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Comput. Methods Appl. Mech. Engrg. 197 (2007) 173–201
ate/cma
Variational multiscale residual-based turbulence modeling for
large eddy simulation of pressible flows
Y. Bazilevs a,*, . Calo a, . Cottrell a, . Hughes a,1, A. Reali b, G. Scovazzi c,2
a Institute putational Engineering and Sciences, The University of Texas at Austin, 201 East 24th Street,
1 University Station C0200, Austin, TX 78712, USA
b Structural Mechanics Department, University of Pavia, via Ferrata 1, 27100 Pavia, Italy
c putational Shock and Multi-physics Department, Sandia National Laboratories, . Box 5800, MS 1319, Albuquerque, NM 87185-1319, USA
Received 2 May 2007; received in revised form 5 July 2007; accepted 19 July 2007
Available online 15 August 2007
Abstract
We present an LES-type variational multiscale theory of turbulence. Our approach pletely from the pressible
Navier–Stokes equations and does not employ any ad hoc devices, such as eddy viscosities. We tested the formulation on forced homo-
geneous isotropic turbulence and turbulent channel flows. In the calculations, we employed linear, quadratic and cubic NURBS. A dis-
persion analysis of simple model problems revealed NURBS elements to be superior to classical finite elements in approximating
advective and diffusive processes, which play a significant role in putations. The numerical results are very good and con-
firm the viability of the theoretical framework.
Ó 2007 Elsevier . All rights reserved.
Keywords: Variational multiscale methods; Large eddy simulation; Turbulence modeling; Optimality; Projection; Small-scale Green’s function; Pertur-
bation series; Isogeometric analysis; NURBS; pressible flows; Homogeneous isotropic turbulence; Turbulent channel flows
1. Introduction the fine-scale equations retains numerical consistency in
the coarse-scale equations and thus permits full rate-of-
Variational multiscale concepts for Large Eddy Simula- convergence of the