Resurrecting Core Spreading Vortex Methods: A New Scheme that is Both Deterministic and Convergent

Abstract

A basic core spreading vortex scheme is inconsistent but can be corrected with a splitting algorithm, yielding a deterministic and efficient grid-free method for viscous flows. The splitting algorithm controls the consistency error by maintaining small vortex core sizes. Routine analysis will show that the core spreading method coupled to this splitting process is convergent in $L^p$ spaces. Analysis of the linearized residual operator establishes the uniform convergence of this method when the exact flow field is known. A sequence of examples demonstrates the sensitivity of the method to numerical parameters as the computed solution converges to the exact solution. These experimental results agree with the linear convergence theory. Finally, direct comparisons between the traditional random walk vortex method and the new method indicate that the new method has several advantages while requiring the same computational effort.