A numerical method for the solution of the Navier-Stokes equations is developed using an integral representation of the conservation equations. The velocity-vorticity formulation is employed, where the kinematics is given with the Poisson equation for a velocity vector, while the kinetics is represented with the vorticity transport equation. The corresponding boundary-domain integral equations are presented along with discussions of the kinetics and kinematics of the fluid flow problem. The boundary-domain integral formulation is developed and tested for natural convection flows in closed cavities with complex geometries.
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