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

被引：9
|
作者：
Michoski, C. [1 ,2 ]
Alexanderian, A. [2 ,3 ]
Paillet, C. [5 ]
Kubatko, E. J. [4 ]
Dawson, C. [2 ]
机构：
[1] Univ Colorado, Computat Mech & Geometry Lab CMGLab, Aerosp Engn Sci, Boulder, CO 80302 USA
[2] Univ Texas Austin, ICES, Austin, TX 78712 USA
[3] North Carolina State Univ, Dept Math, Raleigh, NC 27695 USA
[4] Ohio State Univ, Civil Engn & Geodet Engn Dept, Columbus, OH 43210 USA
[5] Ecole Normale Super, Dept Mech Engn, F-94230 Cachan, France
来源：
JOURNAL OF SCIENTIFIC COMPUTING | 2017年 / 70卷 / 02期
基金：
美国国家科学基金会;
关键词：
Stability analysis; Nonlinear; von Neumann; Discontinuous Galerkin; Runge-Kutta methods; RKSSP; RKC; Convection-Reaction-Diffusion; OPERATOR SPLITTING METHODS; RUNGE-KUTTA METHODS; INDEFINITE OPERATORS; EXPLICIT; ORDER; EQUATIONS;
D O I：
10.1007/s10915-016-0256-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
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页码：516 / 550
页数：35
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