Vortex Flows and Related Numerical Methods

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.

Mathematical and numerical modeling of incompressible flows.- Local spectral analysis of turbulent flows using wavelet transforms.- Operator splitting for Navier-Stokes and Chorin-Marsden product formula.- Velicity methods: Lagrangian numerical methods which preserve the Hamiltonian structure of incompressible fluid flow.- Statistical mechanics for the vortex model.- On singular solutions of the Vlasov-Poisson equations.- Point vortices and localization in Euler flows.- Turbulence modeling for incompressible vortex flow.- Vorticity generation, wakes and boundary layers in two dimensions.- Investigation of the use of the Prandtl/Navier-Stokes equation procedures for two-dimensional incompressible flows.- Vorticity boundary conditions for the Navier-Stokes equation in velocity-vorticity formulation.- A coupled potential-boundary layer calculation method for unsteady flows around airfoils.- Viscous simulation of wake patterns.- Contour dynamics and vortex methods.- The vorton methods.- Numerical simulation of unsteady flows behind cylindrical structures using a finite difference-particle superposition algorithm.- Moment accelerated contour surgery.- Direct numerical simulations using vortex methods.- Numerical study of the motion and deformation of two-dimensional bubbles by a vortex method.- A hybrid vortex method with deterministic diffusion.- A slightly diffusive contour dynamics.- Computations of three dimensional incompressible flow.- Model coherent structure dynamics: vortex reconnection, core dynamics and interaction with turbulence.- The nonlinear dynamics of a jet shear layer with swirl.- Dynamics of vortex tubes in three-dimensional turbulence.- Numerical simulation of axisymmetric vortex sheet roll-up.- Free vortex rings, analogies and differences between vorticity and a passive scalar.- Compressible and reacting flows.- Turbulent eddy structures, combustion and chemical reactions.- Vortex generation and evolution in numerical simulation of transitional shear flows.- Stability analysis of differentially-heated asymmetric vorticity layers.- A particle in cell method for the 2-D compressible Euler equations.