Original Paper

Computational Mechanics

, Volume 41, Issue 3, pp 371-378

Open Access This content is freely available online to anyone, anywhere at any time.

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

  • I. AkkermanAffiliated withDepartment of Aerospace Engineering, Delft University of Technology
  • , Y. BazilevsAffiliated withInstitute for Computational Engineering and Sciences, The University of Texas at Austin Email author 
  • , V. M. CaloAffiliated withInstitute for Computational Engineering and Sciences, The University of Texas at Austin
  • , T. J. R. HughesAffiliated withInstitute for Computational Engineering and Sciences, The University of Texas at Austin
  • , S. HulshoffAffiliated withDepartment of Aerospace Engineering, Delft University of Technology

Abstract

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.

Keywords

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