@Article{CiCP-15-1,
author = {A. Dijkstra , HenkW. Wubs , FredK. Cliffe , AndrewDoedel , EusebiusF. Dragomirescu , IoanaEckhardt , BrunoYu. Gelfgat , AlexanderL. Hazel , AndrewLucarini , ValerioG. Salinger , AndyT. Phipps , ErikSanchez-Umbria , JuanSchuttelaars , HenkS. Tuckerman , Laurette and Thiele , Uwe},
title = {Numerical Bifurcation Methods and Their Application to Fluid Dynamics: Analysis Beyond Simulation},
journal = {Communications in Computational Physics},
year = {2014},
volume = {15},
number = {1},
pages = {1--45},
abstract = {<p style="text-align: justify;">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&nbsp;these transitions, popularly referred to as &#39;tipping points&#39;, 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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.240912.180613a},
url = {http://global-sci.org/intro/article_detail/cicp/7086.html}
}