Leray-deconvolution model to Navier–Stokes equations by finite element

The study of the Navier–Stokes equations arouses interest of researchers in the area of numerical analysis, since from these it is possible to determine velocity and pressure fields of a flow. With these equations, aerodynamic coefficients can also be approximated, a fact of great interest in the automotive and aircraft industry. It is proposed to study the approximation of the Navier–Stokes by the finite element method. We consider two proposals related to time discretization methods for the given time dependent equations. We present a numerical study of a flow around a cylinder in order to calculate aerodynamic coefficients (lift coefficient and drag coefficient). It is known that the numerical simulations of aerodynamics problems require very refined mesh in order to correctly capture all the physical phenomena involved. Therefore, we introduce a regularization model, called Leray-deconvolution model, which is a well-known family of high accuracy turbulence models. We show the efficiency of this model for the calculation of aerodynamic coefficients with coarse meshes.