WENO Schemes and Their Application as Limiters for RKDG Methods Based on Trigonometric Approximation Spaces

Authors:
Jun Zhu;Jianxian Qiu
Affiliations:
College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, P.R. China 210016;School of Mathematical Sciences, Xiamen University, Xiamen, P.R. China 361005
Venue:
Journal of Scientific Computing
Year:
2013

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Abstract

In this paper, we present a class of finite volume trigonometric weighted essentially non-oscillatory (TWENO) schemes and use them as limiters for Runge-Kutta discontinuous Galerkin (RKDG) methods based on trigonometric polynomial spaces to solve hyperbolic conservation laws and highly oscillatory problems. As usual, the goal is to obtain a robust and high order limiting procedure for such a RKDG method to simultaneously achieve uniformly high order accuracy in smooth regions and sharp, non-oscillatory shock transitions. The major advantage of schemes which are based on trigonometric polynomial spaces is that they can simulate the wave-like and highly oscillatory cases better than the ones based on algebraic polynomial spaces. We provide numerical results in one and two dimensions to illustrate the behavior of these procedures in such cases. Even though we do not utilize optimal parameters for the trigonometric polynomial spaces, we do observe that the numerical results obtained by the schemes based on such spaces are better than or similar to those based on algebraic polynomial spaces.