The Study Of Limiter In Discontinuous Galerkin Methods

In this paper,a new class of weighted essentially non-oscillatory(WENO) limiterbased on Hermite polynomials interpolation for solving the solving hyperbolic conserva-tion laws using the Runge-Kutta discontinuous Galerkin(DG) methods is constructed. Thelimiter is a generalization of the limiter introduced in [Jianxian Qiu, Chi-Wang Shu, Her-mite WENO Schemes and Their Application as Limiter for Runge-Kutta DiscontinuousGalerkin Method: One-Dimesional Case, Journal of Computational Physics. 193(2003)115-135 ]. The limiter retains as high order as possible, and accuracy does not degenerates to first order at critical points. Compared to the original Hermite WENO limiter, ourlimiter use the same small stencils and lower order polynomials in reconstrued every mo-ment. The smoothness indicators is computed only once which save the computationaltime. The presented limiter can be used in any order Discontinous Galerkin method.We put emphasis on its insensitivity to the discontinuous detector. Numerical examplesin one space dimension with both smooth and discontinous solution are shown whichdemonstrate the e?ciency of the limiter. The results show that in discontinuous regionslimiter can e?ectively suppress the spurious and can recover the full high order accuracyin smooth regions.