Multi-dimensional Limiting Process for Discontinuous Galerkin Methods on Unstructured Grids

The present chapter deals with the continuous work of extending the multi-dimensional limiting process (MLP), which has been quite successful in finite volume methods (FVM), into discontinuous Galerkin (DG) methods. Based on successful analyses and implementations of the MLP slope limiting in FVM, MLP is applicable into DG framework with the MLP-based troubled-cell marker and the MLP slope limiter. Through several test cases, it is observed that the newly developed MLP combined with DG methods provides quite desirable performances in controlling numerical oscillations as well as capturing key flow features.