ABSTRACT
The accuracy of the numerical analysis was determined by the L2 error norm
er = ||u − u h||2
||u||2 (13)
Where
||u − uh||2 = √√√√ N∑
I=1 (u(XI − uh(XI )))2 (14)
The values u and uh are the exact and numerical solution, respectively, at the node I . For the analysis with cross-sectional areas obtained from the Delaunay scaling, the error is er = 5.795 × 10−10. If the crosssections of the conduit elements are constant and equal to the average of the cross-sectional areas obtained from the Delaunay scaling, the error is er = 0.052. The Delaunay scaling results in an exact description of the flow field. On the other hand, a constant crosssection results in a considerable error. Corresponding results were presented for a lattice of conduit elements based on the Delaunay trianguation by Bolander and Berton (2004). To the authors knowledge, here it is for the first time shown that a conduit element network based on the Voronoi tessellation is also able to represent flow fields accurately. This allows one to model moisture transport in the bulk material and in the fracture by means of the same pipe network, which is different from the approach used in Nakamura et al., (2006).
