Higher order vortex methods with rezoning
The vortex method is a numerical method for approximating the flow of an incompressible, inviscid fluid. We consider the two-dimensional case. The accuracy depends on the choice of the cutoff function which approximates the delta function, on the cutoff parameter delta and on the smoothness of the initial data. We derive a class of infinite-order cutoff functions with arbitrarily high rates of decay at infinity. We also derive an eighth order cutoff function with compact support. We test two versions of rezoning. Version 1 has been suggested and tested by Beale and Majda, while version 2 is new. Using rezoning, we test the eighth order cutoff function and one infinite-order cutoff function on three test problems for which the solution of Euler's equation is known analytically. The accuracies of the two methods are comparable. We also compute the evolution of two circular vorticity patches and the evolution of one square vorticity patch over long time intervals. Finally, we make a comparison between the direct method of velocity evaluation and the Rokhlin-Greengard algorithm. The numerical experiments indicate that for smooth flows, high-order cutoffs combined with rezoning give high accuracy for long time integrations. 27 refs., 28 figs., 10 tabs.
- Research Organization:
- Lawrence Berkeley Lab., CA (USA)
- DOE Contract Number:
- AC03-76SF00098
- OSTI ID:
- 7193992
- Report Number(s):
- LBL-25259; ON: DE88010777
- Country of Publication:
- United States
- Language:
- English
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