A hybrid Taylor-Galerkin variational multi- scale stabilization method for the level set equation

Ahmed Bakkar, Wagdi G. Habashi, Marco Fossati, Guido S. Baruzzi

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


A stabilized finite element formulation of the level set equation is proposed for the numerical simulation of water droplet dynamics for in-flight ice accretion problems. The variational multi-scale and Taylor–Galerkin approaches are coupled such that the temporal derivative in the weak Galerkin formulation is replaced with a Taylor series expansion improving the temporal accuracy of the scheme. The variational multi-scale approach is then applied to the semi-discrete equation, allowing the stabilization terms to appear naturally. Taylor series expansions up to the fourth order have been studied in terms of accuracy and convergence rates. A second order implicit expansion was found to provide a good trade-off between accuracy and computational cost when compared to a fourth order implicit expansion. Validation is done through a number of benchmark cases considering droplet stretching and high-speed advection. Results indicate good mass conservation characteristics compared to other methods available in the literature.
Original languageEnglish
Pages (from-to)192-205
Number of pages14
JournalComputers and Fluids
Early online date18 Aug 2015
Publication statusPublished - 22 Oct 2015


  • level set
  • variational multi-scale
  • Taylor Galerkin
  • multiphase flow

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