A Comparative Solution of Natural Convection in an Open Cavity using Different Boundary Conditions via the Lattice Boltzmann Method

A lattice Boltzmann method is applied to compare the results of simulating natural convection in an open-end cavity using different hydrodynamic and thermal boundary conditions. The Prandtl number in the present simulation is 0.71, Rayleigh numbers are 104,105, and 106, and selected viscosities are 0.02 and 0.05. The on-grid bounce-back method with first-order accuracy and the no-slip method with second-order accuracy are employed for implementation of hydrodynamic boundary conditions. Moreover, two different thermal boundary conditions (with first- and second-order accuracy) also are presented for thermal modelling. The results showed that first- and second-order boundary conditions (thermal/hydrodynamic) are the same for a two-dimensional, single-phase, convective-heat transfer problem, including geometry with straight walls. The obtained results for different hydrodynamic and thermal boundary conditions are useful for researchers in the field of the lattice Boltzmann method in order to implement accurate conditions on the boundaries with different physics.