Second-Order Computational Homogenization of Nonlinear Fluid Flow through Porous Media
Year: 2025
Type: article
Abstract: We present a second-order computational multiscale model for heterogeneous porous media, which allows for the scale bridging of transient fluid-flow processes through porous materials with non-separated scales. The formulation connects a homogenized macroscopic scale described by a local theory of grade two with heterogeneous microstructures described by a local theory of grade one. At the macroscale this leads to đ¶1-continuity requirements on the macroscopic solution field; at the microscale we need to take account of constraints on fluctuation fields that require đ»(div) â© đ»(grad)-conformity of microscopic solutions. Both these challenges are addressed through the development of mixed HuâWashizu formulations that result in a variationally consistent homogenization framework with minimization structure across scales. We validate the second-order multiscale model by means of fully resolved, direct numerical simulations and provide comparisons with results of first-order FE2 simulations. By considering linear Darcy and nonlinear DarcyâForchheimer flow through two- and three-dimensional porous microstructures, we provide further insights into the framework and associated length-scale effects.
Authors: Polukhov, Elten, Keip, Marc-Andre
Institution: University of Stuttgart
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W6949595487
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