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The boundary element method (BEM) is extended for the discretisation of the incompressible Navier-Stokes equations in the velocity-vorticity form for the URANS formulation. BEM uses fundamental solutions as weighting functions, thus the approach enables inclusions of some of the governing physics in the method itself. For testing purposes the flow around the square cylinder in the two-dimensional channel with a blockage ratio of 1/8 was chosen as the appropriate test case. The flow was calculated for the Reynolds numbers ranging from 100 to 1000. At Reynolds number 1000, the governing equations were solved directly in a quasi DNS manner and in the RANS form using the Spalart-Allmaras turbulence model within an URANS simulation.

A numerical study of particle motion in a cubic lid driven cavity is presented. As a computational tool, a boundary element based flow solver with a Lagrangian particle tracking algorithm is derived. Flow simulations were performed using an in-house boundary element based 3D viscous flow solver. The Lagrangian particle tracking algorithm is capable of simulation of dilute suspensions of particles in viscous flows taking into account gravity, buoyancy, drag, pressure gradient and added mass. The derived algorithm is used to simulate particle behaviour in a cellular flow field and in a lid driven cavity flow. Simulations of particle movement in a cellular flow field were used to validate the algorithm. The main goal of the paper was to numerically simulate the flow behaviour of spheres of different densities and different diameters, as experimentally observed in work of Tsorng et al.The study of slightly buoyant and non-buoyant particles in a lid driven cavity was aimed at discovering cases when particles leave the primary vortex and enter into secondary vortices, a phenomenon described in the work of Tsorng et al. A parametric study of this phenomenon was preformed. The presented computational results show excellent agreement with experiments, confirming the accuracy of the developed computational method.