From particle methods to forward-backward Lagrangian schemes

Martin Campos Pinto (1, 2) , Frédérique Charles (1, 3, 4)

1 LJLL - Laboratoire Jacques-Louis Lions
2 CNRS - Centre National de la Recherche Scientifique
3 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
4 SU - Sorbonne Université

In this article we introduce a novel method for improving the accuracy of density reconstructions based on markers pushed forward by some available particle code. The method relies on the backward Lagrangian representation of the transported density, and it evaluates the backward flow using the current position of point particles seen as flow markers. Compared to existing smooth particle methods with either fixed or transformed shapes, the proposed reconstruction achieves higher locality and accuracy. This is confirmed by our error analysis which shows a theoretical gain of one convergence order compared to the LTP/QTP methods introduced in [Campos Pinto, M., 2015. Towards smooth particle methods without smoothing. Journal of Scientific Computing, 65, pp.54–82], and by numerical experiments that demonstrate significative CPU gains and an improved robustness relative to the remapping period.

Domaines: Mathématiques [math]; Analyse numérique [math.NA]

Martin Campos Pinto, Frédérique Charles. From particle methods to forward-backward Lagrangian schemes. SMAI Journal of Computational Mathematics, 2018, 4, pp.121-150. ⟨10.5802/smai-jcm.31⟩. ⟨hal-01385676v2⟩