Stability analysis of two-step finite-difference schemes for the system of kinetic equations

The modified two-step lattice Boltzmann scheme with central differences for the system of kinetic equations is investigated. The schemes with first-order and second-order upwind differences are proposed. Stability of these schemes is investigated using von Neumann method. The problem of stability investigation of unperturbed solution of the constructed schemes is reduced to the problem of stability analysis of the zero solution of system of difference equations with a square matrix. The spatially homogeneous stationary flows in unbounded domain are considered. Values of areas of stability domains for presented schemes are obtained. It is shown that the usage of special approximations of the convective terms in kinetic equations allows to obtain the greatest values of the areas of stability domains in parameter space.