Numerical study and CFD Simulations of Incompressible Newtonian Flow by Solving steady Navier-stokes equations using Newton’s method

Abstract

In this paper, incompressible Newtonian flow is numerically studied by approximating the solution of the steady Navier-Stokes equations in two dimensional case. Computational Fluid Dynamics (CFD) simulations are carried out by using the finite element method. Newton's method is applied to solve the Navier-Stokes equations where the finite element solutions of Stokes equations is considered as the initial guess to obtain the convergence of Newton's sequence. The numerical simulations are presented in terms of the contours of velocity, pressure and streamline. All the meshes and simulations are implemented on the general finite element solver FreeFem++. A two-dimensional benchmark flow was computed with posteriori estimates. It has also been established that the free access solver FreeFem++ can provide a reasonable good numerical simulations of complicated flow behavior.