Contribution of kinetic methods for the simulation of flows in porous media
type: Dataset
description: The lattice Boltzmann method (LBM) have been applied very successfully to hydrodynamic flows in porous media. However, the limitation of these methods to isothermal and hydrodynamic flows, make them inadequate to simulate gas flows in micro-porous media. Indeed, in these conditions, the mean free path of the molecules could be of the same magnitude order as the pore size in which gas flows. Such flows will not be in hydrodynamic regime, but in regimes qualified of, slip or transitional ; for which the LBM are no longer valid. On the other hand, the isothermal character of LBM make them unusable, for example, in the case where the gas undergoes expansion through the media. It is then necessary, to take the kinetic point of view to describe such flows and phenomena. The proposed approach is based on the decomposition of the distribution function on the Hermite polynomials basis and the use of Gauss-Hermite quadrature associated with this projection. The systematic nature of this development naturally leads to consider different order of approximation of the Boltzmann-BGK equation in various quadratures. It then follows from these various approximations, a family of discretizations of the Boltzmann-BGK equation, whose classical LBM are a member. Determining the most suitable approximation is achieved by systematic analysis of the results obtained with different approximation orders. These methods are successfully tested in model cases.
identifier: NNT: 2012ORLE2001
issued: 2026-05-16T14:08:24.762375
language: fr
modified: 2026-05-16T14:08:24.762381
contact point: Organization
  fn: CCSD
keyword: infoeu-reposemanticsdoctoralthesis
keyword: lattice-boltzmann-method
keyword: methodes-de-boltzmann-sur-reseaux
keyword: physcondcm-genphysics-physicscondensed-matter-cond-matother-cond-matother
keyword: regime-transitionnel
keyword: theses
keyword: transitional-regime
landing page: https://theses.hal.science/tel-00675306

Contribution of kinetic methods for the simulation of flows in porous media
type: Distribution
format: HTML
issued: 2026-05-16T14:08:24.787696
modified: 2026-05-16T14:08:24.741498
access URL: https://theses.hal.science/tel-00675306

test_moissonnage_selune
type: Agent