Author(s)

Mahmud A. Mehemed Abughalia

Abstract

This paper introduces a numerical solution for flow over a back facing step. In this study, the continuity equation is replaced by a penalty function and a new formula of penalty parameter is derived and implemented. The new formula of penalty parameter is restricted only to the finite element method and the formula requires the existence of the second derivative of the trial function so that a rectangular element with exponential trial function is proposed and used. A laminar flow over a back facing step is chosen as a test model to examine the numerical solution. The location of the reattachment point is captured accurately only if the penalty parameter is multiplied by a suitable factor and this factor depends on the Jacobian. The current numerical results are validated through a comparison to available numerical and experimental results for the case of flow over a back facing step. The tested range of Reynolds number was 200, 400 and 1000 and the ratio between the step height to the duct height was 0.5. The reattachment point is tabulated against Reynolds number. The comparison shows that the finite element solution using the new penalty parameter is closer to the experimental results than the available numerical results. Keywords: penalty method, back facing step, finite element, laminar flow, Navier Stokes equations, numerical solution. 1 Introduction The Navier Stokes equations govern the physical behavior of most of the fluid flow applications. Thus they have attracted a great deal of attention by most engineering fields, chemical, civil, aeronautical, oil and mechanical engineering. These equations usually are solved numerically and the challenge of the

Keywords

penalty method, back facing step, finite element, laminar flow, NavierStokes equations, numerical solution.