This paper details an efficient algorithm for particles undergoing random walks in the presence of complex, two-dimensional, solid boundaries. The scheme is developed for the simulation of vortex diffusion using the random vortex method. Both vortex blobs and sheets are handled. The relevant modifications for using the algorithm with the vorticity redistribution technique are also discussed. The algorithm is designed to be used in the framework of an existing fast multipole implementation. A measure for the geometric complexity of a body is introduced and the algorithm's efficiency is studied as various parameters are changed for bodies of varying complexity.

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Computers and Mathematics with Applications
Department of Systems and Computer Engineering

Ramachandran, P. (Prabhu), Ramakrishna, M. (M.), & Rajan, S. (2007). Efficient random walks in the presence of complex two-dimensional geometries. Computers and Mathematics with Applications, 53(2), 329–344. doi:10.1016/j.camwa.2006.02.050