Finite difference stencils based on particle strength exchange schemes for improvement of vortex methods

The method of particle strength exchange, solving the viscous part of the Navier–Stokes equations by a splitting time algorithm in the context Vortex Methods This paper presents a few results on the numerical aspects of this Lagrangian diffusion scheme, that is to say computation of the Laplacian of a measure function. The present work follows the classical analysis by Degond and MasGallic whose formulas were obtained by means of integration of continuous functions. One shows that one gets different operators when integration is discrete, and leads to a substantial gain of accuracy. This scheme is then applied to several three- dimensional flows to exhibit convergence rate, and impacts on conservation laws at moderate Reynolds numbers. A sensitivity analysis is finally provided in order to carry out the good behavior of these schemes in both Eulerian and Lagrangian contexts.