Two-dimensional velocity-vorticity based LES for the solution of natural convection in a differentially heated enclosure by wavelet transform based BEM and FEM

A wavelet transform based boundary element method (BEM) numerical scheme is proposed for the solution of the kinematics equation of the velocity-vorticity formulation of Navier–Stokes equations. FEM is used to solve the kinetics equations. The proposed numerical approach is used to perform two-dimensional vorticity transfer based large eddy simulation on grids with 105105 nodes. Turbulent natural convection in a differentially heated enclosure of aspect ratio 4 for Rayleigh number values Ra=107–109Ra=107–109 is simulated. Unstable boundary layer leads to the formation of eddies in the downstream parts of both vertical walls. At the lowest Rayleigh number value an oscillatory flow regime is observed, while the flow becomes increasingly irregular, non-repeating, unsymmetric and chaotic at higher Rayleigh number values. The transition to turbulence is studied with time series plots, temperature–vorticity phase diagrams and with power spectra. The enclosure is found to be only partially turbulent, what is qualitatively shown with second order statistics—Reynolds stresses, turbulent kinetic energy, turbulent heat fluxes and temperature variance. Heat transfer is studied via the average Nusselt number value, its time series and its relationship to the Rayleigh number value.