Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes

Abstract

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, Y. Bazilevs, V. M. Calo, T. J. R. Hughes, S. Hulshoff, The role of continuity in residual-based variational multiscale modeling of turbulence, Comput. Mech. 41 (2008) 371–378; Y. Bazilevs, V.M. Calo, J.A. Cottrell, T.J.R. Hughes, A. Reali, G. Scovazzi, Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows, Comput. Methods Appl. Mech. Engrg., 197 (2007) 173–201], 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, T.J.R. Hughes. Weak imposition of Dirichlet boundary conditions in fluid mechanics, Comput. Fluids 36 (2007) 12–26; Y. Bazilevs, C. Michler, V.M. Calo, T.J.R. Hughes, Weak Dirichlet boundary conditions for wall-bounded turbulent flows. Comput. Methods Appl. Mech. Engrg. 196 (2007) 4853–4862]. 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.