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Applied Mathematics Research eXpress (2006) Vol. 2006 : article ID 17027, 31 pages, doi:10.1155/AMRX/2006/17027
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Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.

Validation of a three-dimensional vortex particle method for fluid flows

André Giovannini and Yves Gagnon

Institut de Mécanique des Fluides de Toulouse, Université Paul Sabatier avenue du Professeur Camille Soula, 31400 Toulouse, France E-mail address: andre.giovannini{at}imft.fr
Chaire K.-C.- Irving en Développment Durable, Université de Moncton Moncton, NB, Canada E1A 3E9 E-mail address: gagnony{at}umoncton.ca

In the context of complex vortex dynamics and interactions studies, an algorithm based on vortex particle methods is developed while a set of validation tests and a detailed comparison with a pseudospectral code are presented. The two physical problems considered are the isolated Lamb-Oseen tube (case A) and the antiparallel tubes (Crow instability, case B). The objectives of the work are to quantify the influence of the temporal and the spatial resolutions on the solution, to evaluate the numerical diffusion, and to look at the robustness and the ability of the algorithm to handle small tubular scales at a maximum Reynolds number. Finally, for the so-called Crow instability (case B), comparisons between the vortex-in-cell algorithm at 64, 128, and 256 spatial resolutions are carried out with a spectral method, for a Reynolds number of 1500. The results contribute to a better knowledge of the stability, accuracy, and dissipative behaviour of 3D vortex methods for modelling fluid flows.


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