Nonlinear Dynamics of Transcritical Flows

INTRODUCTION NONLINEAR DYNAMICS TEMPORAL AND SPATIAL STRUCTURES IN FLUID MECHANICS H. OERTEL JR. ... In the fluid mechanical part, we will deal only with transcritical flows, i.e., flows across and beyond a critical state and therefore ...

Author: Hermann L. Jordan

Publisher: Springer Science & Business Media

ISBN: 9783642825064

Category: Technology & Engineering

Page: 197

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The German Aerospace Research Establishment (DFVLR) has initiated a new series of seminars concerning fundamental problems in applied engineering sciences. These seminars will be devoted to interdisciplinary topics related to the vast variety of DFVLR activities in the fields of fluid mechanics, flight mechanics, guidance and control, materials and struc tures, non-nuclear energetics, communication technology, and remote sensing. The purpose of the series is twofold, namely, to bring modern ideas and techniques to the attention of the DFVLR in order to stimulate internal activi ties, and secondly, to promulgate DFVLR achievements wi thin the international scientific/technical community. To this end, prominent speakers from Germany and other countries will be invited to join in a series of lectures and discussions on certain topics of mutual interest. The first colloquium of this series dealt with the dynamics of nonlinear systems, especially in relation'to its application to fluid mechanics, particularly in transcritical flows. Of special interest are questions concerning the formation of nonlinear three-dimensional structures in classical fluid mechanical stability problems, the physical process of transition to turbulence, and the appearance of chaotic solutions. The scope of lectures reaches from self-organization in physical systems to structural stability of three-dimensional vortex patterns, the treatment of dissipative and conservative systems, the formation of nonlinear structures in the region of laminar-turbulent transition, and numerical simulation of cumulus cloud convection in meteorology. The seminar should provide an insight into the extent to which theoretical findings in Non linear Dynamics apply to the comprehension of fluid-mechanical problems.
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Energy Flow Theory of Nonlinear Dynamical Systems with Applications

6.2 shows the transcritical bifurcations described by Eq. 6.17 for which the eigenvalue of the energy flow matrix at equilibria vanishes. Similar to Fig. 6.1, the arrows parallel to x axis represent the time change rate of x while the ...

Author: Jing Tang Xing

Publisher: Springer

ISBN: 9783319177410

Category: Technology & Engineering

Page: 299

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This monograph develops a generalised energy flow theory to investigate non-linear dynamical systems governed by ordinary differential equations in phase space and often met in various science and engineering fields. Important nonlinear phenomena such as, stabilities, periodical orbits, bifurcations and chaos are tack-led and the corresponding energy flow behaviors are revealed using the proposed energy flow approach. As examples, the common interested nonlinear dynamical systems, such as, Duffing’s oscillator, Van der Pol’s equation, Lorenz attractor, Rössler one and SD oscillator, etc, are discussed. This monograph lights a new energy flow research direction for nonlinear dynamics. A generalised Matlab code with User Manuel is provided for readers to conduct the energy flow analysis of their nonlinear dynamical systems. Throughout the monograph the author continuously returns to some examples in each chapter to illustrate the applications of the discussed theory and approaches. The book can be used as an undergraduate or graduate textbook or a comprehensive source for scientists, researchers and engineers, providing the statement of the art on energy flow or power flow theory and methods.
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Applied Mechanics Reviews

A nonlinear operator equation V = BV + CV is derived from the perturbation problem associated with the motion of a viscous ... It is observed that for the steady flows , the bifurcation generally occurs in the transcritical form .

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Publisher:

ISBN: UIUC:30112008993138

Category: Mechanics, Applied

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Nonlinear Dynamics

7.6.2 Pitchfork and transcritical bifurcations The intuitive idea behind the study of non-generic cases of the bifurcation at a single zero eigenvalue is to consider which special restrictions to the flow will substantially modify the ...

Author: H.G Solari

Publisher: Routledge

ISBN: 9781351428293

Category: Science

Page: 366

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Nonlinear Dynamics: A Two-Way Trip from Physics to Math provides readers with the mathematical tools of nonlinear dynamics to tackle problems in all areas of physics. The selection of topics emphasizes bifurcation theory and topological analysis of dynamical systems. The book includes real-life problems and experiments as well as exercises and work
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Multiphase Flow in Porous Media

13: Nonlinear Dynamics of Transcritical Flows Proceedings of a DFVLR International Colloquium, Bonn, Germany, March 26, 1984 VI, 203 pages. 1985. Vol. 14: A. A. Bakr The Boundary Integral Equation Method in Axisymmetric Stress Analysis ...

Author: Myron B. III Allen

Publisher: Springer Science & Business Media

ISBN: 9781461395980

Category: Science

Page: 306

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The past decade has seen remarkable growth in research related to petroleum reseIVoir simulation. This growth reflects several developments, not the least of which is the increased interest in oil recovery technologies requiring sophisticated engineer ing. Augmenting this interest has been the broader availability of supercomputers capable of handling the tremendous computational demands of a typical reseIVoir simulator. The field of reseIVoir simulation incorporates several major facets of applied mathematics. First, in view of the varieyt and complexity of the processes encoun tered, it is imperative that the modeler adopt a systematic approach to establishing the equations governing reseIVoir flows. Second, the mathematical structure of these flow equations needs to be carefully analyzed in order to develop appropriate and efficient numerical methods for their solution. Third, since some aspects of the discretized flow equations are typically stiff, one must develop efficient schemes for solving large sparse systems of linear equations. This monograph has three parts, each devoted to one of these three aspects of reseIVoir modeling. The text grew out of a set of lectures presented by the authors in the autumn of 1986 at the IBM Scientific Center in Bergen, Norway. We feel that it is only appropriate to caution the reader that many of the ideas that we present in this monograph do not reflect standard approaches in petroleum reseIVoir simulation. In fact, our aim is to outline promising new ways of attacking reseIVoir simulation prob lems, rather than to compile another textbook for the mainstream.
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Filtering Techniques for Turbulent Flow Simulation

Vol.13: Nonlinear Dynamics of Transcritical Flows Proceedings of a DFVLR International Colloquium, Bonn, Germany, March 26, 1984 VI, 203 pages. 1985. Vol. 14: A. A. Bakr The Boundary Integral Equation Method in Axisymmetric Stress ...

Author: Alvaro A. Aldama

Publisher: Springer Science & Business Media

ISBN: 9783642840913

Category: Science

Page: 397

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1. 1 Scope of the Study The detailed and reasonably accurate computation of large scale turbulent flows has become increasingly important in geophysical and engi neering applications in recent years. The definition of water quality management policies for reservoirs, lakes, estuaries, and coastal waters, as well as the design of cooling ponds and solar ponds, requires an ade quate quantitative description of turbulent flows. When the diffusion of some tracer (be it active, such as temperature or salinity, or passive, such as dissolved oxygen) is of relevance to a specific application, the proper determination of the effects of turbulent transport processes has paramount importance. Thus, for instance, the proper understanding of lake and reservoir dynamics requires, as a first step, the ability to simulate turbulent flows. Applications in other areas of geophysical research, such as meteorology and oceanography are easily identified and large in number. It should be stressed that, in this context, the analyst seeks predictive ability to a certain extent. Accordingly, the need for simulation models that closely resemble the natural processes to be repre sented has recently become more evident. Since the late 1960s considerable effort has been devoted to the development of models for the simulation of complex turbulent flows. This has resulted in the establishment of two approaches which have been, or 2 have the potential for being, applied to problems of engineering and geophysical interest.
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Boundary Element Analysis of Viscous Flow

Vol.13: Nonlinear Dynamics of Transcritical Flows Proceedings of a DFVLR International Colloquium, Bonn, Germany, March 26, 1984 VI, 203 pages. 1985. Vol. 14: A. A. Bakr The Boundary Integral Equation Method in Axisymmetric Stress ...

Author: Koichi Kitagawa

Publisher: Springer Science & Business Media

ISBN: 9783642840296

Category: Science

Page: 136

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In recent years, the performance of digital computers has been improved by the rapid development of electronics at remarkable speed. In addition, substantial research has been carried out in developing numerical analysis techniques. Nowadays, a variety of problems in the engineering and scientific fields can be solved by using not only super computers but also personal computers. After the first book titled "Boundary Element" was published by Brebbia in 1978, the boundary element method (BEM) has been recognized as a powerful numerical technique which has some advantages over the finite difference method (FDM) and finite element method (FEM). A great amount of research has been carried out on the applications of BEM to various problems. The numerical analysis of fluid mechanics and heat transfer problems plays a key role in analysing some phenomena and it has become recognized as a new research field called "Computational Fluid Dynamics". In partic ular, the analysis of viscous flow including thermal convection phenomena is one of the most important problems in engineering fields. The FDM and FEM have been generally .applied to solve these problems because of non singularities of governing equations.
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Numerical Simulation of Fluid Flow and Heat Mass Transfer Processes

Vol.13: Nonlinear Dynamics of Transcritical Flows Proceedings of a DFVLR International Colloquium, Bonn, Germany, March 26, 1984 VI, 203 pages. 1985. Vol. 14: A. A. Bakr The Boundary Integral Equation Method in Axisymmetric Stress ...

Author: N.C. Markatos

Publisher: Springer Science & Business Media

ISBN: 9783642827815

Category: Technology & Engineering

Page: 483

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Computational fluid flow is not an easy subject. Not only is the mathematical representation of physico-chemical hydrodynamics complex, but the accurate numerical solution of the resulting equations has challenged many numerate scientists and engineers over the past two decades. The modelling of physical phenomena and testing of new numerical schemes has been aided in the last 10 years or so by a number of basic fluid flow programs (MAC, TEACH, 2-E-FIX, GENMIX, etc). However, in 1981 a program (perhaps more precisely, a software product) called PHOENICS was released that was then (and still remains) arguably, the most powerful computational tool in the whole area of endeavour surrounding fluid dynamics. The aim of PHOENICS is to provide a framework for the modelling of complex processes involving fluid flow, heat transfer and chemical reactions. PHOENICS has now been is use for four years by a wide range of users across the world. It was thus perceived as useful to provide a forum for PHOENICS users to share their experiences in trying to address a wide range of problems. So it was that the First International PHOENICS Users Conference was conceived and planned for September 1985. The location, at the Dartford Campus of Thames Polytechnic, in the event, proved to be an ideal site, encouraging substantial interaction between the participants.
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