Premium
Stability analysis of finite difference schemes revisited: A study of decoupled solution strategies for coupled multifield problems
Author(s) -
Ehlers W.,
Zinatbakhsh S.,
Markert B.
Publication year - 2013
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4480
Subject(s) - decoupling (probability) , stability (learning theory) , flexibility (engineering) , computer science , context (archaeology) , numerical analysis , mathematical optimization , mathematics , control engineering , engineering , paleontology , mathematical analysis , statistics , machine learning , biology
SUMMARY Many problems in engineering, physics or other disciplines require an integrated treatment of coupled heterogeneous fields. The mathematical models of such problems commonly consist of a coupled PDE system. Considerable progress has been made in the development of schemes to solve such systems resulting in a wide spectrum of monolithic and decoupled numerical solution approaches. In particular, the flexibility offered by the decoupled strategies in choosing appropriate solution methods and adjustable time‐step sizes has motivated the elaboration of these schemes. However, the way of decoupling can influence the stability of the resulting solution algorithm and, hence, urges a comprehensive stability analysis. The purpose of this contribution is to elucidate the salient points in the stability analysis of the numerical solution schemes. To this end, we introduce a general framework for the stability analysis of solution strategies and provide an easy‐to‐use procedure to find the necessary stability condition. The procedure is tested against decoupled solution strategies for volume‐ and surface‐coupled problems, namely, thermoelastodynamics, porous media dynamics, and fluid– and structure–structure interaction. In this context, the influence of explicit and implicit predictors and the sequence of the time integration on the stability condition is carefully examined. Copyright © 2013 John Wiley & Sons, Ltd.