A Lagrangian method based on the Voronoi diagram for the incompressible Navier Stokes equations on the periodic domain.

Considers the fractional step method, and studies problems involving immersed boundaries in which the boundaries are modelled by a chain of Lagrangian particles connected by springs. Adapts the algorithm for the construction of Voronoi meshes for the case of a periodic domain, noting possible use of the Delauney triangulation. Proves that the discrete divergence and gradient operators are weakly consistent with the corresponding continuous operators. Describes a two level iteration for the solution of discrete Helmholtz equations and presents a vector field on to its divergence free part. Finally, obtains a fractional step method for the Navier-Stokes equations. (C.J.U.)