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Advances in viscous vortex methods - meshless spatial adaption based on radial basis function interpolation

Barba, L. A. and Leonard, A. and Allen, C. B. (2005) Advances in viscous vortex methods - meshless spatial adaption based on radial basis function interpolation. International Journal for Numerical Methods in Fluids, 47 (5). pp. 387-421. ISSN 0271-2091. doi:10.1002/fld.811.

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Vortex methods have a history as old as finite differences. They have since faced difficulties stemming from the numerical complexity of the Biot–Savart law, the inconvenience of adding viscous effects in a Lagrangian formulation, and the loss of accuracy due to Lagrangian distortion of the computational elements. The first two issues have been successfully addressed, respectively, by the application of the fast multipole method, and by a variety of viscous schemes which will be briefly reviewed in this article. The standard method to deal with the third problem is the use of remeshing schemes consisting of tensor product interpolation with high-order kernels. In this work, a numerical study of the errors due to remeshing has been performed, as well as of the errors implied in the discretization itself using vortex blobs. In addition, an alternative method of controlling Lagrangian distortion is proposed, based on ideas of radial basis function (RBF) interpolation (briefly reviewed here). This alternative is formulated grid-free, and is shown to be more accurate than standard remeshing. In addition to high-accuracy, RBF interpolation allows core size control, either for correcting the core spreading viscous scheme or for providing a variable resolution in the physical domain. This formulation will allow in theory the application of error estimates to produce a truly adaptive spatial refinement technique. Proof-of-concept is provided by calculations of the relaxation of a perturbed monopole to a tripole attractor.

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Additional Information:© 2005 John Wiley & Sons, Ltd. Received 10 October 2003; Revised 20 September 2004; Accepted 14 October 2004; Published online 30 November 2004. Computations were carried out in the Iris Lab computers of the Graduate Aeronautical Laboratories, Caltech. Thanks are due to S. Billings for making available his GMRES code for RBF interpolation.
Subject Keywords:vortex method; radial basis functions; core spreading; viscous flow simulation; mesh-less methods
Issue or Number:5
Record Number:CaltechAUTHORS:20150114-160021492
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Official Citation:Barba, L. A., Leonard, A. and Allen, C. B. (2005), Advances in viscous vortex methods—meshless spatial adaption based on radial basis function interpolation. Int. J. Numer. Meth. Fluids, 47: 387–421. doi: 10.1002/fld.811
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:53742
Deposited By: Tony Diaz
Deposited On:15 Jan 2015 01:17
Last Modified:10 Nov 2021 20:06

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