Towards Three-Dimensional Global Stability Analysis of Transonic Shock Buffet

2016 ◽  
Author(s):  
Sebastian Timme ◽  
Reik Thormann
Keyword(s):  
Stability Analysis ◽  
Global Stability ◽  
Three Dimensional ◽  
Transonic Shock ◽  
Global Stability Analysis

scholarly journals Towards a quantitative comparison between global and local stability analysis

2017 ◽  
Vol 819 ◽  
pp. 147-164 ◽  
Author(s):  
L. Siconolfi ◽  
V. Citro ◽  
F. Giannetti ◽  
S. Camarri ◽  
P. Luchini
Keyword(s):  
Stability Analysis ◽  
Saddle Point ◽  
Global Stability ◽  
Local Stability ◽  
Correction Term ◽  
Three Dimensional ◽  
Higher Order ◽  
Order Correction ◽  
Global Stability Analysis ◽  
Local Stability Analysis

A methodology is proposed here to estimate the stability characteristics of bluff-body wakes using local analysis under the assumption of weakly non-parallel flows. In this connection, a generalisation of the classic spatio-temporal stability analysis for fully three-dimensional flows is first described. Secondly, an additional higher-order correction term with respect to the common saddle-point global frequency estimation is included in the analysis. The proposed method is first validated for the case of the flow past a circular cylinder and then applied to two fully three-dimensional flows: the boundary layer flow over a wall-mounted hemispherical body and the wake flow past a fixed sphere. In all the cases considered, both the estimated unstable eigenvalue and the spatial shape of the associated eigenmode are determined by local stability analysis, and they are compared with the reference counterparts obtained at a definitely higher computational cost by a fully three-dimensional global stability analysis. It is shown that the results of local stability analysis, when the higher-order correction term is included, are in excellent agreement with those obtained by global stability analysis. It is also shown that the retained correction term is of crucial importance in this perspective, leading to a remarkable improvement in accuracy with respect to the classical saddle-point estimation.

scholarly journals Volterra–Lyapunov Stability Analysis of the Solutions of Babesiosis Disease Model

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1272
Author(s):  
Fengsheng Chien ◽  
Stanford Shateyi
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Global Stability ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Disease Model ◽  
Transmission Dynamics ◽  
Global Stability Analysis ◽  
Lyapunov Stability Analysis ◽  
Disease Free

This paper studies the global stability analysis of a mathematical model on Babesiosis transmission dynamics on bovines and ticks populations as proposed by Dang et al. First, the global stability analysis of disease-free equilibrium (DFE) is presented. Furthermore, using the properties of Volterra–Lyapunov matrices, we show that it is possible to prove the global stability of the endemic equilibrium. The property of symmetry in the structure of Volterra–Lyapunov matrices plays an important role in achieving this goal. Furthermore, numerical simulations are used to verify the result presented.

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