Journal ArticleDOI
On Vortex Methods
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In this paper, error estimates for fully discretized two-and three-dimensional vortex methods are given and a new way of evaluating the stretching of vorticity in 3D vortex methods is introduced.Abstract:
We give error estimates for fully discretized two- and three-dimensional vortex methods and introduce a new wy of evaluating the stretching of vorticity in three-dimensional vortex methods. The convergence theory of Beale and Majda is discussed and a simple proof of Cottet’s consistency result is presented. We also describe how to obtain accurate two-dimensional vortex methods in which the initial computational points are distributed on the nodes of nonrectangular grids, and compare several three-dimensional vortex methods.read more
Citations
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Journal ArticleDOI
Meshfree and particle methods and their applications
Shaofan Li,Wing Kam Liu +1 more
TL;DR: A survey of mesh-free and particle methods and their applications in applied mechanics can be found in this article, where the emphasis is placed on simulations of finite deformations, fracture, strain localization of solids; incompressible as well as compressible flows; and applications of multiscale methods and nano-scale mechanics.
Journal ArticleDOI
A study of singularity formation in a vortex sheet by the point-vortex approximation
TL;DR: In this paper, the authors examined Rosenhead's point-vortex approximation and sought to understand better the source of this difficulty, using discrete Fourier analysis, it was shown that perturbations introduced spuriously by computer roundoff error are responsible for the irregular point vortex motion that occurs at a smaller time as the number of points is increased, this source of computational error is controlled here by using either higher precision arithmetic or a new filtering technique.
Journal ArticleDOI
Desingularization of periodic vortex sheet roll-up
TL;DR: In this article, an analytical approach is used in an attempt to model the evolution of a vortex sheet past the critical time by means of a desingularization method, which converges beyond critical time for the vortex sheet.
Journal ArticleDOI
A comparison of vortex and pseudo-spectral methods for the simulation of periodic vortical flows at high Reynolds numbers
TL;DR: Using a fourth order accurate kernel for interpolation between the particles and the mesh, the results of the hybrid vortex method and of the pseudo-spectral method agree well in both flow cases.
Book
Stochastic Tools in Mathematics and Science
Alexandre J. Chorin,Ole H. Hald +1 more
TL;DR: In this article, Brownian motion and its application in statistical mechanics are discussed. But their application is restricted to Brownian Motion and its applications in the context of Brownian Processes.
References
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Book
An introduction to numerical analysis
TL;DR: In this article, the authors present a solution to the Matrix Eigenvalue Problem for linear systems of linear equations, based on linear algebra and linear algebra with nonlinear functions, which they call linear algebraic integration.
Journal ArticleDOI
Numerical study of slightly viscous flow
TL;DR: In this paper, a numerical method for solving the time-dependent Navier-Stokes equations in two space dimensions at high Reynolds number is presented, where the crux of the method lies in the numerical simulation of the process of vorticity generation and dispersal, using computer-generated pseudo-random numbers.
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A mathematical introduction to fluid mechanics
TL;DR: In this paper, the Equations of Motion (EOM) and potential flow and slightly viscous flow are used to describe the gas flow in one dimension in one-dimensional space.
Journal ArticleDOI
Stability theory for a pair of trailing vortices
TL;DR: In this article, the authors considered the early stages of the formation of a train of vortex rings and found that their stability depends on the products of vortex separation 6 and cutoff distance d times the perturbation wavenumber.