A poly-region boundary element method for incompressible viscous fluid flows

A boundary element method (BEM) for steady viscous #uid #ow at high Reynolds numbers is presented. The new integral formulation with a poly-region approach involves the use of the convective kernel with slight compressibility that was previously employed by Grigoriev and Fafurin [1] for driven cavity #ows with Reynolds numbers up to 1000. In order to avoid the overdeterminancy of the global set of equations when using eight-noded rectangular volume cells from that previous work, 12-noded hexagonal volume regions are introduced. As a result, the number of linearly independent integral equations for each node becomes equal to the degrees of freedom of the node. The numerical results for square-driven cavity #ow having Reynolds numbers up to 5000 are compared to those obtained by Ghia et al. [2] and demonstrate a high level of accuracy even in resolving the secondary vortices at the corners of the cavity. Next, a comprehensive study is done for backward-facing step #ows at Re"500 and 800 using the BEM, along with a standard Galerkin-based "nite element methods (FEM). The numerical methods are in excellent agreement with the benchmark solution published by Gartling [3]. However, several additional aspects of the problem are also considered, including the e!ect of the in#ow boundary location and the traction singularity at the step corner. Furthermore, a preliminary comparative study of the poly-region BEM versus the standard FEM indicates that the new method is more than competitive in terms of accuracy and e$ciency