Integral formulation of null-collision Monte Carlo algorithms

M. Galtier (1) , Stéphane Blanco (2) , Cyril Caliot (3) , C. Coustet (4) , J. Dauchet (5) , Mouna El-Hafi (1) , Vincent Eymet (1) , Richard A Fournier (2) , J. Gautrais (6) , A. Khuong (6) , B. Piaud (4) , Guillaume Terrée (1)

1 RAPSODEE - Centre de recherche d'Albi en génie des procédés des solides divisés, de l'énergie et de l'environnement
2 LAPLACE-GREPHE - Groupe de Recherche Energétique, Plasmas et Hors Equilibre
3 PROMES - Procédés, Matériaux et Energie Solaire
4 HPC-SA
5 ENSCCF - Ecole Nationale Supérieure de Chimie de Clermont-Ferrand
6 CRCA - Centre de Recherches sur la Cognition Animale - UMR5169

At the kinetic level, the meaning of null-collisions is straightforward: they correspond to pure-forward scattering events. We here discuss their technical significance in integral terms. We first consider a most standard null-collision Monte Carlo algorithm and show how it can be rigorously justified starting from a Fredholm equivalent to the radiative transfer equation. Doing so, we also prove that null-collision algorithms can be slightly modified so that they deal with unexpected occurrences of negative values of the null-collision coefficient (when the upper bound of the heterogeneous extinction coefficient is nonstrict). We then describe technically, in full details, the resulting algorithm, when applied to the evaluation of the local net-power density within a bounded, heterogeneous, multiple scattering and emitting/absorbing medium. The corresponding integral formulation is then explored theoretically in order to distinguish the statistical significance of introducing null-collisions from that of the integral-structure underlying modification.

Mots clés: Integral formulation; Monte Carlo; Null-collision; Heterogeneous media

Domaines: Sciences de l'ingénieur [physics]

M. Galtier, Stéphane Blanco, Cyril Caliot, C. Coustet, J. Dauchet, et al.. Integral formulation of null-collision Monte Carlo algorithms. Journal of Quantitative Spectroscopy and Radiative Transfer, 2013, 125, pp.57-68. ⟨10.1016/j.jqsrt.2013.04.001⟩. ⟨hal-01688110⟩