Efficient numerical solution of micro–macro models for multicomponent transport and reaction problems in porous media

ABSTRACT

Transport and reaction of dissolved species in hierarchically structured complex media, e.g. porous media, can be described by micro–macro models (models with distributed micro-structure, $F{E}^2$ models). These models offer advantages compared to pure micro- or pure macroscale models but exhibit, compared to pure macroscale models, a strongly increased numerical complexity. We show how parallel computing together with Schur complement techniques can make those models numerically feasible.

KEYWORDS:

• Porous media
• multicomponent reaction and diffusion
• distributed microstructure
• parallel computing
• Schur complement
• $F{E}^2$ models

2020 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 76Sxx
• 35K57
• 36B27

Acknowledgments

The first author gratefully acknowledges financial support from Emerging Fields Initiative for Synthetic Biology of the Friedrich-Alexander-Universität Erlangen-Nürnberg.

Disclosure statement

No potential conflict of interest was reported by the author(s).