An Isogeometric Analysis Approach to Fluid Flow in a Fractured Porous Medium

Abstract

In this paper we present an isogeometric approach for calculating fluid flow in a fractured porous medium. The fluid flow away from the crack is modelled using Darcy's relation. A similar relation is assumed for the fluid flow inside the crack. Here, the higher porosity is modelled using a different permeability. An isogeometric analysis approach with B-splines is used for both the parametrisation of the geometry and the discretisation of the weak form of the equilibrium equations. The crack is described in a discrete manner by using the continuity reduction property of the B-splines. To ease the integration into existing finite element technology, a finite element data structure based on B'ezier extraction is used. The B'ezier extraction operator decomposes the B-spline based elements to B'ezier elements which bear a close resemblance to Lagrange elements. The global smoothness of B-splines is localized to an element level similar to finite element analysis, making isogeometric analysis compatible with existing finite element codes while still exploiting the excellent properties of the spline basis functions. The results of the new model are demonstrated in an example in which the fluid flow is considered around a crack in a specimen under mode-I loading.