Boundary integral-based domain decomposition technique for solution of Navier Stokes equations

Abstract

This paper presents a new domain decomposition technique based on the use of Boundary Integral Equations (BIEs) for the analysis of viscous flow problems. The domain of interest is divided into a number of non-overlapping subdomains and an iterative procedure is then employed to update the boundary conditions at interfaces. The new feature in the present work is that at each iteration, the relevant two subdomains, together containing a particular interface, are assumed to satisfy the governing BI equations which they do at the end of a convergent iterative process. Hence the boundary conditions on such an interface can be updated using the interior point formulas. Updating formulas based on standard and hypersingular BIEs are derived and the final forms obtained are simple. Furthermore, the internal point formula can be used as a means to estimate the initial interface solution. The proposed method is verified in conjunction with the BEM through the simulation of Poiseuille, driven cavity and backward facing step viscous flows.