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The paper considers the fundamental aspects of turbulence modelling for incompressible Boussinesq fluid flow and corresponding numerical models based on the boundary-domain integral equations. Two different solution methodologies of turbulent flow circumstances are considered, e.g. the classical statistical methodology known as Unsteady Reynolds-Averaged Navier–Stokes (URANS) equations and deterministic Large-Eddy-Simulation (LES) formulation. The velocity-vorticity formulation of the mean/filtered equations is applied, while the averaged/filtered pressure field is determined by solving the Poisson velocity equation. Chaotic natural convection in a differentially heated cavity of aspect ratio 4 with adiabatic horizontal walls is studied by both mentioned methodologies of the unsteady two-dimensional governing equations.

URANS and LES methodology for two-dimensional natural convection in a differentially heated cavity by BEM