Constructing a multi-dimensional oscillation preventing scheme for the advection equation by a rational function

Abstract

We recently developed a numerical scheme for solving advection equations based on a rational interpolation function. The scheme shows properties in suppressing spurious numerical oscillations near great gradients and sharing high accuracy in the smooth region. Results in one dimension were reported in a previous paper (F. Xiao, T. Yabe and T. Ito, Comput. Phys. Commun. 93 (1996) 1). In this paper, we, for completion, present the two- and three-dimensional versions of the scheme without directional splitting. Formula are derived in the way such as to recover the CIP method (T. Yabe, T. Aoki, Comput. Phys. Commun. 60 (1991) 219; T. Yabe, T. Ishikawa, P.Y. Wang, T. Aoki, Y. Kadota and F.Ikeda, Comput. Phys. Commun. 66 (1991) 233) by switching. The oscillation preventing quality of the scheme in two and three dimensions is tested by sample calculations.