Mathematical modeling and numerics for transition regions between porous medium and free flow systems

• Applicant: Privatdozentin Dr. Iryna Rybak
• Subject Area: Mathematics
• Term: from 2012 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 217175533

• Final Report Year: 2019

Final Report Abstract

Transition regions between porous medium and free flow systems appear in many environmental settings and technical applications such as surface water and groundwater flows, industrial filtration and water-gas management in fuel cells. The interaction between these two flow systems is dominated by the interface driven processes and, due to their complexity, modelling such coupled problems is a challenging task. Classical approaches to couple porous medium and free flow systems lead to reliable results in limited cases. There is a lack of interface conditions for multiphase systems, complex geometrical interface configurations and general flow regimes. Moreover, physical processes in such coupled systems evolve on different spacial and temporal scales thus also contributing to the complexity of the problem from the numerical point of view. These multiple scales should be taken into account for accurate mathematical modelling and robust and efficient numerical simulation of coupled systems. The work in this project was based on the developments achieved in the first project phase and focused on the extension of the model concepts and numerical methods to different coupled systems. New modelling framework based on the thermodynamically constrained averaging theory was proposed for three-phase flow models involving conservation and balance principles for phases, interfaces and a common curve. The developed framework was applied to evaluate the existing models for sediment transport, and an example is provided showing that existing models violate entropy permissibility conditions having negative entropy production rate. Dimensionally reduced models were proposed and analysed to model fluid flow in fractured porous media as couped porous media and free flow systems. Multiple-time-step schemes developed in the first project phase were successfully applied to efficiently simulate multiscale processes in coupled flow systems.

Publications

• Mathematical modeling of coupled free flow and porous medium systems. Habilitation thesis, University of Stuttgart, 2016
  I. Rybak
  
• Modeling sediment transport in threephase surface water systems. Journal of Hydraulic Research, 2019
  C. T. Miller, W. G. Gray, C. E. Kees, I. V. Rybak, and B. J. Shepherd