Multi-Scale Modeling and Simulation of Transport Processes in an Elastically Deformable Perforated Medium

Knoch J, Gahn M, Neuss-Radu M, Neuß N (2023)

Publication Type: Journal article

Publication year: 2023

Journal

Transport in Porous Media Springer Verlag (Germany)

DOI: 10.1007/s11242-022-01896-z

Abstract

In this paper, we derive an effective model for transport processes in periodically perforated elastic media, taking into account, e.g., cyclic elastic deformations as they occur in lung tissue due to respiratory movement. The underlying microscopic problem couples the deformation of the domain with a diffusion process within a mixed Lagrangian/Eulerian formulation. After a transformation of the diffusion problem onto the fixed domain, we use the formal method of two-scale asymptotic expansion to derive the upscaled model, which is nonlinearly coupled through effective coefficients. The effective model is implemented and validated using an application-inspired model problem. Numerical solutions for both, cell problems and macroscopic equations, are investigated and interpreted. We use simulations to qualitatively determine the effect of the deformation on the transport process.

Authors with CRIS profile

Jonas Knoch Lehrstuhl für Angewandte Mathematik (Wissenschaftliches Rechnen) Maria Neuß Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik) Nicolas Neuß Lehrstuhl für Angewandte Mathematik (Wissenschaftliches Rechnen)

Involved external institutions

Ruprecht-Karls-Universität Heidelberg DE Germany (DE)

How to cite

APA:

Knoch, J., Gahn, M., Neuss-Radu, M., & Neuß, N. (2023). Multi-Scale Modeling and Simulation of Transport Processes in an Elastically Deformable Perforated Medium. Transport in Porous Media. https://dx.doi.org/10.1007/s11242-022-01896-z

MLA:

Knoch, Jonas, et al. "Multi-Scale Modeling and Simulation of Transport Processes in an Elastically Deformable Perforated Medium." Transport in Porous Media (2023).

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