Hermite WENO schemes and their application as limiters for Runge??????Kutta discontinuous Galerkin method II: Two dimensional case

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• 作者：Qiu ; Jianxian ; Shu ; Chi-Wang
• 关键词：65M06 ; 65M60 ; 65M99 ; 35L65
• 刊名：Computers and Fluids
• 出版年：2005
• 出版时间：July, 2005
• 年：2005
• 卷：34
• 期：6
• 页码：642-663
• 全文大小：1.90 M

文摘

A class of fifth-order weighted essentially non-oscillatory (WENO) schemes based on Hermite polynomials, termed HWENO (Hermite WENO) schemes, for solving one dimensional non-linear hyperbolic conservation law systems, was developed and applied as limiters for the RungeaaaKutta discontinuous Galerkin (RKDG) methods in [J. Comput. Phys. 193 (2003) 115]. In this paper, we extend the method to solve two dimensional non-linear hyperbolic conservation law systems. The emphasis is again on the application of such HWENO finite volume methodology as limiters for RKDG methods to maintain compactness of RKDG methods. Numerical experiments for two dimensional Burgersaaa equation and Euler equations of compressible gas dynamics are presented to show the effectiveness of these methods.