| Abstract: | In this paper, we propose a new type of weighted essentially non-oscillatory
(WENO) limiter, which belongs to the class of Hermite WENO (HWENO) limiters, for
the Runge-Kutta discontinuous Galerkin (RKDG) methods solving hyperbolic conservation
laws. This new HWENO limiter is a modification of the simple WENO limiter
proposed recently by Zhong and Shu 29]. Both limiters use information of the DG
solutions only from the target cell and its immediate neighboring cells, thus maintaining
the original compactness of the DG scheme. The goal of both limiters is to obtain
high order accuracy and non-oscillatory properties simultaneously. The main novelty
of the new HWENO limiter in this paper is to reconstruct the polynomial on the target
cell in a least square fashion 8] while the simple WENO limiter 29] is to use the entire
polynomial of the original DG solutions in the neighboring cells with an addition of
a constant for conservation. The modification in this paper improves the robustness
in the computation of problems with strong shocks or contact discontinuities, without
changing the compact stencil of the DG scheme. Numerical results for both one and
two dimensional equations including Euler equations of compressible gas dynamics
are provided to illustrate the viability of this modified limiter. |
