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 journalArticle

1 Citation (Scopus)

Abstract

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.
LanguageEnglish
Pages192-205
Number of pages14
JournalComputers and Fluids
Volume121
Early online date18 Aug 2015
DOIs
Publication statusPublished - 22 Oct 2015

Fingerprint

Stabilization
Taylor series
Ice problems
Advection
Stretching
Conservation
Derivatives
Computer simulation
Costs
Water

Keywords

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

Cite this

Bakkar, Ahmed ; Habashi, Wagdi G. ; Fossati, Marco ; Baruzzi, Guido S. / A hybrid Taylor-Galerkin variational multi- scale stabilization method for the level set equation. In: Computers and Fluids. 2015 ; Vol. 121. pp. 192-205.
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A hybrid Taylor-Galerkin variational multi- scale stabilization method for the level set equation. / Bakkar, Ahmed; Habashi, Wagdi G.; Fossati, Marco; Baruzzi, Guido S.

In: Computers and Fluids, Vol. 121, 22.10.2015, p. 192-205.

Research output: Contribution to journalArticle

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AB - 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.

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