A finite element method for solving the incompressible Navier-Stokes equations at low and high Reynolds numbers using finite calculus. Application to fluid-structure interaction

Abstract

The main objective of this monograph is to develop a stabilized finite element method (FEM) for solving the incompressible Navier-Stokes equations. Using Finite Calculus (FIC), which is a methodology developed by E. Oñate and co-workers at CIMNE (International Center for Numerical Methods in Engineering), flows with a wide range of Reynolds numbers can be modeled. The secondary objective is to test the applicability of the FIC/FEM model to fluid-structure interaction (FSI) emphasizing aero-elasticity. The implementation of the model is carried out within KRATOS, a finite element code for solving multi-physics problems developed at CIMNE.