Pressure Poissen Method For Incompressible Navier-Stokes Equations Using Galerkin Finite Element

Abstract

Most of real situations in fluid flow are characterized by the Navier-Stokes equations that are the model of nonlinear partial differential equation. These nonlinearities make most problems difficult or impossible to solve. In this work we examined the incompressible isothermal NavierStokes equations based on a primitive variable formulation in which the incompressibility constraint replaced by a pressure Poisson equation. For this the Galerkin finite element method is used to obtain the solution for the incompressible Navier-Stokes equations. It is a numerical technique which represents an equation over a particular region as linear combination of finite number of equation variable values within the region. In this work, Galerkin finite element method is proposed to solve the two dimensional incompressible Navier-Stokes equations with appropriate boundary conditions. The element is formulated directly from the Stokes equation of motion, a special case of the Navier-Stokes equations where the inertia terms are dropped, using the method of weight residuals with Galerkin’s criterion applied velocities in two directions and pressure are solved for at all three nodes and solved simultaneously at three corner nodes. For this NSE solved with the help of MATLAB.The numerical results were compared with analytical result and also the velocity contour and pressure contour was also presented .As the result numerical result obtained with minimum numerical error.