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Vortex Dynamics and Vortex Methods
Edited by: Christopher R. Anderson and Claude Greengard

Lectures in Applied Mathematics
1991; 751 pp; softcover
Volume: 28
ISBN-10: 0-8218-1135-9
ISBN-13: 978-0-8218-1135-1
List Price: US$191
Member Price: US$152.80
Order Code: LAM/28
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Understanding vortex dynamics is the key to understanding much of fluid dynamics. For this reason, many researchers, using a great variety of different approaches--analytical, computational, and experimental--have studied the dynamics of vorticity. The AMS-SIAM Summer Seminar on Vortex Dynamics and Vortex Methods, held in June 1990 at the University of Washington in Seattle, brought together experts with a broad range of viewpoints and areas of specialization. This volume contains the proceedings from that seminar.

The focus here is on the numerical computation of high Reynolds number incompressible flows. Also included is a smaller selection of important experimental results and analytic treatments. Many of the articles contain valuable introductory and survey material as well as open problems. Readers will appreciate this volume for its coverage of a wide variety of numerical, analytical, and experimental tools and for its treatment of interesting important discoveries made with these tools.


Table of Contents

  • J. T. Beale, A. Eydeland, and B. Turkington -- Numerical tests of \(3\)-D vortex methods using a vortex ring with swirl
  • O. N. Boratav, R. B. Pelz, and N. J. Zabusky -- Winding and reconnection mechanisms of closely interacting vortex tubes in three dimensions
  • J. D. Buntine and D. I. Pullin -- Does axial strain enhance vortex cancellation?
  • T. F. Buttke -- Fast vortex methods in three dimensions
  • R. E. Caflisch -- Analysis for the evolution of vortex sheets
  • A. J. Chorin -- Statistical mechanics and vortex motion
  • C. G.-H. G.-H. Cottet -- Particle-grid domain decomposition methods for the Navier-Stokes equations in exterior domains
  • K. T. Coughlin and P. S. Marcus -- Vortices in quasiperiodic Taylor-Couette flows
  • O. Daube -- Numerical simulation of axisymmetric vortex breakdown in a closed cylinder
  • D. Fishelov -- Vortex schemes for viscous flow
  • A. F. Ghoniem and O. M. Knio -- The development and application of the transport element method to three dimensional reacting shear layers
  • R. Glowinski -- Finite element methods for the numerical simulation of incompressible viscous flow.Introduction to the control of the Navier-Stokes equations
  • W. D. Henshaw, H.-O. Kreiss, and L. G. Reyna -- On smallest scale estimates and a comparison of the vortex method to the pseudo-spectral method
  • T. Y. Hou -- A survey on convergence analysis for point vortex methods
  • T. Y. Hou, J. Lowengrub, and M. J. Shelley -- Exact desingularization and local regridding for vortex methods
  • T. Y. Hou and B. T. R. Wetton -- Convergence of a finite difference method using vorticity boundary conditions
  • S. Huberson, A. Jollès, and W. Shen -- Numerical simulation of incompressible viscous flows by means of particle methods
  • R. Krasny -- Vortex sheet computations: Roll-up, wakes, separation
  • J. C. Lasheras, A. Lecuona, and P. Rodriguez -- Three-dimensional vorticity dynamics in the near field of co-flowing forced jets
  • J. Lowengrub and M. J. Shelley -- Smooth grid methods for the vorticity formulation of the Euler equations
  • S. Mas-Gallic -- Deterministic particle method: Diffusion and boundary conditions
  • E. Meiburg and J. E. Martin -- Three-dimensional vorticity dynamics in jets
  • B. Merriman -- Particle approximation
  • O. Pironneau and S. Huberson -- Characteristic-Galerkin and the particle method for the convection-diffusion equation and the Navier-Stokes equations
  • E. G. Puckett -- The random vortex method with vorticity creation: Introduction and guide to parameter selection
  • G. Russo -- A Lagrangian vortex method for the incompressible Navier-Stokes equations
  • J. A. Sethian, J.-P. Brunet, A. Greenberg, and J. P. Mesirov -- Vortex methods and massively parallel processors
  • K. Shariff, T. H. Pulliam, and J. M. Ottino -- A dynamical systems analysis of kinematics in the time-periodic wake of a circular cylinder
  • M. J. Shelley and D. I. Meiron -- Vortex reconnection and smoothness of the Euler equations
  • G. Tryggvason, S. O. Unverdi, M. Song, and J. Abdollahi-Alibeik -- Interaction of vortices with a free surface and density interfaces
  • L. L. Van Dommelen -- Lagrangian description of unsteady separation
  • C. H. K. Williamson -- \(2\)-D and \(3\)-D aspects of the wake of a cylinder, and their relation to wake computations
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