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

Transition regions between porous medium and free flow systems appear in a variety of environmental settings and industrial applications. Classical approaches to couple these two flow systems lead to reliable results in limited cases such as single-fluid-phase flows, elementary geometrical interface configurations and simple flow regimes. However, many applications involve multiphase physics andcomplex interfaces, which makes coupling such flow systems a challenging task. The lack of interface conditions for general flow regimes is exacerbated by the multiscale nature of the processes in the coupled system thus also contributing to the complexity of the problem from the numerical point of view. These multiple length and time scales should be taken into account for accurate modeling and efficient numerical implementation of transitions between the flow domains. Therefore, both advanced model formulations and efficient numerical techniques are required to provide new tools to simulate the coupled phenomena with the necessary precision and reliability.The project will focus on the continuation of the work done in the first project phase and on the extension of the model concepts and numerical methods to different coupled systems. The specific goals of the project are: (i) further development of the porous medium models with interfacial area dynamics; (ii) modeling transitions between porous medium and free flow systems for flowsnon-parallel to the fluid-porous interface; (iii) development and analysis of robust numerical algorithms to tackle effectively multiscale phenomena in coupled flow systems.

• DFG Programme: Research Grants
• Co-Investigators: Professor Dr.-Ing. Rainer Helmig; Professor Dr. Christian Rohde