The multi-dimensional limiters for discontinuous Galerkin method on unstructured grids

Accuracy-preserving and non-oscillatory shock-capturing technique is the bottle neck in the development of discontinuous Galerkin method. Inspired by the success of the k-exact WENO limiters for high order finite volume methods, this paper generalize the k-exact WENO limiter to discontinuous Galerkin methods. Also several improvements are put forward to keep the compactness and high-order accurate properties of DG method. The resulting schemes are easy to implement and effective in capturing the shock waves. Some standard cases are performed to validate the accuracy and robustness of the proposed limiters for the DG methods.