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DynScale: Reactive flow and transport models in complex media with evolving interfaces at the micro scale (R-7119)
This project deals with mathematical models defined in complex, hierarchically organized media. Such models appear in a broad range of real-life applications like geothermal energy, CO2 sequestration, biosystems, or coated nano-materials. The particularity here is in the occurrence of moving interfaces at the micro scale. These are either evolving micro structures, or interfaces separating two different fluids. The movement of such interfaces is not known a-priori and depends on the model unknowns. The goal is to provide a methodology to construct reliable and computable mathematical models for multi scale processes in complex domains, accounting for the micro scale interfaces in evolution. Such issues will be addressed within a generic mathematical and numerical framework, but inspired by the applications mentioned above. Three representative processes are considered, leading to different models: reactive flow where adsorption/desorption affects the micro structure, the flow of two immiscible fluids in complex media, and the elastic deformation of solid materials with complex structure. Besides interfaces in evolution, the focus will be on the interplay between these processes. Two modelling strategies are envisaged at the micro scale: free boundaries and phase fields. For the resulting models, upscaled models are derived to describe the averaged behavior of the solutions, and numerical schemes and strategies based on multi scale techniques are developed.
Date:1 Oct 2016 → 30 Sep 2021
Keywords:numerical methods and algorithms, upscaling and multi-scale techniques
Disciplines:Applied mathematics in specific fields, Statistics and numerical methods