High Order Semi-Lagrangian Particle Methods

Abstract

Semi-lagrangian (or remeshed) particle methods are conservative particle methods where the particles are remeshed at each time-step. The numerical analysis of these methods show that their accuracy is governed by the regularity and moment properties of the remeshing kernel and that their stability is guaranteed by a lagrangian condition which does not rely on the grid size. Turbulent transport and more generally advection dominated flows are applications where these features make them appealing tools. The adaptivity of the method and its ability to capture fine scales at minimal cost can be further reinforced by remeshing particles on adapted grids, in particular through wavelet-based multi-resolution analysis.