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Abstract

In this study, Boundary Element Method (BEM) is applied to the Navier-Stokes equations in the driven cavity. BEM plays an important role in CFD analysis especially heat transfer computations. One of its main advantages is reduction of the problem dimensionality by one, since it will be required to discretize only the boundary of computational domain. The main difficulty of applying BEM to general nonlinear problems, e.g., Navier-Stokes equations, is the lack of a fundamental solution for such equations. To overcome this difficulty one can separate nonlinear term and treat it as a nonlinear source term. This approach generates an additional problem, i.e., existence of source term which produces an integral term on the whole domain. Initial attempts to deal with volume integral term are domain discretization and numerical integration over the whole domain that makes the method rather time consuming and inefficient. Dual Reciprocity Method (DRM) is an alternative that can be used to transform volume integral to the equivalent boundary integrals and therefore saves the unneeded volume cell integration. These steps are discussed in detail and the results are compared with finite difference method by Ghia et al.