Monotonicity of Multi-dimensional Limiting Process on Unstructured Grids

Abstract

The present paper deals with the continuous work of extending multi-dimensional limiting process (MLP), which has been quite successfully proposed on two- and three-dimensional structured grids, onto the unstructured grids. The basic idea of the present limiting strategy is to control the distribution of both cell-centered and cell-vertex physical properties to mimic a multi-dimensional nature of flow physics, which can be formulated as so called the MLP condition. This condition satisfies the maximum principle, which ensures monotonicity, and numerical results show that MLP is effective to prevent unwanted oscillations as well as to capture multi-dimensional flow features accurately.