The role of continuity in residual-based variational multiscale modeling of turbulence

I. Akkerman, Y. Bazilevs*, V. M. Calo, T. J.R. Hughes, S. Hulshoff

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

200 Scopus citations


This paper examines the role of continuity of the basis in the computation of turbulent flows. We compare standard finite elements and non-uniform rational B-splines (NURBS) discretizations that are employed in Isogeometric Analysis (Hughes et al. in Comput Methods Appl Mech Eng, 194:4135-4195, 2005). We make use of quadratic discretizations that are C 0-continuous across element boundaries in standard finite elements, and C 1-continuous in the case of NURBS. The variational multiscale residual-based method (Bazilevs in Isogeometric analysis of turbulence and fluid-structure interaction, PhD thesis, ICES, UT Austin, 2006; Bazilevs et al. in Comput Methods Appl Mech Eng, submitted, 2007; Calo in Residual-based multiscale turbulence modeling: finite volume simulation of bypass transition. PhD thesis, Department of Civil and Environmental Engineering, Stanford University, 2004; Hughes et al. in proceedings of the XXI international congress of theoretical and applied mechanics (IUTAM), Kluwer, 2004; Scovazzi in Multiscale methods in science and engineering, PhD thesis, Department of Mechanical Engineering, Stanford Universty, 2004) is employed as a turbulence modeling technique. We find that C 1-continuous discretizations outperform their C 0- continuous counterparts on a per-degree-of-freedom basis. We also find that the effect of continuity is greater for higher Reynolds number flows.

Original languageEnglish (US)
Pages (from-to)371-378
Number of pages8
JournalComputational Mechanics
Issue number3
StatePublished - Feb 2008
Externally publishedYes


  • Boundary layers
  • Continuity of discretization
  • Finite elements
  • Incompressible flows
  • Isogeometric Analysis
  • Navier-Stokes equations
  • Residual-based turbulence modeling
  • Turbulent channel flows
  • Variational multiscale formulation

ASJC Scopus subject areas

  • Computational Mechanics
  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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