Develop lattice Boltzmann method and its related boundary conditions models for the benchmark oscillating walls by modifying hydrodynamic and thermal distribution functions

Present works aims to develop the lattice Boltzmann method ability to simulate the periodic supposed problems. Hence, a two-dimensional rectangular enclosure is considered so that its top cold lid oscillates horizontally with time. The stationary sidewalls are kept insulated. It would be necessary to present an appropriate boundary condition model of LBM for the oscillating lid, based on the hydrodynamic and thermal distribution functions. The influences of various lid oscillation frequencies (Strouhal number) are investigated at different values of Richardson numbers at free, mixed and force convections states by using D2Q9 lattice. It is seen that the lid oscillation frequency effect is more significant at less amounts of Richardson number.