Segmentation based boundary domain integral method for the numerical solution of Navier-Stokes equations

This contribution deals with further development of Boundary Domain Integral algorithm for computation of laminar viscous fluid flows governed by the Navier-Stokes equations. The algorithm uses the velocity-vorticity formulation and is based on vector-potential formulation of flow kinematics. This results in an accurate determination of the boundary vorticity values, a crucial step in constructing an accurate numerical algorithm for the computation of flows in complex geometries, i.e. geometries with sharp corners. In order to lower computational costs the domain velocity computations are done by the segmentation technique using large subdomains. After the kinematics equation is resolved, the vorticity transport equation is solved using a macro-element approach. This enables us to use a macro-element based diffusion-convection fundamental solution, a key factor in assuring accuracy of the computations for high Reynolds number flows. The proposed numerical algorithm is tested on several test problems, including the standard driven cavity and backward facing step flow, together with driven cavity flow in an L shaped cavity. The comparison of computational results show that the developed algorithm is capable of an accurate resolution of the flow fields in complex geometries.