Numerical analysis of two-step finite-difference-based lattice Boltzmann scheme

The modified two-step lattice Boltzmann scheme with central differences is proposed. It is shown that the scheme approximates the system of discrete Boltzmann equations with the second order on space variables, and with first order on time. Values of the Courant parameter for the scheme proposed and the values for the finite difference schemes presented in other studies are compared. The scheme shows the efficiency in solution of two test problems: the problem of cavity flow and the Couette problem.