Comparison of Direct and Indirect Boundary Element Methods for the Flow Past a Circular Cylinder with Constant Element Approach

Abstract

In this paper, a comparison of direct and indirect boundary element methods is applied for calculating the flow past(i.e. velocity distribution) a circular cylinder with a constant element (i.e a new) approach. To check the accuracy of the method, the computed flow velocity is compared with the analytical solution for the flow over the boundary of a circular cylinder. (Journal of American Science 2009;5(4):13-16). (ISSN: 1545-1003). From the time of fluid flow modeling, it had been struggled to find the solution of a complicated system of partial differential equations (PDE) for the fluid flows which needed more efficient numerical methods. With the passage of time, many numerical techniques such as finite difference method, finite element method, finite volume method and boundary element method etc. came into beings which made possible the calculation of practical flows. Due to discovery of new algorithms and faster computers, these methods were evolved in all areas in the past. These methods are CPU time and storage hungry. One of the advantages is that with boundary elements one has to discretize the entire surface of the body, whereas with domain methods it is essential to discretize the entire region of the flow field. The most important characteristics of boundary element method are the much smaller system of equations and considerable reduction in data which is prerequisite to run a computer program efficiently. These method have been successfully applied in a number of fields, for example elasticity, potential theory, elastostatics and elastodynamics (Brebbia, 1978; Brebbia and Walker, 1980).Furthermore, this method is well- suited to problems with an infinite domain. From above discussion, it is concluded that boundary element method is a time saving, accurate and efficient numerical technique as compared to other numerical techniques which can be classified into direct boundary element method and indirect boundary element method. The direct method takes the form of a statement which provides the values of the unknown variables at any field point in terms of the complete set of all the boundary data. Whereas the indirect method utilizes a distribution of singularities over the boundary of the body and computes this distribution as the solution of integral equation. The direct boundary element method was used for flow field calculations around complicated bodies (Morino et al.,1975;Mushtaq,2008). While the indirect method has been used in the past for flow