A boundary element analysis of Oseen flow past a porous body of arbitrary shape

The aim of this paper is to develop a 3D numerical model for the problem of creeping viscous flow past porous bodies based upon an integral equation formulation, extending the original work done by Higdon and Kojima (1981). Initially, Stokes Bow past a porous body was considered, the external flow being represented in terms of the Stokes integral representation formula and the internal flow by means of the Brinkman integral representation formula. It is important to note here that the Brinkman formulation is chosen over the more traditional Darcy solution due to its all round effectiveness and lack of analytical restrictions. Finally, inertial effects are incorporated into the formulation by use of the Oseen approximation, in this case the external flow field being given in terms of Oseen integral representation formulae rather than the Stokes one. To the knowledge of the authors this is the first time in the open literature that inertial effects have been taken into account in the present problem. Numerical results are presented for different flow configurations around a porous sphere in which the accuracy of the method is shown.