The dissipative structure of variational multiscale methods for incompressible flows

• Published in: Computer methods in applied mechanics and engineering 2010-02, Vol.199 (13), p.791-801
• Main Authors: Principe, Javier, Codina, Ramon, Henke, Florian
• Format: Article
• Language: English
• Subjects: Aplicacions de la informàtica; Aplicacions informàtiques a la física i l‘enginyeria; Boundary layer and shear turbulence; Computational techniques; Elements finits, Mètode dels; Energy transfer; Exact sciences and technology; Finite element method; Fluid dynamics; Fundamental areas of phenomenology (including applications); General theory; Informàtica; Mathematical methods in physics; Mathematical models; Orthogonal subscales; Physics; Stabilized finite elements; Transient subscales; Turbulence simulation and modeling; Turbulent flows, convection, and heat transfer; Àrees temàtiques de la UPC
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2008.09.007

In this paper, we present a precise definition of the numerical dissipation for the orthogonal projection version of the variational multiscale method for incompressible flows. We show that, only if the space of subscales is taken orthogonal to the finite element space, this definition is physically reasonable as the coarse and fine scales are properly separated. Then we compare the diffusion introduced by the numerical discretization of the problem with the diffusion introduced by a large eddy simulation model. Results for the flow around a surface-mounted obstacle problem show that numerical dissipation is of the same order as the subgrid dissipation introduced by the Smagorinsky model. Finally, when transient subscales are considered, the model is able to predict backscatter, something that is only possible when dynamic LES closures are used. Numerical evidence supporting this point is also presented.