A Low Degree Non–Conforming Approximation of the Steady Stokes Problem with an Eddy Viscosity

Abstract

AbstractIn the context of Large Eddy Simulation, the use of a turbulence model brings the question of the implementation of the eddy–viscosity. In this communication, we propose to assess the discretization of the diffusive term based on a low–order non–conforming finite element. For this, we build a manufactured solution of the incompressible steady Stokes problem, for which the turbulent viscosity is given either by the Smagorinsky or WALE models. Numerical tests are performed for both models with the finite element approximation and the MAC scheme.KeywordsLarge Eddy SimulationWALE and Smagorinsky modelsincompressible steady Stokes equationslow-order finite element approximation