Multi-dimensional limiting process for hyperbolic conservation laws on unstructured grids

The present paper deals with a robust, accurate and efficient limiting strategy on unstructured grids within the framework of finite volume method. 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. The design principle of the proposed method is based on the multidimensional limiting condition and the maximum principle, which can ensure the multidimensional monotonicity through the global/local L∞ stability. Consequently, it can be shown that the MLP limiting does satisfy the local extremum diminishing (LED) condition in a truly multi-dimensional way. Various numerical analyses and extensive computations validate superior characteristics, such as efficient controlling multi-dimensional oscillations and accurate capturing of both discontinuous and continuous multi-dimensional flow features.