The DRM subdomain decomposition approach to solve the two-dimensional Navier–Stokes system of equations

Abstract

This work presents a domain decomposition boundary integral equation method for the solution of the two-dimensional Navier–Stokes system of equations. It is known that, within this topic, the standard boundary element method is at a disadvantage when compared with classical domain schemes, such as finite difference and finite elements methods. In the present approach the original domain is divided into several subdomains. In each of them the integral representation formula of a non-homogeneous Stokes flow field is applied, and on the interface of the adjacent sub-regions the full matching conditions of the problem are imposed. The domain integrals resulting from the non-homogeneous terms of the formulation are transformed into surface integrals at the contour of each sub-region via the dual reciprocity method. Finally, some examples showing the accuracy, efficiency and flexibility of the proposed method are presented.