An investigation of the diffusion errors in diffusion vortex methods

Abstract

To model the viscous effect, the core area of particles in Leonard's core spreading vortex method must grow linearly in time, which however results in growing convective errors and consequently causes the failure of a correct convergence of the method to the Navier-Stokes equations. The so-called diffusion vortex method was proposed and claimed to have smaller core-area growth rates because part of the viscous effect is modeled into the movement of particles. The growth rates however are non-uniform and an additional diffusion error arises due to the nonzero divergence of the diffusion velocity. The goal of this work is to analyze the associated errors of several existing versions of the diffusion vortex method and compare them with that of Leonard's. Simulations of two axisymmetric flows are performed to measure the involved diffusion errors and consequently distinguish these diffusion vortex methods. The results show that the circulation conservation is important, besides a small core-area growth rate, in obtaining a good accuracy. Under the consideration of both efficiency and accuracy, the diffusion vortex method in which each vortex particle conserves its own circulation on its core area alone is recommended.