A time-implicit filling algorithm

C. R. Swaminathan, V. R. Voller

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43 Scopus citations


The volume of fluid (VOF) equation is a well-known method for tracking the liquid/air interface during a filling process. Standard numerical approximations of the VOF equation fail to preserve a sharp interface. Methods that ensure a sharp interface in VOF calculations are investigated in this paper. At first, two previous VOF schemes that limit the smearing of the interface, via appropriate approximation of the convective flux, are outlined. These schemes are explicit in nature and hence subject to time step restrictions. A new scheme for approximating the convective flux is introduced. Implicit solutions based on this modified scheme are smear free and are not subject to any time step restrictions. Solutions to example filling problems are in close agreement with solutions based on traditional VOF approaches. Some potential drawbacks of the new method are investigated. In the context of filling problems it is shown that these drawbacks are not significant.

Original languageEnglish (US)
Pages (from-to)101-108
Number of pages8
JournalApplied Mathematical Modelling
Issue number2
StatePublished - Feb 1994

Bibliographical note

Funding Information:
This work was supported by the National Center for Excellence in Metalworking Technology, operated by Concurrent Technologies Corporation, Johnstown, PA, under contract to the U.S. Navy as part of the U.S. Navy Manufacturing Technology Program. The authors would also like to acknowledge Professor S. V. Patankar and Dr. Kanchan Kelkar for useful discussions and input and the Minnesota Supercomputer Institute for a computer resources grant.


  • front tracking
  • mold filling


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