Numerical Simulations of Lid-Driven Cavity Flows Using Multi-relaxation Time Lattice Boltzmann Method

Abstract

Lattice Boltzmann method is implemented to study two and three dimensional flows in a square cavity. D2Q9 is used to predict the velocity field in a two dimensional cavity while both D3Q15 and D3Q19 lattice arrangements are employed to predict three dimensional flows in a cavity. The second order and non-equilibrium type of boundary conditions are used to discretize the conditions imposed on the velocity field at both moving and stationary walls. Multi-relaxation time method is applied for two dimensional lattice arrangements while single relaxation time method is employed for three dimensional arrangements. Multi relaxation time provides an accurate and stable simulations at high Re flows. The velocity field predicted here for both two and three dimensional cavity flows agrees well with those documented by previous investigators. It has been shown here that the Lattice Boltzmann method is an effective computational fluid dynamics tool to study high Re flows.