Multi-dimensional Limiting Process and Maximum Principle for the Computations of Hyperbolic Conservation Laws on Unstructured Grids

Abstract

The present paper presents an efficient and accurate limiting strategy for the multidimensional hyperbolic conservation laws on unstructured grids within the framework of finite volume method. The basic idea 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 MLP condition. Mathematically, this condition satisfies the maximum principle which is a complementary condition ensuring monotonicity. Various numerical results show that the MLP is quite effective and accurate in preventing unwanted oscillations and capturing multi-dimensional flow features.