### Abstract

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 (mÎ± (m,n)) and O (n), respectively, where m is the number of edges, n is the number of vertices, and Î± (â,â) 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 (mÎ± (m,n)).

Original language | English (US) |
---|---|

Article number | 031128 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 77 |

Issue number | 3 |

DOIs | |

State | Published - Mar 25 2008 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*77*(3), [031128]. https://doi.org/10.1103/PhysRevE.77.031128

**Invasion percolation through minimum-weight spanning trees.** / Glantz, Roland; Hilpert, Markus.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 77, no. 3, 031128. https://doi.org/10.1103/PhysRevE.77.031128

}

TY - JOUR

T1 - Invasion percolation through minimum-weight spanning trees

AU - Glantz, Roland

AU - Hilpert, Markus

PY - 2008/3/25

Y1 - 2008/3/25

N2 - 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 (mÎ± (m,n)) and O (n), respectively, where m is the number of edges, n is the number of vertices, and Î± (â,â) 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 (mÎ± (m,n)).

AB - 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 (mÎ± (m,n)) and O (n), respectively, where m is the number of edges, n is the number of vertices, and Î± (â,â) 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 (mÎ± (m,n)).

UR - http://www.scopus.com/inward/record.url?scp=41549132209&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=41549132209&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.77.031128

DO - 10.1103/PhysRevE.77.031128

M3 - Article

C2 - 18517350

AN - SCOPUS:41549132209

VL - 77

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 3

M1 - 031128

ER -