Accurate, non-oscillatory, remeshing schemes for particle methods
In this article we propose and validate new remeshing schemes for the simulation of transport equations by particle methods. Particle remeshing is a common way to control the regularity of the particle distribution which is necessary to guarantee the accuracy of particle methods in presence of strong strain in a flow. Using a grid-based analysis, we derive remeshing schemes that can be used in a consistent way at every time-step in a particle method. The schemes are obtained by local corrections of classical third order and fifth order interpolation kernels. The time-step to be used in the resulting push-and-remesh particle method is determined on the basis of rigorous bounds and can significantly exceed values obtained by CFL conditions in usual grid-based Eulerian methods. In addition, we extend the analysis of [5] to obtain TVD remeshing schemes that avoid oscillations of remeshing formulas near sharp variations of the solution. These methods are illustrated in several flow conditions in 1D, 2D and 3D.
remeshing scheme particle methods transport equation tvd method level set method navierstokes equations