Flow simulation by the lattice Boltzmann method with multiple-relaxation times

The lattice Boltzmann method with a multirelaxation collision integral is considered to simulate two-dimensional flows of an incompressible viscous Newtonian fluid. On the basis of this method, a software package that allows one to simulate two-dimensional turbulent flows in a medium with a given shape of obstacles is developed. This package is verified using the following three test problems: a steady Poiseuille flow in a plane channel, a flow in a square cavity with a moving top wall, and the second Stokes problem. The numerical results are in good agreement with the theoretical results and with the results of previous studies. For the second Stokes problem, the dependence of the penetration depth of oscillations on their period and the viscosity coefficient is studied.