Bifurcation Analysis Software and Chaotic Dynamics for Some Problems in Fluid Dynamics Laminar–Turbulent Transition

The analysis of bifurcations and chaotic dynamics for nonlinear systems of a large size is a difficult problem. Analytical and numerical approaches must be used to deal with this problem. Numerical methods include solving some of the hardest problems in computational mathematics, which include syste...

Full description

Saved in:
Bibliographic Details
Published in:Mathematics (Basel) 2023-09, Vol.11 (18), p.3875
Main Authors: Evstigneev, Nikolay M., Magnitskii, Nikolai A.
Format: Article
Language:English
Subjects:
Automation
bifurcation analysis
Bifurcations
Boundary value problems
chaotic dynamics
deflation
Differential equations
Dynamical systems
Eigenvalues
Fluid dynamics
Fluid flow
Globalization
Incompressible flow
Krylov methods
laminar–turbulent transition
Methods
Newton method
Nonlinear dynamics
Nonlinear systems
Numerical analysis
Numerical methods
Partial differential equations
Software
Three dimensional flow
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The analysis of bifurcations and chaotic dynamics for nonlinear systems of a large size is a difficult problem. Analytical and numerical approaches must be used to deal with this problem. Numerical methods include solving some of the hardest problems in computational mathematics, which include system spectral and algebraic problems, specific nonlinear numerical methods, and computational implementation on parallel architectures. The software structure that is required to perform numerical bifurcation analysis for large-scale systems was considered in the paper. The software structure, specific features that are used for successful bifurcation analysis, globalization strategies, stabilization, and high-precision implementations are discussed. We considered the bifurcation analysis in the initial boundary value problem for a system of partial differential equations that describes the dynamics of incompressible ABC flow (3D Navier–Stokes equations). The initial stationary solution is characterized by the stability and connectivity to the main solutions branches. Periodic solutions were considered in view of instability transition problems. Finally, some questions of higher dimensional attractors and chaotic regimes are discussed.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11183875