Monotonicity and Maximum Principle for Multidimensional Hyperbolic Conservation Laws

The present paper deals with an efficient and accurate multi-dimensional limiting strategy for hyperbolic conservation laws on structured and unstructured grids. The multi-dimensional limiting process (MLP) which was successfully proposed on structured grid system is extended to unstructured grids. The MLP condition satisfies the maximum principle, and various numerical results show that MLP is effective to prevent unwanted oscillations on multi-dimensional flow, which is a favorable feature of monotonicity.