English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this series of studies, we establish homogenized lattice Boltzmann methods(HLBM) for simulating fluid flow through porous media. Our contributions inpart I are twofold. First, we assemble the targeted partial differentialequation system by formally unifying the governing equations for nonstationaryfluid flow in porous media. A matrix of regularly arranged, equally sizedobstacles is placed into the domain to model fluid flow through porousstructures governed by the incompressible nonstationary Navier--Stokesequations (NSE). Depending on the ratio of geometric parameters in the matrixarrangement, several homogenized equations are obtained. We review existingmethods for homogenizing the nonstationary NSE for specific porosities anddiscuss the applicability of the resulting model equations. Consequently, thehomogenized NSE are expressed as targeted partial differential equations thatjointly incorporate the derived aspects. Second, we propose a kinetic model,the homogenized Bhatnagar--Gross--Krook Boltzmann equation, which approximatesthe homogenized nonstationary NSE. We formally prove that the zeroth and firstorder moments of the kinetic model provide solutions to the mass and momentumbalance variables of the macrocopic model up to specific orders in the scalingparameter. Based on the present contributions, in the sequel (part II), thehomogenized NSE are consistently approximated by deriving a limit consistentHLBM discretization of the homogenized Bhatnagar--Gross--Krook Boltzmannequation.

Homogenized lattice Boltzmann methods for fluid flow through porous media -- part I: kinetic model derivation