding viscous terms to the six-equation model are considered, and the potential impact of these implications on the stability of the finite difference solution is evaluated.