Runge-Kutta Discontinuous Galerkin Method with a Simple and Compact Hermite WENO Limiter (Communications in Computational Physics, 2018)
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, forthe Runge-Kutta discontinuous Galerkin (RKDG) methods solving hyperbolic conservationlaws. This new HWENO limiter is a modification of the simple WENO limiterproposed recently by Zhong and Shu [29]. Both limiters use information of the DGsolutions only from the target cell and its immediate neighboring cells, thus maintainingthe original compactness of the DG scheme. The goal of both limiters is to obtainhigh order accuracy and non-oscillatory properties simultaneously. The main noveltyof the new HWENO limiter in this paper is to reconstruct the polynomial on the targetcell in a least square fashion [8] while the simple WENO limiter [29] is to use the entirepolynomial of the original DG solutions in the neighboring cells with an addition ofa constant for conservation. The modification in this paper improves the robustnessin the computation of problems with strong shocks or contact discontinuities, withoutchanging the compact stencil of the DG scheme. Numerical results for both one andtwo dimensional equations including Euler equations of compressible gas dynamicsare provided to illustrate the viability of this modified limiter.