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Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics

Author: Alexander Gelfgat

Publisher: Springer

Published: 2018-07-06

Total Pages: 527

ISBN-13: 3319914944

Instabilities of fluid flows and the associated transitions between different possible flow states provide a fascinating set of problems that have attracted researchers for over a hundred years. This book addresses state-of-the-art developments in numerical techniques for computational modelling of fluid instabilities and related bifurcation structures, as well as providing comprehensive reviews of recently solved challenging problems in the field.

Computational Modeling for Fluid Flow and Interfacial Transport

Author: Wei Shyy

Publisher: Courier Corporation

Published: 2014-06-10

Total Pages: 529

ISBN-13: 0486150011

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Practical applications and examples highlight this treatment of computational modeling for handling complex flowfields. A reference for researchers and graduate students of many different backgrounds, it also functions as a text for learning essential computation elements. Drawing upon his own research, the author addresses both macroscopic and microscopic features. He begins his three-part treatment with a survey of the basic concepts of finite difference schemes for solving parabolic, elliptic, and hyperbolic partial differential equations. The second part concerns issues related to computational modeling for fluid flow and transport phenomena. In addition to a focus on pressure-based methods, this section also discusses practical engineering applications. The third and final part explores the transport processes involving interfacial dynamics, particularly those influenced by phase change, gravity, and capillarity. Case studies, employing previously discussed methods, demonstrate the interplay between the fluid and thermal transport at macroscopic scales and their interaction with the interfacial transport.

Computational Modelling of Instability and Transition Using High-resolution Methods

Author:

Publisher:

Published: 2003

Total Pages:

ISBN-13:

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This thesis concerns the numerical investigation of suddenly expanded flows featuring separation, instabilities and transition, in the context of Implicit Large Eddy Simulation (ILES). The study of separated flows through suddenly expanded geometries is a classic yet complex area of research. These types of flows feature instabilities which may lead to bifurcation. Non-linear bifurcation is of great importance when considering hydrodynamic stability and the mechanism of laminar to turbulent flow transition. A detailed numerical investigation of various high-resolution methods and their ability to correctly predict the flow through a suddenly expanded and contracted geometry demonstrates that the choice of the particular numerical method employed can lead to an incorrect solution of the flow. The key di erence between the various highresolution methods employed is in the calculation of the nonlinear wave-speed dependent term. It is shown that the nonlinearity of this term provides an asymmetric dissipation to the flow which triggers symmetry-breaking bifurcation in a fully symmetric computational set-up. High-resolution simulations of three-dimensional flow through a plane suddenly expanded channel at low Reynolds numbers show that this type of flow is characterised by a symmetric separation of the fluid which is nominally two-dimensional in the spanwise direction. Increasing the Reynolds number reveals a symmetry-breaking bifurcation of the fluid flow which becomes three-dimensional as Reynolds number is further increased. Simulations confirm that it is this threedimensional disturbance which leads to the onset of time-dependent flow characterised by the periodic shedding of vortices from the upstream recirculation zones. Preconditioning techniques which aim to alleviate sti ness in the calculation of the advective fluxes for low Reynolds number flows are shown to be unsuitable for flows featuring instabilities. The added dissipation to the flow causes the predictio.

Bifurcation Analysis of Fluid Flows

Author: Henk A. Dijkstra

Publisher: Cambridge University Press

Published: 2023-06-30

Total Pages: 343

ISBN-13: 1108852521

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A better understanding of the mechanisms leading a fluid system to exhibit turbulent behavior is one of the grand challenges of the physical and mathematical sciences. Over the last few decades, numerical bifurcation methods have been extended and applied to a number of flow problems to identify critical conditions for fluid instabilities to occur. This book provides a state-of-the-art account of these numerical methods, with much attention to modern linear systems solvers and generalized eigenvalue solvers. These methods also have a broad applicability in industrial, environmental and astrophysical flows. The book is a must-have reference for anyone working in scientific fields where fluid flow instabilities play a role. Exercises at the end of each chapter and Python code for the bifurcation analysis of canonical fluid flow problems provide practice material to get to grips with the methods and concepts presented in the book.

Turbulent Flow Computation

Author: D. Drikakis

Publisher: Springer Science & Business Media

Published: 2006-04-11

Total Pages: 390

ISBN-13: 0306484218

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In various branches of fluid mechanics, our understanding is inhibited by the presence of turbulence. Although many experimental and theoretical studies have significantly helped to increase our physical understanding, a comp- hensive and predictive theory of turbulent flows has not yet been established. Therefore, the prediction of turbulent flow relies heavily on simulation stra- gies. The development of reliable methods for turbulent flow computation will have a significant impact on a variety of technological advancements. These range from aircraft and car design, to turbomachinery, combustors, and process engineering. Moreover, simulation approaches are important in materials - sign, prediction of biologically relevant flows, and also significantly contribute to the understanding of environmental processes including weather and climate forecasting. The material that is compiled in this book presents a coherent account of contemporary computational approaches for turbulent flows. It aims to p- vide the reader with information about the current state of the art as well as to stimulate directions for future research and development. The book puts part- ular emphasis on computational methods for incompressible and compressible turbulent flows as well as on methods for analysing and quantifying nume- cal errors in turbulent flow computations. In addition, it presents turbulence modelling approaches in the context of large eddy simulation, and unfolds the challenges in the field of simulations for multiphase flows and computational fluid dynamics (CFD) of engineering flows in complex geometries. Apart from reviewing main research developments, new material is also included in many of the chapters.

Instabilities and Turbulence in Engineering Flows

Author: D. Ashpis

Publisher: Springer

Published: 1993-02-28

Total Pages: 444

ISBN-13:

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This book contains contributions by colleagues, former students and friends of Professor Eli Reshotko in celebration of his 60th birth day. Since Professor Reshotko's scientific and engineering contribu tions have been in the areas of hydrodynamic stability, transition to turbulence, and boundary layer flows, it is only appropriate that the articles in this volume be devoted to these and related topics. The first two sections focus on instabilities and transition in sub sonic and supersonic flows, respectively. The third section deals with developing turbulence, while the the final section treats related prob lems in engineering fluid mechanics. The diversity and scope of the articles contained herein exemplify the insight and expertise required in the study of transitional and turbulent flows today - traits which also exemplify Eli Reshotko's contributions to these fields. A few of the articles in this volume were presented at a sym posium in honor of Eli Reshotko's 60th birthday, held in Newport News, Virginia, on July 28, 1991. The symposium was sponsored by lCASE, and organized by M.Y. Hussaini (lCASE) and R. Hirsh (U.S. National Science Foundation). Of those who could not attend, many chose to honor Professor Reshotko by a contribution to the volume dedicated to him. We would like to use this opportunity to express our deep ap preciation to M.Y. Hussaini for initiating this very special tribute to Eli, and to Ms. Emily Todd for her efforts in the volume preparation and in the organization of the symposium.

Numerical Continuation and Bifurcation in Nonlinear PDEs

Author: Hannes Uecker

Publisher: SIAM

Published: 2021-08-19

Total Pages: 380

ISBN-13: 1611976618

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This book provides a hands-on approach to numerical continuation and bifurcation for nonlinear PDEs in 1D, 2D, and 3D. Partial differential equations (PDEs) are the main tool to describe spatially and temporally extended systems in nature. PDEs usually come with parameters, and the study of the parameter dependence of their solutions is an important task. Letting one parameter vary typically yields a branch of solutions, and at special parameter values, new branches may bifurcate. After a concise review of some analytical background and numerical methods, the author explains the free MATLAB package pde2path by using a large variety of examples with demo codes that can be easily adapted to the reader's given problem. Numerical Continuation and Bifurcation in Nonlinear PDEs will appeal to applied mathematicians and scientists from physics, chemistry, biology, and economics interested in the numerical solution of nonlinear PDEs, particularly the parameter dependence of solutions. It can be used as a supplemental text in courses on nonlinear PDEs and modeling and bifurcation.

Computational Fluid Dynamics

Author: Takeo Kajishima

Publisher: Springer

Published: 2016-10-01

Total Pages: 364

ISBN-13: 3319453041

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This textbook presents numerical solution techniques for incompressible turbulent flows that occur in a variety of scientific and engineering settings including aerodynamics of ground-based vehicles and low-speed aircraft, fluid flows in energy systems, atmospheric flows, and biological flows. This book encompasses fluid mechanics, partial differential equations, numerical methods, and turbulence models, and emphasizes the foundation on how the governing partial differential equations for incompressible fluid flow can be solved numerically in an accurate and efficient manner. Extensive discussions on incompressible flow solvers and turbulence modeling are also offered. This text is an ideal instructional resource and reference for students, research scientists, and professional engineers interested in analyzing fluid flows using numerical simulations for fundamental research and industrial applications.

Computational Fluid Dynamics

Author:

Publisher:

Published: 1992

Total Pages: 246

ISBN-13:

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Fluid Dynamics of Viscoelastic Liquids

Author: Daniel D. Joseph

Publisher: Springer

Published: 1990-05-02

Total Pages: 0

ISBN-13: 9780387971551

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This book is about two special topics in rheological fluid mechanics: the elasticity of liquids and asymptotic theories of constitutive models. The major emphasis of the book is on the mathematical and physical consequences of the elasticity of liquids; seventeen of twenty chapters are devoted to this. Constitutive models which are instantaneously elastic can lead to some hyperbolicity in the dynamics of flow, waves of vorticity into rest (known as shear waves), to shock waves of vorticity or velocity, to steady flows of transonic type or to short wave instabilities which lead to ill-posed problems. Other kinds of models, with small Newtonian viscosities, give rise to perturbed instantaneous elasticity, associated with smoothing of discontinuities as in gas dynamics. There is no doubt that liquids will respond like elastic solids to impulses which are very rapid compared to the time it takes for the molecular order associated with short range forces in the liquid, to relax. After this, all liquids look viscous with signals propagating by diffusion rather than by waves. For small molecules this time of relaxation is estimated as lQ-13 to 10-10 seconds depending on the fluids. Waves associated with such liquids move with speeds of 1 QS cm/s, or even faster. For engineering applications the instantaneous elasticity of these fluids is of little interest; the practical dynamics is governed by diffusion, ·say, by the Navier-Stokes equations. On the other hand, there are other liquids which are known to have much longer times of relaxation.