Different classes of physical systems with common interfaces arise in a variety of environmental and industrial problems. Striking examples originate from terrestrial-atmospheric contact zones, surface water-groundwater interaction, filters and fuel cells, where a free fluid system is in contact with a porous medium. Flow and transport processes in these systems evolve on multiple length and time scales, contributing to the complexity of these systems both from the modeling and the numerical side. An additional contributing factor to this complexity is the existence of multiple classes of entities, which include phases, interfaces between phases, and common curves that form at the boundary between three phases. Classical coupling approaches and traditional porous medium model formulations lead to reliable results in limited cases, however, applications require more realistic settings. The focus of the thesis is on derivation of mathematical models for multiphase multi-component porous medium systems that take into account lower dimensional entities, formulation of coupling conditions at the sharp interface and the transition region between porous medium and free flow systems, computation of effective parameters for the macroscale models, development and analysis of efficient numerical algorithms for coupled problems, and numerical simulation of applications.
