Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics
Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics

Author: Alexander Gelfgat

Publisher: Springer

Published: 2018-07-06

Total Pages: 524

ISBN-13: 3319914944

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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.

Bifurcation Analysis of Fluid Flows
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.

Numerical Continuation and Bifurcation in Nonlinear PDEs
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.

Introduction to Hydrodynamic Stability
Introduction to Hydrodynamic Stability

Author: P. G. Drazin

Publisher: Cambridge University Press

Published: 2002-09-09

Total Pages: 278

ISBN-13: 1316582876

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Instability of flows and their transition to turbulence are widespread phenomena in engineering and the natural environment, and are important in applied mathematics, astrophysics, biology, geophysics, meteorology, oceanography and physics as well as engineering. This is a textbook to introduce these phenomena at a level suitable for a graduate course, by modelling them mathematically, and describing numerical simulations and laboratory experiments. The visualization of instabilities is emphasized, with many figures, and in references to more still and moving pictures. The relation of chaos to transition is discussed at length. Many worked examples and exercises for students illustrate the ideas of the text. Readers are assumed to be fluent in linear algebra, advanced calculus, elementary theory of ordinary differential equations, complex variables and the elements of fluid mechanics. The book is aimed at graduate students but will also be very useful for specialists in other fields.

Bifurcations, Instabilities and Degradations in Geomaterials
Bifurcations, Instabilities and Degradations in Geomaterials

Author: Richard Wan

Publisher: Springer Science & Business Media

Published: 2011-03-16

Total Pages: 366

ISBN-13: 3642182844

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Geomaterials exhibit complex but rich mechanical behaviour with a variety of failure modes ranging from diffuse to localized deformation depending on stress, density, microstructure, and loading conditions. These failure modes are a result of an instability of material and/or geometric nature that can be studied within the framework of bifurcation theory. Degradation is another related phenomenon arising from cyclic loading, ageing, weathering, chemical attack, and capillary effects, among others. The methodology of analyzing the various types of instabilities is crucial in the adequate modelling and safe design of numerous problems in geomechanics. The present volume contains a sampling of enlarged versions of papers presented at the International Workshop on Bifurcation and Degradations in Geomaterials (IWBDG 2008) held in Lake Louise, Alberta, Canada, May 28-31, 2008. These papers capture the state-of-the-art in the specialized field of geomechanics and contemporary approaches to solving the central issue of failure. Some engineering applications are presented in the areas of energy resource extraction and soil-machine interaction.

Computational Fluid Dynamics Review 1998 (In 2 Volumes)
Computational Fluid Dynamics Review 1998 (In 2 Volumes)

Author: Mohamed M Hafez

Publisher: World Scientific

Published: 1998-11-20

Total Pages: 1169

ISBN-13: 9814495778

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The first volume of CFD Review was published in 1995. The purpose of this new publication is to present comprehensive surveys and review articles which provide up-to-date information about recent progress in computational fluid dynamics, on a regular basis. Because of the multidisciplinary nature of CFD, it is difficult to cope with all the important developments in related areas. There are at least ten regular international conferences dealing with different aspects of CFD.It is a real challenge to keep up with all these activities and to be aware of essential and fundamental contributions in these areas. It is hoped that CFD Review will help in this regard by covering the state-of-the-art in this field.The present book contains sixty-two articles written by authors from the US, Europe, Japan and China, covering the main aspects of CFD. There are five sections: general topics, numerical methods, flow physics, interdisciplinary applications, parallel computation and flow visualization. The section on numerical methods includes grids, schemes and solvers, while that on flow physics includes incompressible and compressible flows, hypersonics and gas kinetics as well as transition and turbulence. This book should be useful to all researchers in this fast-developing field.

Coanda Effect
Coanda Effect

Author: Noor A Ahmed

Publisher: CRC Press

Published: 2019-08-28

Total Pages: 266

ISBN-13: 0429805438

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Coanda effect is a complex fluid flow phenomenon enabling the production of vertical take-off/landing aircraft. Other applications range from helicopters to road vehicles, from flow mixing to combustion, from noise reduction to pollution control, from power generation to robot operation, and so forth. Book starts with description of the effect, its history and general formulation of governing equations/simplifications used in different applications. Further, it gives an account of this effect’s lift boosting potential on a wing and in non-flying vehicles including industrial applications. Finally, occurrence of the same in human body and associated adverse medical conditions are explained.

Adaptive High-order Methods in Computational Fluid Dynamics
Adaptive High-order Methods in Computational Fluid Dynamics

Author: Z. J. Wang

Publisher: World Scientific

Published: 2011

Total Pages: 471

ISBN-13: 9814313181

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This book consists of important contributions by world-renowned experts on adaptive high-order methods in computational fluid dynamics (CFD). It covers several widely used, and still intensively researched methods, including the discontinuous Galerkin, residual distribution, finite volume, differential quadrature, spectral volume, spectral difference, PNPM, and correction procedure via reconstruction methods. The main focus is applications in aerospace engineering, but the book should also be useful in many other engineering disciplines including mechanical, chemical and electrical engineering. Since many of these methods are still evolving, the book will be an excellent reference for researchers and graduate students to gain an understanding of the state of the art and remaining challenges in high-order CFD methods.