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CONVERGENCE CHARACTERISTICS AND COMPUTATIONAL COST OF TWO ALGEBRAIC KERNELS IN VORTEX METHODS WITH A TREE-CODE ALGORITHM.
- Source :
- SIAM Journal on Scientific Computing; 2009, Vol. 31 Issue 4, p2510-2527, 18p, 1 Chart, 8 Graphs
- Publication Year :
- 2009
-
Abstract
- We study the convergence characteristics of two algebraic kernels used in vortex calculations: the Rosenhead-Moore kernel, which is a low-order kernel, and the Winckelmans-Leonard kernel, which is a high-order kernel. To facilitate the study, a method of evaluating particle-cluster interactions is introduced for the Winckelmans-Leonard kernel. The method is based on Taylor series expansion in Cartesian coordinates, as initially proposed by Lindsay and Krasny [J. Comput. Phys., 172 (2001), pp. 879-907] for the Rosenhead-Moore kernel. A recurrence relation for the Taylor coefficients of the Winckelmans-Leonard kernel is derived by separating the kernel into two parts, and an error estimate is obtained to ensure adaptive error control. The recurrence relation is incorporated into a tree-code to evaluate vorticity-induced velocity. Next, comparison of convergence is made while utilizing the tree-code. Both algebraic kernels lead to convergence, but the Winckelmans-Leonard kernel exhibits a superior convergence rate. The combined desingularization and discretization error from the Winckelmans-Leonard kernel is an order of magnitude smaller than that from the Rosenhead-Moore kernel at a typical resolution. Simulations of vortex rings are performed using the two algebraic kernels in order to compare their performance in a practical setting. In particular, numerical simulations of the side-by-side collision of two identical vortex rings suggest that the three-dimensional evolution of vorticity at finite resolution can be greatly affected by the choice of the kernel. We find that the Winckelmans-Leonard kernel is able to perform the same task with a much smaller number of vortex elements than the Rosenhead-Moore kernel, greatly reducing the overall computational cost. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10648275
- Volume :
- 31
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- SIAM Journal on Scientific Computing
- Publication Type :
- Academic Journal
- Accession number :
- 44510619
- Full Text :
- https://doi.org/10.1137/080726872