Development of central-upwind-WENO scheme for two-phase 1-D drift-flux model

Abstract

The two-phase drift flux model is extensively used in multiphase flow applications. In this study, we focus on possible numerical schemes for solving the drift flux model. Due to the complexity of the primitive equations and empirical parameters, it is challenging to achieve stability of the numerical scheme used for the drift flux model. The high resolution second order central scheme, the high resolution second order central-upwind scheme, and the high resolution third order and fifth order weighted essentially non-oscillatory schemes (WENO) were successfully implemented for the drift flux model. The schemes were tested with the shock tube discontinuity problem. The central-upwind-WENO scheme was developed and applied to the drift flux model. In the central-upwind-WENO scheme, the cell interface values were taken from the WENO reconstruction, and the monotone flux is calculated from the central-upwind flux. The central-upwind-WENO scheme can achieve higher order accuracy than the central-upwind scheme by using the same stencils which are used for the central-upwind scheme. The central-upwind-WENO scheme gives more accurate results than the central scheme, central-upwind scheme and the WENO scheme. Especially at the rarefaction and shock wave fronts, the central-upwind-WENO scheme gives sharper gradients compared to the other schemes. Instead of a limiter function, the central-upwind-WENO scheme uses a smoothness indicator. All the schemes used in the study are suitable for two-phase drift flux model simulation.