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Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes. (English) Zbl 1406.76023
Summary: In this work, we combine (i) NURBS-based isogeometric analysis, (ii) residual-driven turbulence modeling and iii) weak imposition of no-slip and no-penetration Dirichlet boundary conditions on unstretched meshes to compute wall-bounded turbulent flows. While the first two ingredients were shown to be successful for turbulence computations at medium-to-high Reynolds number [I. Akkerman et al., Comput. Mech. 41, No. 3, 371–378 (2008; Zbl 1162.76355); Y. Bazilevs et al., Comput. Methods Appl. Mech. Eng. 197, No. 1–4, 173–201 (2007; Zbl 1169.76352)], it is the weak imposition of no-slip boundary conditions on coarse uniform meshes that maintains the good performance of the proposed methodology at higher Reynolds number [Y. Bazilevs and T. J. R. Hughes, Comput. Fluids 36, No. 1, 12–26 (2007; Zbl 1115.76040); Y. Bazilevs et al., Comput. Methods Appl. Mech. Eng. 196, No. 49–52, 4853–4862 (2007; Zbl 1173.76397)]. These three ingredients form a basis of a possible practical strategy for computing engineering flows, somewhere between RANS and LES in complexity. We demonstrate this by solving two challenging incompressible turbulent benchmark problems: channel flow at friction-velocity Reynolds number 2003 and flow in a planar asymmetric diffuser. We observe good agreement between our calculations of mean flow quantities and both reference computations and experimental data. This lends some credence to the proposed approach, which we believe may become a viable engineering tool.

##### MSC:
 76F65 Direct numerical and large eddy simulation of turbulence 76F40 Turbulent boundary layers 76M10 Finite element methods applied to problems in fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids
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