On stability of a lattice Boltzmann kinetic scheme for simulating plane flows

The stability problem is considered for a lattice Boltzmann kinetic scheme for simulating the plane flows of a viscous fluid. Stability is studied for two steady modes of flow in an unbounded domain. The stability analysis is performed with respect to initial data using the Neumann method in a linear approximation. A number of stability domains are constructed and studied in the input parameter space. It is shown that the scheme under consideration is conditionally stable.