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

被引：10

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.

引用

页码：516 / 550

页数：35

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