Numerical Bifurcation Methods and their Application to Fluid Dynamics: Analysis 
beyond Simulation

Dijkstra, Henk A.; Wubs, Fred W.; Cliffe, Andrew K.; Doedel, Eusebius; Dragomirescu, Ioana F.; Eckhardt, Bruno; Gelfgat, Alexander Yu.; Hazel, Andrew L.; Lucarini, Valerio; Salinger, Andy G.; Phipps, Erik T.; Sanchez-Umbria, Juan; Schuttelaars, Henk; Tuckerman, Laurette S.; Thiele, Uwe

doi:10.4208/cicp.240912.180613a

Item

ITEM ACTIONSEXPORT

Add to Basket

Local TagsRelease HistoryDetailsSummary

Released

Journal Article

Numerical Bifurcation Methods and their Application to Fluid Dynamics: Analysis beyond Simulation

MPS-Authors

There are no MPG-Authors in the publication available

External Resource

No external resources are shared

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

Fulltext (public)

There are no public fulltexts stored in PuRe

Supplementary Material (public)

There is no public supplementary material available

Citation

Dijkstra, H. A., Wubs, F. W., Cliffe, A. K., Doedel, E., Dragomirescu, I. F., Eckhardt, B., et al. (2014). Numerical Bifurcation Methods and their Application to Fluid Dynamics: Analysis beyond Simulation. COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 15(1), 1-45. doi:10.4208/cicp.240912.180613a.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0019-B6D1-E

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.