ON THE USE OF SOME WEIGHTED UPWIND SCHEMES FOR STRONGLY CONVECTIVE FLOWS

Abstract

Several upwind schemes for the discretization of first-order derivatives appearing in the governing equations describing fluid flow are derived to avoid formation of wiggles. This is achieved by a generalization of concepts introduced by Leonard, resulting in schemes that depend on the fluid flow characteristics, through the cell Reynolds number. After the presentation of such schemes, the most efficient one, combining the best observed features, is used to simulate several test problems, in most cases with superior results. However, in presence of steep gradients inside the region, under- or overshoot may be produced, similar to other available schemes. The implementation of the proposed scheme in existing codes is very easy and the generalizations for three-dimensional situations pose no additional difficulties.