Upscaling the flow and transport in an evolving porous medium with general interaction potentials

Ray N, Elbinger T, Knabner P (2015)


Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2015

Journal

Publisher: Society for Industrial and Applied Mathematics

Book Volume: 75

Pages Range: 2170-2192

Journal Issue: 5

URI: https://www1.am.uni-erlangen.de/research/publications/Jahr_2015/2015_RayElbingerKn_UpscalingFlowTransInAnEvolvingPMWithGeneralInterPotentials

DOI: 10.1137/140990292

Abstract

The objective of this research is to investigate the upscaling of flow and transport models including both an evolving solid-liquid interface and a quite general potentially even oscillating interaction potential. Starting from a comprehensive pore-scale model, formal, two-scale, asymptotic expansion in a level set framework is applied. In doing so, the interplay between flow, transport, interaction potential, and evolving geometry becomes evident. As a result of an averaging procedure, a fully coupled micro-macro model is established with new main variables. Moreover, time-and spacedependent coefficient functions are explicitly characterized by means of supplementary, fully coupled cell problems. The theoretical results obtained are complemented by the numerical computations of a heterogeneous multiscale scenario with a focus on the development of anisotropic transport. Because of the general framework considered in this research, numerous application are expected, such as in biology or colloidal dynamics.

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How to cite

APA:

Ray, N., Elbinger, T., & Knabner, P. (2015). Upscaling the flow and transport in an evolving porous medium with general interaction potentials. SIAM Journal on Applied Mathematics, 75(5), 2170-2192. https://dx.doi.org/10.1137/140990292

MLA:

Ray, Nadja, Tobias Elbinger, and Peter Knabner. "Upscaling the flow and transport in an evolving porous medium with general interaction potentials." SIAM Journal on Applied Mathematics 75.5 (2015): 2170-2192.

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