A discrete nine-velocity model of the Boltzmann equation: solution in the form of Wild sum and applications to simulating incompressible flows

A discrete kinetic nine-velocity model of the Boltzmann equation on a plane is considered. In the limit of small free path and low bulk velocities, this model describes flows of viscous incompressible fluids. The complete discretization of the model over the time and spatial variables, which is, in particular, required for the numerical solution, is carried out using the truncated Wild sum. It is shown that the scheme has the second order of accuracy. As an example of the application of the proposed method, numerical solutions of two benchmark problems are obtained—Taylor–Green vortices and flow in a cavity with a moving boundary. The simulation results are compared with the solutions obtained on the basis of the classical nine-velocity lattice Boltzmann model.