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Numerical Bifurcation Methods and Their Application to Fluid Dynamics: Analysis Beyond Simulation

Numerical Bifurcation Methods and Their Application to Fluid Dynamics: Analysis Beyond Simulation
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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

Keywords:   

Author Details

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

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