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Vorticity plays a key role in determining fluid flow dynamics, especially in vortex-dominated flows. Vortex methods, which are based on the vorticity-based formulation of the Navier-Stokes equations, have provided deeper insight into physical reality in a variety of flows using vorticity as a primary variable. The penalized vortex-in-cell (VIC) method is a state-of-the-art variant of vortex methods. In the penalized VIC method, Lagrangian fluid particles are traced by continuously updating their position and strength from solutions at an Eulerian grid. This hybrid method retains beneficial features of pure Lagrangian and Eulerian methods. It offers an efficient and effective way to simulate unsteady viscous flows, thereby enabling application to a wider range of problems in flows. This article presents the fundamentals of the penalized VIC method and its implementations.
This monograph provides in-depth analyses of vortex dominated flows via matched and multiscale asymptotics, and demonstrates how insight gained through these analyses can be exploited in the construction of robust, efficient, and accurate numerical techniques. The book explores the dynamics of slender vortex filaments in detail, including fundamental derivations, compressible core structure, weakly non-linear limit regimes, and associated numerical methods. Similarly, the volume covers asymptotic analysis and computational techniques for weakly compressible flows involving vortex-generated sound and thermoacoustics. The book is addressed to both graduate students and researchers.
The contents of the book cover a wide variety of topics related to the analysis of the dynamics of vortices and describe the results of experiments, computational modeling and their interpretation. The book contains 13 chapters reaching areas of physics in vortex dynamics and optical vortices including vortices in superfluid atomic gases, vortex laser beams, vortex-antivortex in ferromagnetic hybrids, and optical vortices illumination in chiral nanostructures. Also, discussions are presented on particle motion in vortex flows, on the simulation of vortex-dominated flows, on vortices in saturable media, on achromatic vortices, and on ultraviolet vortices. Fractal light vortices, coherent vortex beams, together with vortices in electric dipole radiation, and spin wave dynamics in magnetic vortices are examined as well.
Honoring the contributions of one of the field''s leading experts, Lu Ting, this indispensable volume contains important new results at the cutting edge of research. A wide variety of significant new analytical and numerical results in critical areas are presented, including point vortex dynamics, superconductor vortices, cavity flows, vortex breakdown, shock/vortex interaction, wake flows, magneto-hydrodynamics, rotary wake flows, and hypersonic vortex phenomena. The book will be invaluable for those interested in the state of the art of vortex dominated flows, both from a theoretical and applied perspective. Professor Lu Ting and Joe Keller have worked together for over 40 years. In their first joint work entitled OC Periodic vibrations of systems governed by nonlinear partial differential equationsOCO, perturbation analysis and bifurcation theory were used to determine the frequencies and modes of vibration of various physical systems. The novelty was the application to partial differential equations of methods which, previously, had been used almost exclusively on ordinary differential equations. Professsor Lu Ting is an expert in both fluid dynamics and the use of matched asymptotic expansions. His physical insight into fluid flows has led the way to finding the appropriate mathematical simplications used in the solutions to many difficult flow problems."
Over the last several years, Vorticity Confinement has been shown to be a very efficient method to simulate the vortex-dominated flows over complex configurations. To calculate these flows, no high-order numerical scheme and body conforming grids are required for this method and only a fixed, uniform Cartesian grid is employed. First, an overall description of the original Vorticity Confinement method (VC1) is presented, followed by an introduction of the newly developed Vorticity Confinement method (VC2). The advantage of VC2 over VC1 is the ability to conserve the Momentum. Two different numerical schemes are shown for VC1 and VC2. The one for VC2 is much simpler than that of VC1. Results of VC1 and VC2 for convecting vortices and scalars in 1-D and 2-D will be presented. Numerical results are presented for the three dimensional flow over a surface-mounted cube. Comparisons have been made with experimental and Large Eddy Simulation (LES) data. It is observed that with a coarse uniform Cartesian grid, Vorticity Confinement is able to get results in better agreement with the experimental results than the LES simulation results on a fine grid. This method is shown to be more effective than trying to model and discretize more complex system of equations in the traditional methods, when solving complex high Reynolds number flow problems.
Many important phenomena in fluid motion are evident in vortex flow, i.e., flows in which vortical structures are significant in determining the whole flow. This book, which consists of lectures given at a NATO ARW held in Grenoble (France) in June 1992, provides an up-to-date account of current research in the study of these phenomena by means of numerical methods and mathematical modelling. Such methods include Eulerian methods (finite difference, spectral and wavelet methods) as well as Lagrangian methods (contour dynamics, vortex methods) and are used to study such topics as 2- or 3-dimensional turbulence, vorticity generation by solid bodies, shear layers and vortex sheets, and vortex reconnection. For researchers and graduate students in computational fluid dynamics, numerical analysis, and applied mathematics.
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.
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.