Invasion percolation through minimum-weight spanning trees.
Invasion percolation is often used to simulate capillary-dominated drainage and imbibition in pore networks. More than a decade ago it was observed that the part of a pore network that is involved in an invasion bond percolation is a minimum-weight spanning tree of the network, where the weights indicate resistances associated with the bonds. Thus, one can determine a minimum-weight spanning tree first and then run the invasion bond percolation on the minimum-weight spanning tree. The time complexities of the two steps are O(malpha(m,n)) and O(n) , respectively, where m is the number of edges, n is the number of vertices, and alpha(,) denotes the inverse Ackermann function. In this paper we (1) formulate the property of minimum-weight spanning trees that justifies the two-step approach to invasion bond percolation, (2) extend the two-step approach to invasion site percolation, and (3) further extend it to simulations of drainage (imbibition) that include trapping of the wetting (nonwetting) phase. In case of imbibition we also take snap-off into account. As a consequence, all these simulations can now be done in O(malpha(m,n)) .
Glantz
Roland
R
Department of Geography and Environmental Engineering, The Johns Hopkins University, 313 Ames Hall, 3400 North Charles Street, Baltimore, Maryland 21218-2686, USA. roland_glantz@jhu.edu
Hilpert
Markus
M