Une méthode particulaire aléatoire reposant sur une équation cinétique pour la simulation numérique des sprays denses de gouttelettes liquides

Monte-Carlo simulation of colliding particles or coalescing droplets transported by a turbulent flow in the framework of a joint fluid–particle pdf approach

“…It is worth noticing that, by construction, the above Monte-Carlo algorithm is a generalization of chaos assumption based algorithms used by O'Rourke (1981) and Villedieu and Hylkema (1997). Indeed if the mesh M c f only contains one cell corresponding to the whole velocity space, one has: P fj ¼ 1 and one recovers the usual expression for the collision probability.…”

“…(23). Initially, people implicitly used the classical molecular chaos assumption to close the collision kernel (O'Rourke, 1981;Villedieu and Hylkema, 1997):…”

Hybrid Eulerian-Lagrangian method for soot modelling applied to ethylene-air premixed flames

“…Collisions are described through a four-step algorithm, presented as part of the Supplementary materials, designed to reproduce the real physics of collisions from the tracking of numerical particles, the number of which being necessarily limited compared to the real number of physical particles. The underlying theory of the algorithm is out of the scope of this study and the interested reader is referred to the original work of Villedieu and Hylkema [35,36,37] for details.…”

A spatially homogeneous Boltzmann equation for elastic, inelastic and coalescing collisions

“…The Boltzmann formalism we adopt here (description of droplets by the density function) has been introduced by Williams [60] and then developed in [45,57,58,5,59]. There have been a lot of fundamental studies to improve the understanding of the complex physical effects that play a role in such a two-phase flow.…”