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**On zero-thickness interface elements for diffusion problems.**
*(English)*
Zbl 1075.76580

Summary: The present study focuses on the hydraulic behaviour of joints, and, specially, on its numerical implementation in terms of the FEM analysis using a discrete fracture flow approach. Fluid flow through discontinuities has traditionally been modelled using special elements of zero-thickness, which we can classify into single, double and triple-nodded. Single node elements are the simplest and consist of line or pipe elements which are superimposed onto the standard continuum mesh and that can only model the longitudinal conductivity through the discontinuity. On the other hand, some authors have included the influence of a transversal conductivity, and the subsequent localized potential drop, by using triple node interface elements. In those, the two nodes of the adjacent continuum elements represent the potentials in the pore system on each side of the interface, and a third node in the middle represents the average potential of the fluid in the channel represented by the discontinuity. Finally, double node interface elements have also been proposed, which have the advantage of making it possible to use the same FE mesh for both mechanical and flow analysis. In some cases the influence of a transversal conductivity is not considered and, therefore, although geometrically double-nodded, these elements belong to the single node type and when time comes to solve the system the two nodes must have the same potential, which can only be obtained by the trick of prescribing the equivalence of these two d.o.f. before solving the global system of equations. This limitation may, however, be avoided by assuming that the potential in the channel is the average of the two sides of the interface. Based in this simple assumption, an alternative flow interface model has been recently developed and implemented, which preserves both longitudinal and transversal conductivities. An application example is developed and solved with the three types of interfaces described. The results offer useful information regarding the range of applicability and limitations of the new double-nodded interface element proposed.

### MSC:

76M10 | Finite element methods applied to problems in fluid mechanics |

76S05 | Flows in porous media; filtration; seepage |

76R50 | Diffusion |

74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |