This paper details an efficient algorithm for particles undergoing random walks in the presence of complex, two-dimensional, solid boundaries. The scheme is developed for the simulation of vortex diffusion using the random vortex method. Both vortex blobs and sheets are handled. The relevant modifications for using the algorithm with the vorticity redistribution technique are also discussed. The algorithm is designed to be used in the framework of an existing fast multipole implementation. A measure for the geometric complexity of a body is introduced and the algorithm's efficiency is studied as various parameters are changed for bodies of varying complexity. © 2007 Elsevier Ltd. All rights reserved.

M Ramakrishna

Department of Aerospace Engineering

Surya C. Rajan

Algorithms

Computational complexity

Domain decomposition methods

Vortex flow

Vorticity

Domain decomposition

GEOMETRIC COMPLEXITY

RANDOM VORTEX METHOD

Random Walks

SOLID BOUNDARIES

VORTEX DIFFUSION

VORTICITY REDISTRIBUTION TECHNIQUE

Random processes

Fulltext

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Computers and Mathematics with Applications

Vortex methods offer a grid-free alternative to simulating incompressible, viscous, fluid flows. They require the use of fairly sophisticated algorithms and can be complicated to implement for general flows. This article describes an object-oriented design used to implement a vortex particle based flow solver in two dimensions. We provide an overview of the various abstractions that arose as a result of this design. Several of the algorithms have common components that may be abstracted and reused. We demonstrate how the design allowed us to derive the traditional benefits of OOD. In addition, we show how the design directly suggested elegant generalizations of existing algorithms. Finally, we show the benefits of using software testing techniques and building a powerful scripting layer for the library. © 2009 ACM.

ACM Transactions on Mathematical Software

An object-oriented design for two-dimensional vortex particle methods

Journal of Computational Physics

Vortex Methods for High-Resolution Simulations of Viscous Flow Past Bluff Bodies of General Geometry

ESAIM: Proceedings

Parallel discrete vortex methods on commodity supercomputers; an investigation into bluff body far wake behaviour

Vortex particles and tree codes: I. flows with arbitrary crossing between solid boundaries and particle redistribution lattice; II. vortex ring encountering a plane at an angle.

A New Diffusion Procedure for Vortex Methods

Journal of Fluid Mechanics

High-resolution simulations of the flow around an impulsively started cylinder using vortex methods

Efficient random walks in the presence of complex two-dimensional geometries

Journal	Computers and Mathematics with Applications
ISSN	08981221
Open Access	No