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

Kurzfassung/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 space-dependent 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 …