A Study on Numerical Instability of Inviscid Two-Fluid Model Near Ill-Posedness Condition

The two-fluid model is widely used in studying gas-liquid flow inside pipelines because it can qualitatively predict the flow field at low computational cost. However, the two-fluid model becomes ill-posed when the slip velocity exceeds a critical value, and computations can be quite unstable before flow reaches the unstable condition. In this study computational stability of various convection schemes for the two-fluid model is analyzed. A pressure correction algorithm for inviscid flow is carefully implemented to minimize its effect on numerical stability. Von Neumann stability analysis for the wave growth rates by using the 1^st order upwind, 2^nd order upwind, QUICK, and the central difference schemes shows that the central difference scheme is more accurate and more stable than the other schemes. The 2^nd order upwind scheme is much more susceptible to instability at long waves than the 1^st order upwind and inaccurate for short waves. The instability associated with ill-posedness of the two-fluid model is significantly different from the instability of the discretized two-fluid model. Excellent agreement is obtained between the computed and predicted wave growth rates. The connection between the ill-posedness of the two-fluid model and the numerical stability of the algorithm used to implement the inviscid two-fluid model is elucidated.