On stabilized integration for time-dependent PDEs

JOURNAL OF COMPUTATIONAL PHYSICS

卷:224

Article

Sommeijer, B. P. ; Verwer, J. G.

关键词: numerical integration;    stabilized explicit integration;    Runge-Kutta-Chebyshev methods;    reactive flow problems;    damped wave equations;    coupled sound and heat flow;   

DOI  :  10.1016/j.jcp.2006.11.013

来源: Elsevier

【 摘 要 】

An integration method is discussed which has been designed to treat parabolic and hyperbolic terms explicitly and stiff reaction terms implicitly. The method is a special two-step form of the one-step IMEX (implicit-explicit) RKC (Runge-Kutta-Chebyshev) method. The special two-step form is introduced with the aim of getting a non-zero imaginary stability boundary which is zero for the one-step method. Having a non-zero imaginary stability boundary allows, for example, the integration of pure advection equations space-discretized with centered schemes, the integration of damped or viscous wave equations, the integration of coupled sound and heat flow equations, etc. For our class of methods it also simplifies the choice of temporal step sizes satisfying the von Neumann stability criterion, by embedding a thin long rectangle inside the stability region. Embedding rectangles or other tractable domains with this purpose is an idea of Wesseling. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free