Year: 2014
Author: Henk A. Dijkstra, Fred W. Wubs, Andrew K. Cliffe, Eusebius Doedel, Ioana F. Dragomirescu, Bruno Eckhardt, Alexander Yu. Gelfgat, Andrew L. Hazel, Valerio Lucarini, Andy G. Salinger, Erik T. Phipps, Juan Sanchez-Umbria, Henk Schuttelaars, Laurette S. Tuckerman, Uwe Thiele
Communications in Computational Physics, Vol. 15 (2014), Iss. 1 : pp. 1–45
Abstract
We provide an overview of current techniques and typical applications of numerical bifurcation analysis in fluid dynamical problems. Many of these problems are characterized by high-dimensional dynamical systems which undergo transitions as parameters are changed. The computation of the critical conditions associated with these transitions, popularly referred to as 'tipping points', is important for understanding the transition mechanisms. We describe the two basic classes of methods of numerical bifurcation analysis, which differ in the explicit or implicit use of the Jacobian matrix of the dynamical system. The numerical challenges involved in both methods are mentioned and possible solutions to current bottlenecks are given. To demonstrate that numerical bifurcation techniques are not restricted to relatively low-dimensional dynamical systems, we provide several examples of the application of the modern techniques to a diverse set of fluid mechanical problems.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.240912.180613a
Communications in Computational Physics, Vol. 15 (2014), Iss. 1 : pp. 1–45
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 45