FEM Approach for Efficient Solution of Two-Dimensional Navier-Stokes Equations

In this paper, the Galerkin finite element method was used to solve the Navier-Stokes equations for two dimensional steady flow of Newtonian and incompressible fluid with no body forces usingMATLAB. The method was applied to the lid-driven cavity problem. The eight-noded rectangular element was used for the formulation of element equations. The velocity and pressure components were located at all of 8 nodes of the element. From location of velocity components and pressure, it is obvious that this element consists of 20 unknowns for velocities and pressure. The quadratic interpolation functions represent velocity components while bilinear interpolation function represents pressure. Finite element codes were developed for implementation.