Abstract: Modeling flow in fractures in porous media presents many challenges, especially when an exchange between the flow in the fracture and that in the surrounding rock matrix is taken into account. As the width of the fractures is very small in comparison with the other spatial dimensions of the domain, it is difficult to take into account flow in the fractures as well as flow in the rock matrix in a standard numerical model. Here we consider some models in which the fractures are treated as interfaces in a domain decomposition setting with nonstandard interface conditions. Issues of intersecting fractures, of non-matching grids and of non-Darcy flow in the fractures will be discussed.
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