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A simulation of fluid flow in the square and simple cubic lattices with invasion percolation
KTH, School of Engineering Sciences (SCI), Theoretical Physics.
KTH, School of Engineering Sciences (SCI), Theoretical Physics.
2015 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

Descriptions of the propagation of a fluid in a porous structure with percolation theory led to the introduction of invasion percolation. Invasion percolation is significantly different from ordinary percolation which is why its fractal characteristics can differ from ordinary percolation. Rules can be invoked on a percolation model and it is of interest to investigate their influence on the behaviour of the percolation. In this paper simulations of invasion percolation have been carried out in square and cubic lattices and fractal dimensions have been calculated numerically from the acquired simulation data. A rule called trapping have been invoked on invasion percolation model and was found to be affecting the result significantly in two dimensions. Without the trapping rule, similarities to ordinary percolation was found. In three dimensional lattices the effect of this rule diminished to almost insignificant levels and similarities to ordinary percolation was found regardless the trapping rule.

Abstract [sv]

Beskrivningar av vätskeflödet genom en porös struktur med hjälp av perkolationsteori ledde till introduktionen av invasionsperkolation. Invasionsperkolation skiljer sig märkbartfrån vanlig perkolation vilket är varför de resulterande fraktala egenskaperna i under vissa villkor kan skiljas åt i dessa processer. Ytterligare regler kan appliceras på en perkolationsmodel vilkas effekt på perkolationenklusters beteende är intressanta att undersöka. Idenna uppsats utförs simuleringar av invasionsperkolation i kvadratiska och kubiska gitteroch de fraktal dimension har beräknats numeriskt från den erhållna simuleringsdatan. En regel kallad trapping har applicerats på invasionsperkolationsmodellen och dess effekt på resultaten var påtagliga i två dimensioner. Utan denna regel ses likheter mellan invasionperkolation och vanlig perkolation. I tredimentionella gitter är effekten av denna regelknappt påtaglig, och likheter mellan vanlig perkolation ses oavsett hurvida trapping regelnimplementeras eller ej.

Place, publisher, year, edition, pages
2015.
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-168077OAI: oai:DiVA.org:kth-168077DiVA: diva2:814208
Available from: 2015-05-26 Created: 2015-05-26 Last updated: 2015-05-26Bibliographically approved

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf