Abstract
Recently several different approaches have been developed for the simulation of three-dimensional incompressible fluid flows using vortex methods. Some versions use detailed tracking of vortex filament structures and often local curvatures of these filaments, while other methods require only crude information, such as the vortex blobs of the two-dimensional case. Can such "crude" algorithms accurately account for vortex stretching and converge? We answer this question affirmatively by constructing a new class of "crude" three-dimensional vortex methods and then proving that these methods are stable and convergent, and can even have arbitrarily high order accuracy without being more expensive than other "crude" versions of the vortex algorithm.
Original language | English (US) |
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Pages (from-to) | 1-27 |
Number of pages | 27 |
Journal | Mathematics of Computation |
Volume | 39 |
Issue number | 159 |
DOIs | |
State | Published - Jul 1982 |
Keywords
- Incompressible flow
- Vortex method
ASJC Scopus subject areas
- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics