Runge-Kutta Discontinuous Galerkin Method with a Simple and Compact Hermite WENO Limiter on Unstructured Meshes (Communications in Computational Physics, 2018)
In this paper we generalize a new type of compact Hermite weighted essentiallynon-oscillatory (HWENO) limiter for the Runge-Kutta discontinuous Galerkin(RKDG) method, which was recently developed in [38] for structured meshes, to twodimensional unstructured meshes. The main idea of this HWENO limiter is to reconstructthe new polynomial by the usage of the entire polynomials of the DG solutionfrom the target cell and its neighboring cells in a least squares fashion [11] while maintainingthe conservative property, then use the classical WENO methodology to forma convex combination of these reconstructed polynomials based on the smoothness indicatorsand associated nonlinear weights. The main advantage of this new HWENOlimiter is the robustness for very strong shocks and simplicity in implementation especiallyfor the unstructured meshes considered in this paper, since only informationfrom the target cell and its immediate neighbors is needed. Numerical results for bothscalar and system equations are provided to test and verify the good performance ofthis new limiter.