[1] Domains composed of a porous part and an adjacent free-flow region are of special interest in many fields of application. So far, the coupling of free flow with porous-media flow has been considered only for single-phase systems. Here we extend this classical concept to two-component nonisothermal flow with two phases inside the porous medium and one phase in the free-flow region. The mathematical modeling of flow and transport phenomena in porous media is often based on Darcy's law, whereas in free-flow regions the (Navier-) -Stokes equations are used. In this paper, we give a detailed description of the employed subdomain models. The main contribution is the developed coupling concept, which is able to deal with compositional (miscible) flow and a two-phase system in the porous medium. It is based on the continuity of fluxes and the assumption of thermodynamic equilibrium, and uses the Beavers-Joseph-Saffman condition. The phenomenological explanations leading to a simple, solvable model, which accounts for the physics at the interface, are laid out in detail. Our model can account for evaporation and condensation processes at the interface and is used to model evaporation from soil influenced by a wind field in a first numerical example.
Flow in fractured porous media occurs in the earth's subsurface, in biological tissues, and in man-made materials. Fractures have a dominating influence on flow processes, and the last decade has seen an extensive development of models and numerical methods that explicitly account for their presence. To support these developments, four benchmark cases for single-phase flow in three-dimensional fractured porous media are presented. The cases are specifically designed to test the methods' capabilities in handling various complexities common to the geometrical structures of fracture networks. Based on an open call for participation, results obtained with 17 numerical methods were collected. This paper presents the underlying mathematical model, an overview of the features of the participating numerical methods, and their performance in solving the benchmark cases.
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