Bifurcation Analysis for Timesteppers

By L. Tuckerman, Dwight Barkley. 2000

201 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/a01600755e12784dd5114b6f61f6d10ea02e12ea

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In Computational Mechanics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Feedback control of unstable steady states of flow past a flat plate using reduced-order estimators (2009, methodology): “This section concerns this steady-state analysis, using a ‘time-stepper-based’ approach as outlined in Tuckerman & Barkley (2000) and Kelley, Kevrekidis & Qiao (2004).”
Global three-dimensional optimal disturbances in the Blasius boundary-layer flow using time-steppers (2010, methodology): “This so-called time-stepper technique has indeed become increasingly popular in stability analysis (Tuckerman & Barkley 2000).”
The Significance of Simple Invariant Solutions in Turbulent Flows (2011, background): “If the eigenvalues are unfavourable, we need to precondition the linear problem (see, e.g. Tuckerman & Barkley 2000, for an example in Navier–Stokes flow).”
Secondary instabilities in the flow around two circular cylinders in tandem (2010, methodology): “These solutions are obtained by employing an Arnoldi algorithm, in the way explained in Carmo et al. (2008) and based on the earlier work of Tuckerman & Barkley (2000).”
Direct optimal growth analysis for timesteppers (2008, methodology): “Application of the joint operator requires only a straightforward extension of the original methodology [1], which was based on the first half of this iteration.”
Effective bifurcation analysis: a time-stepper-based approach (2002, methodology): “Our procedure is motivated by numerical bifurcation techniques for dissipative PDEs that belong to a family called ‘time-stepper-based methods’; examples of these methods can be found in [ 44 ].”
Convective instability and transient growth in flow over a backward-facing step (2007, methodology): “There are algorithms and numerical techniques which allow us to obtain leading (critical or near critical) eigenvalues and eigenmodes for the resulting large problems (Tuckerman & Barkley 2000).”
Modal Analysis of Fluid Flows: An Overview (2017, methodology): “If the unstable steady state is needed, techniques such as the selective frequency damping method [165] or a Newton–Krylov-type iterative solver [166,167]”