Global Stability Analysis of the Wake behind a Circular Cylinder Based on the POD-Chiba Method

A proper orthogonal decomposition (POD) method is applied to study the global stability analysis for flow past a stationary circular cylinder. The flow database at Re=100 is obtained by CFD software, i.e. FLUENT, with which POD bases are constructed by a snapshot method. Based on the POD bases, a low-dimensional model is established for solving the two-dimensional incompressible NS equations. The stability of the flow solution is evaluated by a POD-Chiba method in the way of the eigensystem analysis for the velocity disturbance. The linear stability analysis shows that the first Hopf bifurcation takes place at Re=46.9, which is in good agreement with available results by other high-order accurate stability analysis methods. However, the calculated amount of POD is little, which shows the availability and advantage of the POD method.

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Global stability analysis of structures and actions to control their effects

Revista IBRACON de Estruturas e Materiais ◽

10.1590/s1983-41952016000200003 ◽

2016 ◽

Vol 9 (2) ◽

pp. 192-213 ◽

Cited By ~ 1

Author(s):

F. C. Freitas ◽

L. A. R. Luchi ◽

W. G. Ferreira

Keyword(s):

Stability Analysis ◽

Global Stability ◽

Local Stability ◽

Structural Systems ◽

Stability Parameters ◽

Global Stability Analysis ◽

Basic Concepts ◽

The Stability ◽

Global And Local ◽

Brazilian Standard

ABSTRACT In this moment in which civil engineering is undergoing a phase where structural projects have been developed with structural systems composed of different and complex elements, some methods and criteria are used for the purpose of evaluating important aspects with regard to global and local stability. Among them, it is necessary to mention the parameters of instability a and ?z. In this sense, this work has the objective to present the basic concepts of the instability parameters a and ?z in accordance with what is clearly defined in the Brazilian standard ABNT NBR 6118; to present the results of simulations of models in the Brazilian structural software TQS varying the stress of compression in the columns in order to relate these values with the stability parameters.

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A low-dimensional model for simulating three-dimensional cylinder flow

Journal of Fluid Mechanics ◽

10.1017/s0022112002007991 ◽

2002 ◽

Vol 458 ◽

pp. 181-190 ◽

Cited By ~ 194

Author(s):

XIA MA ◽

GEORGE EM KARNIADAKIS

Keyword(s):

Limit Cycle ◽

Three Dimensional ◽

Orthogonal Decomposition ◽

Direct Numerical Simulations ◽

Two Dimensional ◽

Dimensional Model ◽

The Stability ◽

Low Dimensional ◽

Cylinder Flow ◽

Proper Orthogonal

We investigate the stability and dynamics of three-dimensional limit-cycle states in flow past a circular cylinder using low-dimensional modelling. High-resolution direct numerical simulations are employed to obtain flow snapshots from which the most energetic modes are extracted using proper orthogonal decomposition. We show that the limit cycle is reproduced very accurately with only twenty three-dimensional modes. The addition of two-dimensional modes to the Karhunen–Loeve expansion basis improves the ability of the model to capture the three-dimensional bifurcation, including the discontinuity in the Strouhal number discovered experimentally.

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On the Global Stability Analysis of Corona Virus Disease (COVID-19) Mathematical Model

Asian Research Journal of Mathematics ◽

10.9734/arjom/2021/v17i630312 ◽

2021 ◽

pp. 81-87

Author(s):

William Atokolo ◽

Achonu Omale Joseph ◽

Rose Veronica Paul ◽

Abdul Sunday ◽

Thomas Ugbojoide Onoja

Keyword(s):

Stability Analysis ◽

Global Stability ◽

Initial Conditions ◽

Virus Disease ◽

Disease Model ◽

Asymptotically Stable ◽

Globally Asymptotically Stable ◽

Global Stability Analysis ◽

Corona Virus ◽

The Stability

In this present work, we investigated the Global Stability Analysis of Corona virus disease model formulated by Atokolo et al in [11]. The COVID‑19 pandemic, also known as the coronavirus pandemic, is an ongoing pandemic that is ravaging the whole world. By constructing a Lyapunov function, we investigated the stability of the model Endemic Equilibrium state to be globally asymptotically stable. This results epidemiologically implies that the COVID-19 will invade the population in respective of the initial conditions (population) considered.

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