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Solution of the Stefan problem with general time-dependent boundary conditions using a random walk method
Örebro universitet, Institutionen för naturvetenskap och teknik.
2019 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

This work deals with the one-dimensional Stefan problem with a general time- dependent boundary condition at the fixed boundary. The solution will be obtained using a discrete random walk method and the results will be compared qualitatively with analytical- and finite difference method solutions. A critical part has been to model the moving boundary with the random walk method. The results show that the random walk method is competitive in relation to the finite difference method and has its advantages in generality and low effort to implement. The finite difference method has, on the other hand, higher accuracy for the same computational time with the here chosen step lengths. For the random walk method to increase the accuracy, longer execution times are required, but since the method is generally easily adapted for parallel computing, it is possible to speed up. Regarding applications for the Stefan problem, there are a large range of examples such as climate models, the diffusion of lithium-ions in lithium-ion batteries and modelling steam chambers for oil extraction using steam assisted gravity drainage.

Place, publisher, year, edition, pages
2019. , p. 29
Series
TVE-F ; 19007
Keywords [en]
Stefan problem, random walk method, moving boundary, heat transfer
National Category
Physical Sciences Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-385147OAI: oai:DiVA.org:uu-385147DiVA, id: diva2:1325632
Educational program
Master Programme in Engineering Physics
Supervisors
Examiners
Available from: 2019-08-07 Created: 2019-06-16 Last updated: 2019-08-07Bibliographically approved

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • 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