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

Abstract

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 1st order upwind, 2nd 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 2nd order upwind scheme is much more susceptible to instability at long waves than the 1st 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.