Moving-boundary problems solved by adaptive radial basis functions

L. Vrankar*, E. J. Kansa, L. Ling, F. Runovc, G. Turk

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

19 Citations (Scopus)
31 Downloads (Pure)


The objective of this paper is to present an alternative approach to the conventional level set methods for solving two-dimensional moving-boundary problems known as the passive transport. Moving boundaries are associated with time-dependent problems and the position of the boundaries need to be determined as a function of time and space. The level set method has become an attractive design tool for tracking, modeling and simulating the motion of free boundaries in fluid mechanics, combustion, computer animation and image processing. Recent research on the numerical method has focused on the idea of using a meshless methodology for the numerical solution of partial differential equations. In the present approach, the moving interface is captured by the level set method at all time with the zero contour of a smooth function known as the level set function. A new approach is used to solve a convective transport equation for advancing the level set function in time. This new approach is based on the asymmetric meshless collocation method and the adaptive greedy algorithm for trial subspaces selection. Numerical simulations are performed to verify the accuracy and stability of the new numerical scheme which is then applied to simulate a bubble that is moving, stretching and circulating in an ambient flow to demonstrate the performance of the new meshless approach.

Original languageEnglish
Pages (from-to)1480-1490
Number of pages11
JournalComputers and Fluids
Issue number9
Early online date6 May 2010
Publication statusPublished - Oct 2010

Scopus Subject Areas

  • Computer Science(all)
  • Engineering(all)

User-Defined Keywords

  • Moving-boundary problems
  • Stefan problems
  • Level set method
  • Multiquadric
  • Partial differential equations
  • Adaptive greedy algorithm


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