A FINITE ELEMENT SCHEME BASED ON THE VELOCITY CORRECTION METHOD FOR THE SOLUTION OF THE TIME-DEPENDENT INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

In this paper a finite element solution for two-dimensional incompressible viscous flow is considered. The velocity correction method (explicit forward Euler) is applied for time integration. Discretization in space is carried out by the Galerkin weighted residual method. The solution is in terms of primitive variables, which are approximated by piecewise bilinear basis functions defined on isoparametric rectangular elements. The second step of the obtained algorithm is the solution of the Poisson equation derived for pressure. Emphasis is placed on the prescription of the proper boundary conditions for pressure in order to achieve the correct solution. The scheme is completed by the introduction of the balancing tensor viscosity; this makes this method stable (for the advection-dominated case) and permits us to employ a larger time increment. Two types of example are presented in order to demonstrate the performance of the developed scheme. In the first case all normal velocity components on the boundary are specified (e.g. lid-driven cavity flow). In the second type of example the normal derivative of velocity is applied over a portion of the boundary (e.g. flow through sudden expansion). The application of the described method to non-isothermal flows (forced convection) is also included.