A simple, high-order and compact WENO limiter for RKDG method

Abstract

In this paper, a new limiter using weighted essentially non-oscillatory (WENO) methodology is investigated for the Runge–Kutta discontinuous Galerkin (RKDG) methods for solving hyperbolic conservation laws. The idea is to use the high-order DG solution polynomial itself in the target cell and the linear polynomials which are reconstructed by the cell averages of solution in the target cell and its neighboring cells to reconstruct a new high-order polynomial in a manner of WENO methodology. Since only the linear polynomials need to be prepared for reconstruction, this limiter is very simple and compact with a stencil including only the target cell and its immediate neighboring cells. Numerical examples of various problems show that the new limiting procedure can simultaneously achieve uniform high-order accuracy and sharp, non-oscillatory shock transitions.