On the interaction between dynamic model dissipation and numerical dissipation due to streamline upwind/Petrov–Galerkin stabilization Andre ´s E. Tejada-Martı ´nez * ,1 , Kenneth E. Jansen Scientific Computation Research Center and Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA Received 2 June 2003; received in revised form 20 January 2004; accepted 8 June 2004 Abstract Here we investigate the roles of physical and numerical subgrid-scale modeling. The subgrid-scales are represented by a physical large-eddy simulation model, namely the popular dynamic Smagorinsky model (or simply dynamic model), as well as by a numerical model in the form of the well-known streamline upwind/Petrov–Galerkin stabilization for finite element discretizations of advection–diffusion systems. The latter is not a physical model, as its purpose is to provide sufficient algorithmic dissipation for a stable, consistent, and convergent numerical method. We study the inter- action between the physical and numerical models by analyzing energy dissipation associated to the two. Based on this study, a modification to the dynamic model is proposed as a way to discount the numerical methodÕs algorithmic dis- sipation from the total subgrid-scale dissipation. The modified dynamic model is shown to be successful in simulations of turbulent channel flow. Ó 2004 Elsevier B.V. All rights reserved. 1. Introduction The classical Galerkin method for the incompressible Navier–Stokes equations is well-known to be unstable in the advective dominated limit, as discussed in [3]. A second instability can occur for certain interpolation combinations of the velocity and pressure which violate the so-called Babus ˘ka–Brezzi 0045-7825/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cma.2004.06.037 * Corresponding author. 1 Present address: Center for Coastal Physical Oceanography, Old Dominion University, Crittenton Hall, 768 West 52nd Street, Norfolk, VA 23529, USA. Comput. Methods Appl. Mech. Engrg. 194 (2005) 1225–1248 www.elsevier.com/locate/cma