2025/05/05 - New paper "Homogenized lattice Boltzmann methods for fluid flow through porous media - Part I: Kinetic model derivation" published in ESAIM: Mathematical Modelling and Numerical Analysis (M2AN)

Sun, 14 Dec 2025 13:52:31 +0100
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We are excited to announce the publication of our article "Homogenized lattice Boltzmann methods for fluid flow through porous media - Part I: Kinetic model derivation" in the esteemed open-access journal ESAIM: Mathematical Modelling and Numerical Analysis (M2AN). In our paper, we establish homogenized lattice Boltzmann methods (HLBM) for simulating fluid flow through porous media. Our contributions in this first part are twofold. First, we assemble the targeted partial differential equation system by formally unifying the governing equations for nonstationary fluid flow in porous media. Second, we propose a kinetic model, the homogenized Bhatnagar-Gross-Krook Boltzmann equation, which approximates the homogenized nonstationary Navier-Stokes equations (NSE). We formally prove that the zeroth and first order moments of the kinetic model provide solutions to the mass and momentum balance variables of the macroscopic model up to specific orders in the scaling parameter. The article is published open-access in the ESAIM M2AN journal here Based on the present paper, in the sequel (Part II appearing soon), the homogenized NSE will be consistently approximated by deriving a limit-consistent HLBM discretization of the homogenized Bhatnagar-Gross-Krook Boltzmann equation, and numerical limits will be explored based on efficient implementations in OpenLB