Fast algorithms for vortex methods

L. Greengard; V. Rokhlin

Fast algorithms for vortex methods

Mathematics

Research output: Contribution to conference › Paper › peer-review

Abstract

In the random vortex method for viscous incompressible flow, the vorticity field is represented by a collection of vortex blobs which are alternately convected and diffused via a random walk. For a fluid modelled by n vortex blobs, the bulk of the computational burden at each time step is the evaluation of all pairwise interactions which, by direct summation, requires O(n²) work. In this paper, we discuss the incorporation of fast algorithms to reduce the cost of this calculation. By using the recently developed Fast Multipole Method (FMM), it is possible to compute all pairwise interactions in an amount of time proportional to n, making the overall scheme significantly more practical for large-scale problems.

Original language	English (US)
State	Published - 1988
Event	1st National Fluid Dynamics Conference, 1988 - Cincinnati, United States Duration: Jul 25 1988 → Jul 28 1988

Other

Other	1st National Fluid Dynamics Conference, 1988
Country/Territory	United States
City	Cincinnati
Period	7/25/88 → 7/28/88

ASJC Scopus subject areas

Aerospace Engineering
Engineering (miscellaneous)

Cite this

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title = "Fast algorithms for vortex methods",

abstract = "In the random vortex method for viscous incompressible flow, the vorticity field is represented by a collection of vortex blobs which are alternately convected and diffused via a random walk. For a fluid modelled by n vortex blobs, the bulk of the computational burden at each time step is the evaluation of all pairwise interactions which, by direct summation, requires O(n2) work. In this paper, we discuss the incorporation of fast algorithms to reduce the cost of this calculation. By using the recently developed Fast Multipole Method (FMM), it is possible to compute all pairwise interactions in an amount of time proportional to n, making the overall scheme significantly more practical for large-scale problems.",

author = "L. Greengard and V. Rokhlin",

note = "Publisher Copyright: {\textcopyright} 1988 by the American Institute of Aeronautics and Astronautics, Inc. All right reserved.; 1st National Fluid Dynamics Conference, 1988 ; Conference date: 25-07-1988 Through 28-07-1988",

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T1 - Fast algorithms for vortex methods

AU - Greengard, L.

AU - Rokhlin, V.

PY - 1988

Y1 - 1988

N2 - In the random vortex method for viscous incompressible flow, the vorticity field is represented by a collection of vortex blobs which are alternately convected and diffused via a random walk. For a fluid modelled by n vortex blobs, the bulk of the computational burden at each time step is the evaluation of all pairwise interactions which, by direct summation, requires O(n2) work. In this paper, we discuss the incorporation of fast algorithms to reduce the cost of this calculation. By using the recently developed Fast Multipole Method (FMM), it is possible to compute all pairwise interactions in an amount of time proportional to n, making the overall scheme significantly more practical for large-scale problems.

AB - In the random vortex method for viscous incompressible flow, the vorticity field is represented by a collection of vortex blobs which are alternately convected and diffused via a random walk. For a fluid modelled by n vortex blobs, the bulk of the computational burden at each time step is the evaluation of all pairwise interactions which, by direct summation, requires O(n2) work. In this paper, we discuss the incorporation of fast algorithms to reduce the cost of this calculation. By using the recently developed Fast Multipole Method (FMM), it is possible to compute all pairwise interactions in an amount of time proportional to n, making the overall scheme significantly more practical for large-scale problems.

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T2 - 1st National Fluid Dynamics Conference, 1988

Y2 - 25 July 1988 through 28 July 1988

ER -

Fast algorithms for vortex methods

Abstract

Other

ASJC Scopus subject areas

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