A convergent 3-D vortex method with grid-free stretching

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Abstract
We prove the convergence of a vortex method for three-dimensional, incompressible, inviscid flow without boundaries. This version differs from an earlier one whose convergence was shown in [4] in that the calculation does not depend explicitly on the arrangement of the vorticity elements in a Lagrangian frame. Thus, it could be used naturally in a more general context in which boundaries and viscosity are present. It is also shown that previous estimates for the velocity approximation can be improved by taking into account the fact that the integral kernel has average value zero. Implications for the design of the method are discussed.

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