A new LES model derived from generalized Navier–Stokes equations with nonlinear viscosity. (15th January 2017)

• Record Type: Journal Article
• Authors: Rodríguez, J.M.; Taboada-Vázquez, R.
• Is Part Of: Computers & mathematics with applications. Volume 73:issue 2(2017)
• Page Start: 294
• Page End: 303
• Publication Date: 2017-01-15
• Subjects: Large Eddy Simulation -- Nonlinear viscosity -- Clark approximation; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2016.11.024
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: Large Eddy Simulation (LES) is a very useful model for simulating turbulent flows (see Argyropoulos and Markatos, 2015, Guermond et al., 2004 or Sagaut, 2006, for example). One of the possible ways to derive the LES equations is to apply a filter operator to the Navier–Stokes equations, obtaining a new equation governing the behavior of the filtered velocity. This approach introduces the so called subgrid-scale stress tensor in the equations, that must be expressed in terms of the filtered velocity to close the problem. One of the most popular models is that proposed by Smagorinsky (1963), where the subgrid-scale stress tensor is modeled by introducing an eddy viscosity . In this work, we shall propose a new approximation to this problem by applying the filter, not to the Navier–Stokes equations, but to a generalized version of these equations with nonlinear viscosity. That is, we shall introduce a nonlinear viscosity, not as a procedure to close the subgrid-scale stress tensor, but as part of the model itself (see below). Consequently, we shall need a different method to close the subgrid-scale stress tensor, and we shall use the Clark approximation, where the Taylor expansion of the subgrid-scale stress tensor is computed (see Carati et al., 2001 and Vreman et al., 1966).