## A reduced model for flow and transport in fractured porous media with non-matching grids.(English)Zbl 1273.76398

Cangiani, Andrea (ed.) et al., Numerical mathematics and advanced applications 2011. Proceedings of ENUMATH 2011, the 9th European conference on numerical mathematics and advanced applications, Leicester, UK, September 5–9, 2011. Berlin: Springer (ISBN 978-3-642-33133-6/hbk; 978-3-642-33134-3/ebook). 499-507 (2013).
Summary: In this work we focus on a model reduction approach for the treatment of fractures in a porous medium, represented as interfaces embedded in a $$n$$-dimensional domain, in the form of a $$(n-1)$$-dimensional manifold, to describe fluid flow and transport in both domains. We employ a method that allows for non-matching grids, thus very advantageous if the position of the fractures is uncertain and multiple simulations are required. To this purpose we adopt an extended finite element approach, XFEM, to represent discontinuities of the variables at the interfaces, which can arbitrarily cut the elements of the grid. The method is applied to the solution of the Darcy and advection-diffusion problems in porous media.
For the entire collection see [Zbl 1257.65002].

### MSC:

 76S05 Flows in porous media; filtration; seepage
Full Text: