Potential Flow in Channels.
Abstract
A method is presented for calculating potential flows in infinite channels. Given a collection of N sources in the channel and a zero normal flow boundary condition, the method requires an amount of work proportional to N to evaluate the induced velocity field at each source position. Previous schemes have been based either on conformal mapping, which experiences numerical difficulties with the domain boundary, or direct evaluation of the Green's function. Both require O (N-sq) work. A fast algorithm for potential flow in channels has been developed. It is based on asymptotic expansions which we refer to as S-expansions, some analytic observations concerning classical multipole expansions and Taylor series, and the Fast Multipole Method. The asymptotic CPU time requirements for the algorithm grow linearly with the number of sources and, despite its complex structure, numerical experiments demonstrate that dramatic speedups can be obtained for even moderate size particle systems. In its current form, the algorithm requires that the channel boundaries be straight. A method applicable to channels with perturbed boundaries will be described in a subsequent paper.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1988
- Accession Number
- ADA198706
Entities
People
- L. Greengard
Organizations
- Yale University