TY - JOUR
T1 - Numerical bifurcation methods and their application to fluid dynamics: Analysis beyond simulation
AU - Dijkstra, Henk A.
AU - Wubs, Fred W.
AU - Cliffe, Andrew K.
AU - Doedel, Eusebius
AU - Dragomirescu, Ioana F.
AU - Eckhardt, Bruno
AU - Gelfgat, Alexander Yu
AU - Hazel, Andrew L.
AU - Lucarini, Valerio
AU - Salinger, Andy G.
AU - Phipps, Erik T.
AU - Juan, Sanchez Umbria
AU - Schuttelaars, Henk
AU - Tuckerman, Laurette S.
AU - Thiele, Uwe
PY - 2014/1
Y1 - 2014/1
N2 - 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 arementioned 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. ©c 2014 Global-Science Press.
AB - 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 arementioned 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. ©c 2014 Global-Science Press.
KW - High-dimensional dynamical systems
KW - Numerical bifurcation analysis
KW - Transitions in fluid flows
U2 - 10.4208/cicp.240912.180613a
DO - 10.4208/cicp.240912.180613a
M3 - Article
SN - 1815-2406
VL - 15
SP - 1
EP - 45
JO - Communications in Computational Physics
JF - Communications in Computational Physics
IS - 1
ER -