Vortex Methods


Book Description

Vortex methods have matured in recent years, offering an interesting alternative to finite difference and spectral methods for high resolution numerical solutions of the Navier Stokes equations. In the past three decades, research into the numerical analysis aspects of vortex methods has provided a solid mathematical background for understanding the accuracy and stability of the method. At the same time vortex methods retain their appealing physical character, which was the motivation for their introduction. This book presents and analyzes vortex methods as a tool for the direct numerical simulation of impressible viscous flows. It will interest graduate students and researchers in numerical analysis and fluid mechanics and also serve as an ideal textbook for courses in fluid dynamics.




Vorticity and Incompressible Flow


Book Description

This book is a comprehensive introduction to the mathematical theory of vorticity and incompressible flow ranging from elementary introductory material to current research topics. While the contents center on mathematical theory, many parts of the book showcase the interaction between rigorous mathematical theory, numerical, asymptotic, and qualitative simplified modeling, and physical phenomena. The first half forms an introductory graduate course on vorticity and incompressible flow. The second half comprise a modern applied mathematics graduate course on the weak solution theory for incompressible flow.




Quantized Vortex Dynamics and Superfluid Turbulence


Book Description

This book springs from the programme Quantized Vortex Dynamics and Sup- ?uid Turbulence held at the Isaac Newton Institute for Mathematical Sciences (University of Cambridge) in August 2000. What motivated the programme was the recognition that two recent developments have moved the study of qu- tized vorticity, traditionally carried out within the low-temperature physics and condensed-matter physics communities, into a new era. The ?rst development is the increasing contact with classical ?uid dynamics and its ideas and methods. For example, some current experiments with - lium II now deal with very classical issues, such as the measurement of velocity spectra and turbulence decay rates. The evidence from these experiments and many others is that super?uid turbulence and classical turbulence share many features. The challenge is now to explain these similarities and explore the time scales and length scales over which they hold true. The observed classical aspects have also attracted attention to the role played by the ?ow of the normal ?uid, which was somewhat neglected in the past because of the lack of direct ?ow visualization. Increased computing power is also making it possible to study the coupled motion of super?uid vortices and normal ?uids. Another contact with classical physics arises through the interest in the study of super?uid vortex - connections. Reconnections have been studied for some time in the contexts of classical ?uid dynamics and magneto-hydrodynamics (MHD), and it is useful to learn from the experience acquired in other ?elds.




Vortex Methods: Selected Papers Of The First International Conference On Vortex Methods


Book Description

Vortex methods have been developed and applied to many kinds of flows related to various problems in wide engineering and scientific fields. The purpose of the First International conference on Vortex methods was to provide an opportunity for engineers and scientists to present their achievements, exchange ideas and discuss new developments in mathematical and physical modeling techniques and engineering applications of vortex methods.




Vortex, Molecular Spin and Nanovorticity


Book Description

The subject of this book is the physics of vortices. A detailed analysis of the dynamics of vortices will be presented. The important topics of vorticity and molecular spin will be dealt with, including the electromagnetic analogy and quantization in superfluids. The effect of molecular spin on the dynamics of molecular nano-confined fluids using the extended Navier-Stokes equations will also be covered –especially important to the theory and applicability of nanofluidics and associated devices. The nanoscale boundary layer and nanoscale vortex core are regions of intense vorticity (molecular spin). It will be shown, based on molecular kinetic theory and thermodynamics, that the macroscopic (solid body) rotation must be accompanied by internal rotation of the molecules. Electric polarization of the internal molecular rotations about the local rotation axis –the Barnett effect – occurs. In such a spin aligned system, major changes in the physical properties of the fluid result.




Applied Analysis And Differential Equations


Book Description

This volume contains refereed research articles written by experts in the field of applied analysis, differential equations and related topics. Well-known leading mathematicians worldwide and prominent young scientists cover a diverse range of topics, including the most exciting recent developments.A broad range of topics of recent interest are treated: existence, uniqueness, viability, asymptotic stability, viscosity solutions, controllability and numerical analysis for ODE, PDE and stochastic equations. The scope of the book is wide, ranging from pure mathematics to various applied fields such as classical mechanics, biomedicine, and population dynamics.




Vortex Methods and Vortex Motion


Book Description

Vortex methods have emerged as a new class of powerful numerical techniques to analyze and compute vortex motion. This book addresses the theoretical, numerical, computational, and physical aspects of vortex methods and vortex motion. Vortex phenomena in fluid flows and the experimental, theoretical, and numerical methods used to characterize them are discussed in reviews by leading experts. Extensive photographs and sample computer graphics are provided. The development of large vortex structure in fluid flow is responsible for some of the most fascinating aspects of fluid dynamics, such as mixing, shearing, transport, and instability. Such issues arise in a variety of flow regimes, ranging from fundamental mathematical questions in laminar, transitional, and turbulent flow to sophisticated engineering settings and devices.




Rotating Flow


Book Description

Rotating flow is critically important across a wide range of scientific, engineering and product applications, providing design and modeling capability for diverse products such as jet engines, pumps and vacuum cleaners, as well as geophysical flows.Developed over the course of 20 years' research into rotating fluids and associated heat transfer at the University of Sussex Thermo-Fluid Mechanics Research Centre (TFMRC), Rotating Flow is an indispensable reference and resource for all those working within the gas turbine and rotating machinery industries.Traditional fluid and flow dynamics titles offer the essential background but generally include very sparse coverage of rotating flows—which is where this book comes in. Beginning with an accessible introduction to rotating flow, recognized expert Peter Childs takes you through fundamental equations, vorticity and vortices, rotating disc flow, flow around rotating cylinders and flow in rotating cavities, with an introduction to atmospheric and oceanic circulations included to help deepen understanding.Whilst competing resources are weighed down with complex mathematics, this book focuses on the essential equations and provides full workings to take readers step-by-step through the theory so they can concentrate on the practical applications. - A detailed yet accessible introduction to rotating flows, illustrating the differences between flows where rotation is significant and highlighting the non-intuitive nature of rotating flow fields - Written by world-leading authority on rotating flow, Peter Childs, making this a unique and authoritative work - Covers the essential theory behind engineering applications such as rotating discs, cylinders, and cavities, with natural phenomena such as atmospheric and oceanic flows used to explain underlying principles - Provides a rigorous, fully worked mathematical account of rotating flows whilst also including numerous practical examples in daily life to highlight the relevance and prevalence of different flow types - Concise summaries of the results of important research and lists of references included to direct readers to significant further resources




An Introduction to Magnetohydrodynamics


Book Description

This book is an introductory text on magnetohydrodynamics (MHD) - the study of the interaction of magnetic fields and conducting fluids.