Modeling incompressible flows at low and high Reynolds numbers via a finite calculus–finite element approach

We present a formulation for incompressible flows analysis using the finite element method (FEM). The necessary stabilization for dealing with convective effects and the incompressibility condition is modeled via the finite calculus (FIC) method. The stabilization terms introduced by the FIC formulation allow to solve a wide range of fluid flow problems for low and high Reynolds numbers flows without the need for a turbulence model. Examples of application of the FIC/FEM formulation to the analysis of 2D and 3D incompressible flows with moderate and large Reynolds numbers are presented.