Upscaling of pore-scale processes involving microstructural evolution (R-9879)

Combined flow and reactive transport processes in porous media are encountered in many important fields including environmental and civil engineering, technological applications, or biological systems. These processes occur and interact at different scales, involving complex media with hierarchically-organized structures. The goal of this project is to construct reliable and computable mathematical models for multi-scale problems in complex domains, which account for the interfaces evolving at the pore scale. Such issues will be addressed within a generic mathematical and computational framework, which covers in particular multi-phase flow and bio-chemical processes. The outcome will be in the rational derivation of effective (REV-scale) mathematical models and appropriate numerical algorithms. The development of the new models and methods will be accompanied by validation through rigorous well-posedness and error analysis. In detail, pore-scale models for viscous two-phase flow with reactive multi-component transport will be developed based on diffuse interface modeling with phase fields. For these phase field models numerical discretizations will be implemented. At last, these models will be upscaled to the REV-scale. Pore-scale model components remain involved in the determination of the upscaled parameters, having a local influence.

Keywords:applied mathematics

Disciplines:Numerical analysis, Analytic aspects and differential equations of physics, Computational physics, Nonlinear sciences

Project type:Collaboration project