scholarly journals A General Numerical Method for Analyzing the Linear Stability of Stratified Parallel Shear Flows

2014 ◽  
Vol 31 (12) ◽  
pp. 2795-2808 ◽  
Author(s):  
Tim Rees ◽  
Adam Monahan
Keyword(s):  
Stability Analysis ◽  
Numerical Method ◽  
Shear Flows ◽  
Numerical Solutions ◽  
Analytical Approximations ◽  
Onset Of Turbulence ◽  
Parallel Shear Flows ◽  
Critical Layers ◽  
The Stability ◽  
Stability Results

Abstract The stability analysis of stratified parallel shear flows is fundamental to investigations of the onset of turbulence in atmospheric and oceanic datasets. The stability analysis is performed by considering the behavior of small-amplitude waves, which is governed by the Taylor–Goldstein (TG) equation. The TG equation is a singular second-order eigenvalue problem, whose solutions, for all but the simplest background stratification and shear profiles, must be computed numerically. Accurate numerical solutions require that particular care be taken in the vicinity of critical layers resulting from the singular nature of the equation. Here a numerical method is presented for finding unstable modes of the TG equation, which calculates eigenvalues by combining numerical solutions with analytical approximations across critical layers. The accuracy of this method is assessed by comparison to the small number of stratification and shear profiles for which analytical solutions exist. New stability results from perturbations to some of these profiles are also obtained.

scholarly journals Solving Volterra Integrodifferential Equations via Diagonally Implicit Multistep Block Method

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Nur Auni Baharum ◽  
Zanariah Abdul Majid ◽  
Norazak Senu
Keyword(s):  
Stability Analysis ◽  
Numerical Solution ◽  
Numerical Method ◽  
Numerical Computation ◽  
Numerical Solutions ◽  
Numerical Results ◽  
Integrodifferential Equations ◽  
Block Method ◽  
The Stability ◽  
Predictor Corrector

The performance of the numerical computation based on the diagonally implicit multistep block method for solving Volterra integrodifferential equations (VIDE) of the second kind has been analyzed. The numerical solutions of VIDE will be computed at two points concurrently using the proposed numerical method and executed in the predictor-corrector (PECE) mode. The strategy to obtain the numerical solution of an integral part is discussed and the stability analysis of the diagonally implicit multistep block method was investigated. Numerical results showed the competence of diagonally implicit multistep block method when solving Volterra integrodifferential equations compared to the existing methods.

The Solution of Lateral Heat Loss Problem Using Collocation Method with Cubic B-Splines Finite Element

2011 ◽  
Vol 110-116 ◽  
pp. 3184-3190
Author(s):  
Necdet Bildik ◽  
Duygu Dönmez Demir
Keyword(s):  
Finite Element ◽  
Stability Analysis ◽  
Heat Loss ◽  
Collocation Method ◽  
Numerical Solutions ◽  
Analytic Solutions ◽  
B Splines ◽  
Stability Method ◽  
The Stability ◽  
Lateral Heat

This paper deals with the solutions of lateral heat loss equation by using collocation method with cubic B-splines finite elements. The stability analysis of this method is investigated by considering Fourier stability method. The comparison of the numerical solutions obtained by using this method with the analytic solutions is given by the tables and the figure.

scholarly journals Unconditional Stability of a Numerical Method for the Dual-Phase-Lag Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-5
Author(s):  
M. A. Castro ◽  
J. A. Martín ◽  
F. Rodríguez
Keyword(s):  
Numerical Method ◽  
Numerical Solutions ◽  
Unconditional Stability ◽  
Bioheat Transfer ◽  
Phase Lag ◽  
Dual Phase ◽  
Stability Properties ◽  
The Stability ◽  
Transfer Problems ◽  
Uniformly Bounded

The stability properties of a numerical method for the dual-phase-lag (DPL) equation are analyzed. The DPL equation has been increasingly used to model micro- and nanoscale heat conduction in engineering and bioheat transfer problems. A discretization method for the DPL equation that could yield efficient numerical solutions of 3D problems has been previously proposed, but its stability properties were only suggested by numerical experiments. In this work, the amplification matrix of the method is analyzed, and it is shown that its powers are uniformly bounded. As a result, the unconditional stability of the method is established.

On the stability analysis of sharply stratified shear flows

2018 ◽  
Vol 68 (7) ◽  
pp. 867-884 ◽  
Author(s):  
Semyon Churilov
Keyword(s):  
Stability Analysis ◽  
Shear Flows ◽  
The Stability

scholarly journals Purely elastic linear instabilities in parallel shear flows with free-slip boundary conditions

2021 ◽  
Vol 928 ◽  
Author(s):  
Martin Lellep ◽  
Moritz Linkmann ◽  
Bruno Eckhardt ◽  
Alexander Morozov
Keyword(s):  
Boundary Condition ◽  
Stability Analysis ◽  
Constitutive Model ◽  
Spatial Structure ◽  
Boundary Conditions ◽  
Shear Flows ◽  
Body Force ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Parallel Shear Flows

We perform a linear stability analysis of viscoelastic plane Couette and plane Poiseuille flows with free-slip boundary conditions. The fluid is described by the Oldroyd-B constitutive model, and the flows are driven by a suitable body force. We find that both types of flow become linearly unstable, and we characterise the spatial structure of the unstable modes. By performing a boundary condition homotopy from the free-slip to no-slip boundaries, we demonstrate that the unstable modes are directly related to the least stable modes of the no-slip problem, destabilised under the free-slip situation. We discuss how our observations can be used to study recently discovered purely elastic turbulence in parallel shear flows.

On the stability of parallel shear flows with embedded swirl

2021 ◽  
Vol 150 (4) ◽  
pp. A177-A177
Author(s):  
Lu Zhao ◽  
Saeed Farokhi ◽  
Ray Taghavi
Keyword(s):  
Shear Flows ◽  
Parallel Shear Flows ◽  
The Stability

scholarly journals Dynamics of a New Strain of the H1N1 Influenza A Virus Incorporating the Effects of Repetitive Contacts

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Puntani Pongsumpun ◽  
I-Ming Tang
Keyword(s):  
Stability Analysis ◽  
Equilibrium State ◽  
Influenza A Virus ◽  
Influenza A ◽  
Present Model ◽  
Numerical Solutions ◽  
H1n1 Influenza ◽  
Dynamical Modeling ◽  
Mathematical Equations ◽  
The Stability

The respiratory disease caused by the Influenza A Virus is occurring worldwide. The transmission for new strain of the H1N1 Influenza A virus is studied by formulating a SEIQR (susceptible, exposed, infected, quarantine, and recovered) model to describe its spread. In the present model, we have assumed that a fraction of the infected population will die from the disease. This changes the mathematical equations governing the transmission. The effect of repetitive contact is also included in the model. Analysis of the model by using standard dynamical modeling method is given. Conditions for the stability of equilibrium state are given. Numerical solutions are presented for different values of parameters. It is found that increasing the amount of repetitive contacts leads to a decrease in the peak numbers of exposed and infectious humans. A stability analysis shows that the solutions are robust.

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