A Splitting-free Vorticity Redistribution Method

TL;DR

This paper introduces a splitting-free vorticity redistribution method that improves computational efficiency and stability, demonstrating higher convergence order and faster performance compared to existing methods.

Contribution

It proposes a novel splitting-free approach with a new neighborhood strategy, enhancing stability, accuracy, and computational speed in vorticity redistribution.

Findings

Second order convergence observed in experiments

Method is approximately three times faster than fast multipole code

Prevents excessive particle growth while maintaining accuracy

Abstract

We present a splitting-free variant of the vorticity redistribution method. Spatial consistency and stability when combined with a time-stepping scheme are proven. We propose a new strategy preventing excessive growth in the number of particles while retaining the order of consistency. The novel concept of small neighbourhoods significantly reduces the method's computational cost. In numerical experiments the method showed second order convergence, one order higher than predicted by the analysis. Compared to the fast multipole code used in the velocity computation, the method is about three times faster.