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

✍ Scribed by L. A. Barba; A. Leonard; C. B. Allen

• Publisher: John Wiley and Sons
• Year: 2005
• Tongue: English
• Weight: 872 KB
• Volume: 47
• Category: Article
• ISSN: 0271-2091
• DOI: 10.1002/fld.811

✦ Synopsis

Vortex methods have a history as old as ÿnite di erences. They have since faced di culties stemming from the numerical complexity of the Biot-Savart law, the inconvenience of adding viscous e ects in a Lagrangian formulation, and the loss of accuracy due to Lagrangian distortion of the computational elements. The ÿrst 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 brie y 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 (brie y 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 reÿnement technique. Proof-of-concept is provided by calculations of the relaxation of a perturbed monopole to a tripole attractor.