TVD remeshing formulas for particle methods

Abstract

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

Accurate, non-oscillatory, remeshing schemes for particle methods

“…In this section we extend the approach of [5] to derive limiting techniques for remeshing formulas in the case when the CFL number is larger than 1.…”

“…Throughout this work, we assume that particles are initialized and remeshed on a uniform grid of grid-size h. In [5,26] an analysis of remeshed particle methods in terms of grid-based schemes was given, and is summarized below.…”

“…In [13] a similar analysis is used to take into account remeshing in the solution of diffusion for viscous terms. The work of [11] was further pursued in [5] with the objective of understanding and overcoming oscillations generated by remeshing formulas near discontinuities. TVD remeshing formulas were derived for both linear and nonlinear advection equations.…”

“…The TVD remeshing formula removes the oscillations that are visible when a classical remeshing scheme is used. One goal of the present work is to extend the work in [5] in the case of linear equations by relaxing the constraint on the time-step.…”

“…In [5] this analysis is further used to derive limiters in order to remove oscillations that are produced in remeshed particle methods near discontinuities. In this reference, limiters inspired by finitedifference formulas, are derived under CFL conditions for constant coefficient linear equations and for the Burgers equation, and turned into non linear remeshing schemes.…”