On the stability of distorted laminar flow(III)—The nonlinear stability analysis of distorted parallel shear flow

1989 ◽  
Vol 10 (4) ◽  
pp. 297-307
Author(s):  
Zhou Zhe-wei
Keyword(s):  
Stability Analysis ◽  
Laminar Flow ◽  
Shear Flow ◽  
Nonlinear Stability ◽  
Nonlinear Stability Analysis ◽  
Parallel Shear Flow ◽  
The Stability

Spatio-temporal structure of the ‘fully developed’ transitional flow in a symmetric wavy channel. Linear and weakly nonlinear stability analysis

2014 ◽  
Vol 764 ◽  
pp. 250-276 ◽  
Author(s):  
S. Blancher ◽  
Y. Le Guer ◽  
K. El Omari
Keyword(s):  
Stability Analysis ◽  
Laminar Flow ◽  
Steady Flow ◽  
Nonlinear Stability ◽  
Temporal Structure ◽  
Main Stream ◽  
Nonlinear Stability Analysis ◽  
Wavy Channel ◽  
Weakly Nonlinear ◽  
Spatio Temporal

AbstractThis work addresses the transition from 2D steady to 2D unsteady laminar flow for a fully developed regime in a symmetric wavy channel geometry. We investigate the existence and characteristics of the spatio-temporal structure of the fully developed unsteady laminar flow for those particular geometries for which the steady flow presents a periodic variation of the main stream velocity component. We perform a 2D global linear stability analysis of the fully developed steady laminar flow, and we show that, for all the geometries studied, the transition is triggered by a Hopf bifurcation associated with the breaking of the symmetries and the invariance of the steady flow. Critical Reynolds numbers, most unstable modes and their characteristics are presented for large ranges of the geometric parameters, namely wavenumber${\it\alpha}$from 0.3 to 5 and amplitude from 0 (straight channel) to 0.5. We show that it is possible to define geometries for which the wavenumber is proportional to the most unstable mode wavenumber for the critical Reynolds number. From this modal study we address a weakly nonlinear stability analysis with a view to obtaining the Landau coefficient$g$, and then the sub- or supercritical nature of the first bifurcation characterising the transition. We show that a critical geometric amplitude beyond which the first bifurcation is supercritical is associated with each geometric wavenumber.

A Nonlinear Stability Analysis for Difference Equations Using Semi-Implicit Mobility

1977 ◽  
Vol 17 (01) ◽  
pp. 79-91 ◽  
Author(s):  
D.W. Peaceman
Keyword(s):  
Porous Media ◽  
Stability Analysis ◽  
Finite Difference ◽  
Nonlinear Stability ◽  
Difference Equations ◽  
Nonlinear Stability Analysis ◽  
Time Step ◽  
Two Phase ◽  
Linearized Stability ◽  
The Stability

Abstract The usual linearized stability analysis of the finite-difference solution for two-phase flow in porous media is not delicate enough to distinguish porous media is not delicate enough to distinguish between the stability of equations using semi-implicit mobility and those using completely implicit mobility. A nonlinear stability analysis is developed and applied to finite-difference equations using an upstream mobility that is explicit, completely implicit, or semi-implicit. The nonlinear analysis yields a sufficient (though not necessary) condition for stability. The results for explicit and completely implicit mobilities agree with those obtained by the standard linearized analysis; in particular, use of completely implicit mobility particular, use of completely implicit mobility results in unconditional stability. For semi-implicit mobility, the analysis shows a mild restriction that generally will not be violated in practical reservoir simulations. Some numerical results that support the theoretical conclusions are presented. Introduction Early finite-difference, Multiphase reservoir simulators using explicit mobility were found to require exceedingly small time steps to solve certain types of problems, particularly coning and gas percolation. Both these problems are characterized percolation. Both these problems are characterized by regions of high flow velocity. Coats developed an ad hoc technique for dealing with gas percolation, but a more general and highly successful approach for dealing with high-velocity problems has been the use of implicit mobility. Blair and Weinaug developed a simulator using completely implicit mobility that greatly relaxed the time-step restriction. Their simulator involved iterative solution of nonlinear difference equations, which considerably increased the computational work per time step. Three more recent papers introduced the use of semi-implicit mobility, which proved to be greatly superior to the fully implicit method with respect to computational effort, ease of use, and maximum permissible time-step size. As a result, semi-implicit mobility has achieved wide use throughout the industry. However, this success has been pragmatic, with little or no theoretical work to justify its use. In this paper, we attempt to place the use of semi-implicit mobility on a sounder theoretical foundation by examining the stability of semi-implicit difference equations. The usual linearized stability analysis is not delicate enough to distinguish between the semi-implicit and completely implicit difference equation. A nonlinear stability analysis is developed that permits the detection of some differences between the stability of difference equations using implicit mobility and those using semi-implicit mobility. DIFFERENTIAL EQUATIONS The ideas to be developed may be adequately presented using the following simplified system: presented using the following simplified system: horizontal, one-dimensional, two-phase, incompressible flow in homogeneous porous media, with zero capillary pressure. A variable cross-section is included so that a variable flow velocity may be considered. The basic differential equations are (1) (2) The total volumetric flow rate is given by (3) Addition of Eqs. 1 and 2 yields =O SPEJ P. 79

Nonlinear Stability Analysis of Thin-Walled Pier

2013 ◽  
Vol 361-363 ◽  
pp. 1251-1254
Author(s):  
Xiao Mei Dong
Keyword(s):  
Stability Analysis ◽  
Nonlinear Stability ◽  
Shell Element ◽  
Nonlinear Stability Analysis ◽  
Nonlinearity Effect ◽  
Updated Lagrangian Formulation ◽  
Thin Walled ◽  
Displacement Theory ◽  
The Stability ◽  
Updated Lagrangian

Shell element was used to simulate thin-walled piers. Mander constitutive model was adopted for analysis about the material nonlinearity. By finite displacement theory the geometric nonlinearity effect was reckoned in stability analysis based on Updated Lagrangian formulation. Nonlinear stability analysis during different construction stages indicates that the stability of pier in cantilever stage is weakest. Considered the dual non-linearity, the stability coefficient descends distinctly.

Instability Analysis of High Pier of Continuous Rigid Frame Bridges

2012 ◽  
Vol 178-181 ◽  
pp. 1989-1993
Author(s):  
Xiao Mei Dong
Keyword(s):  
Stability Analysis ◽  
Nonlinear Stability ◽  
Geometric Nonlinearity ◽  
Material Nonlinearity ◽  
Thin Wall ◽  
Nonlinear Stability Analysis ◽  
Stability Coefficient ◽  
Rigid Frame ◽  
High Pier ◽  
The Stability

The linear and nonlinear stability of continuous rigid frame bridge with thin-wall piers is analyzed by using the current FEM software. Linear stability analysis indicates that coefficient of stability in cantilever stage is poorest. Two aspects are included in nonlinear stability analysis. The first one, only geometric nonlinearity is considered and the other one, geometric nonlinearity and material nonlinearity are considered simultaneously. The results show that material nonlinearity is a factor to stability coefficient that can not be overlooked. Considered the dual non-linearity, the stability coefficient descends consumedly.

scholarly journals Nonlinear stability analysis of rotor-bearing systems

PAMM ◽  
2009 ◽  
Vol 9 (1) ◽  
pp. 279-280 ◽  
Author(s):  
Aydin Boyaci ◽  
Wolfgang Seemann ◽  
Carsten Proppe
Keyword(s):  
Stability Analysis ◽  
Nonlinear Stability ◽  
Nonlinear Stability Analysis ◽  
Rotor Bearing
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