Convergent 3-D vortex method with grid-free stretching.

This document proves 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 another work 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 an average value of zero. Implications for the design of the method are discussed. (A)

Duke Scholars

Author J. Thomas Beale Mathematics