Stability of Nonlinear Convection–Diffusion–Reaction Systems in Discontinuous Galerkin Methods

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• 作者：C. Michoski ; A. Alexanderian ; C. Paillet ; E. J. Kubatko…
• 关键词：Stability analysis ; Nonlinear ; von Neumann ; Discontinuous Galerkin ; Runge–Kutta methods ; RKSSP ; RKC ; Convection–Reaction–Diffusion
• 刊名：Journal of Scientific Computing
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：70
• 期：2
• 页码：516-550
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Algorithms; Computational Mathematics and Numerical Analysis; Appl.Mathematics/Computational Methods of Engineering; Theoretical, Mathematical and Computational Physics;
• 出版者：Springer US
• ISSN：1573-7691
• 卷排序：70

文摘

In this work we provide an extension of the classical von Neumann stability analysis for high-order accurate discontinuous Galerkin methods applied to generalized nonlinear convection–reaction–diffusion systems. We provide a partial linearization under which a sufficient condition emerges that guarantees stability in this context. The stability behavior of these systems is then closely analyzed relative to Runge–Kutta Chebyshev (RKC) and strong stability preserving (RKSSP) temporal discretizations over a nonlinear system of reactive compressible gases arising in the study of atmospheric chemistry.