Robust space-time multiscale upscaling via multicontinuum homogenization for evolving perforated media

TL;DR

This paper introduces a multiscale modeling framework based on multicontinuum homogenization for accurately and efficiently simulating evolving perforated media with dynamic geometries in engineering applications.

Contribution

It develops a robust, generalizable homogenization method that incorporates temporal evolution and multiple continua for large-scale, time-dependent porous media simulations.

Findings

The method accurately captures macroscopic behavior of evolving perforated domains.

Numerical experiments demonstrate improved efficiency and accuracy.

Applicable to complex engineering problems with dynamic geometries.

Abstract

Time-evolving perforated domains arise in many engineering and geoscientific applications, including reactive transport, particle deposition, and structural degradation in porous media. Accurately capturing the macroscopic behavior of such systems poses significant computational challenges due to the dynamic fine-scale geometries. In this paper, we develop a robust and generalizable multiscale modeling framework based on multicontinuum homogenization to derive effective macroscopic equations in shrinking domains. The method distinguishes multiple continua according to the physical characteristics (e.g., channel widths), and couples them via space-time local cell problems formulated on representative volume elements. These local problems incorporate temporal derivatives and domain evolution, ensuring consistency with underlying fine-scale dynamics. The resulting upscaled system yields computable macroscopic coefficients and is suitable for large-scale simulations. Several numerical experiments are presented to validate the accuracy, efficiency, and potential applicability of the method to complex time-dependent engineering problems.