PreprintInternational audienceIn 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 fth 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 signi cantly 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

International audienceWe derive TVD remeshing formulas for particle methods. The derivation is inspired from a finite-difference analysis but the method retains the essential features of particle methods. Numerical illustrations give evidence of the improved stability and computational cost resulting from these new algorithms

The aim of this work is to couple vortex methods with the penalization methods in order to take advantage from both of them. This immersed boundary approach maintains the efficiency of vortex methods for high Reynolds numbers focusing the computational task on the rotational zones and avoids their lack on the no-slip boundary conditions replacing the vortex sheet method by the penalization of obstacles. This method that is very appropriate for bluff-body flows is validated for the flow around a circular cylinder on a wide range of Reynolds numbers.