Numerical techniques for solving hybrid Eulerian Lagrangian models for particulate flows
Résumé
This report describes to the analysis of some computational techniques devoted to the prediction of solutions of a set of partial differential equations containing non-smooth data. This data arises when coupling an Eulerian approach and a Lagrangian approach, in the framework of the modelling of gas-particle flows, where the particulate phase is described with both formalisms. The main idea of the whole algorithm is to take advantage of the inherent hyperbolic patterns of the whole set of equations, while using an instantaneous relaxation approach simultaneously. We start by describing the approach in a pure one-dimensional framework, and then we turn to the two-dimensional case. Both the analytical and numerical solutions are considered. The coupled system requires specific attention, due to realisability constraints pertaining to the Reynolds stress tensor.