A compensation method to eliminate the spurious term in CA fluid pressure

The lattice gas automata (LGA) is a microscopic model recently introduced to the field of fluid dynamics. The lattice Boltzmann equation (LBE) is an alternative implementing scheme of the LGA, which is totally free of noise. The modeled fluid is called as the cellular automaton (CA) fluid. It is known that the pressure of the CA fluid contains a velocity dependent part. It reflects the simple and discrete nature of the model and either brings about unphysical oscillation in the flow energy or spoils the pressure field of the simulated flow. In this paper, we begin with a general introduction of the lattice gas models. Then we give a full description for such spurious terms and suggest a compensation method to eliminate the effect in the lattice Boltzmann model. Four numerical simulations are used as illustration for the effectiveness of this method.