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

*(English)*Zbl 1162.76355Summary: 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 [T.J. R.
Hughes et al., Comput. Methods Appl. Mech. Eng. 194, No. 39–41, 4135–4195 (2005; Zbl 1151.74419)]. 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 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.

##### MSC:

76F65 | Direct numerical and large eddy simulation of turbulence |

76M10 | Finite element methods applied to problems in fluid mechanics |

76D05 | Navier-Stokes equations for incompressible viscous fluids |

76M30 | Variational methods applied to problems in fluid mechanics |

##### 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
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\textit{I. Akkerman} et al., Comput. Mech. 41, No. 3, 371--378 (2008; Zbl 1162.76355)

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