An implicit monolithic formulation based on finite element formulation for incompressible Navier-Stokes equations

The aim of this paper is to present a mathematical formulation developed using the finite element method with stabilization and fractional step method for the simulation of three-dimensional (3D) laminar incompressible Navier-Stokes problems written in the primitive variables. A second-order stable monolithic formulation was obtained. An edge-based data structure was adopted, and the computational system developed was implemented using FORTRAN 90 and parallel computing concepts allowing the computation of large-scale 3D problems, which will be described in the sequel to the present paper. An alternative form of stabilization was implemented and compared with the one used in the formulation, which represents the core of the developed computational code. Several applications were analyzed in order to verify and validate the computational system developed. The obtained results are in good agreement with the experimental, theoretical, and numerical data available in the literature.