An indicator-based hybrid limiter in discontinuous Galerkin methods for hyperbolic conservation laws

Abstract

This paper proposes a hybrid limiter in discontinuous Galerkin (DG) methods for hyperbolic conservation laws. This hybrid limiter combines the high-order DG approximation with the low-order limited solution to achieve better resolution for multiscale structures. Meanwhile, the essentially non-oscillatory property can also be retained. The indicator, based on the jump information at the cell interface, provides the non-linear weight for the hybrid limiter, which also acts as a shock detection technique to identify troubled cells in the DG approximation. The presented limiter also maintains the conservation of mass cell by cell. In addition, the hybrid limiter maintains the local data structure and can, therefore, preserve the parallel efficiency of the DG method. The hybrid limiter is very simple in design and can be easily implemented with arbitrary high-order accuracy on both structured and unstructured meshes. Benchmark examples, mainly on Euler equations, are presented to demonstrate the performance of these DG methods with associated hybrid limiters.