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New strategies for the simulation of the flow in three dimensional poro-fractured media. (English) Zbl 1425.76130

Radu, Florin Adrian (ed.) et al., Numerical mathematics and advanced applications. ENUMATH 2017. Selected papers based on the presentations at the European conference, Bergen, Norway, September 25–29, 2017. Cham: Springer. Lect. Notes Comput. Sci. Eng. 126, 715-723 (2018).
Summary: Two novel approaches are presented for dealing with three dimensional flow simulations in porous media with fractures: one method is based on the minimization of a cost functional to enforce matching conditions at the interfaces, thus allowing for non conforming grids at the interfaces; the other, instead, takes advantage of the new Virtual Elements to easily build conforming polygonal grids at the fracture-porous matrix interfaces. Both methods are designed to minimize the effort in mesh generation process for problems characterized by complex geometries. The methods are described in their simplest fashion in order to keep the notation as compact and simple as possible.
For the entire collection see [Zbl 1411.65009].

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76S05 Flows in porous media; filtration; seepage
74R99 Fracture and damage
49K20 Optimality conditions for problems involving partial differential equations
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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