1993 Volume 7 Issue 3 Pages 241-249
Numerical solutions based on the two-fluid model are likely to be unstable due to its ill-posedness. The first-order upwind scheme is usually adopted for the convection terms for stabilization while high-order upwind schemes are seldom used. In this study, the applicability of high-order upwind schemes was examined by analyzing the amplification factor of finite difference equations for a single linear model equation of the two-fluid model. The numerical stability of various schemes was systematically clarified by making use of a concept of mapping in a complex plane. It was confirmed that high-order upwind schemes tend to yield unstable numerical solutions. It was also demonstrated that the inclusion of an explicit diffusion term into the basic equation can remove the numerical instability.
