Applicability of High-Order Upwind Schemes to Two-Fluid Model

Abstract

The first-order upwind difference method is usually used for the two-phase flow analysis in order to maintain numerical stability whereas the high-order upwind difference method is seldom used. It is, however, difficult to obtain a highly accurate numerical solution using the first-order method because it has large numerical diffusion when the distributions of velocity and void fraction are discontinuous. In the previous reports, the numerical stability of the high-order upwind difference method was clarified using a linear model equation of the two-fluid model and the actual two-fluid model. In this report, we calculated the problem having discontinuous velocity and void fraction distributions with the two-fluid model and examined the accuracy of the numerical solution when the high-order upwind difference method was used. It was shown that the high-order upwind difference method gives a more accurate numerical solution than the first-order method. It was also shown that the maximum time step that can be used for stable calculation hardly increases by using the high-order method. The computational efficiency is, hence, almost the same between the high-order method and the first-order method.