Higher-order dynamics in lattice-based models using the Chapman-Enskog method.

In this paper, we investigate the existence of higher-order dynamics in lat tice-based models. We have identified two conditions that determine whether a model would allow some Burnett-like equations when the Chapman-Enskog ex pansion is used. These two conditions are the number of the conserved quant ity as well as the space and time discretization. We shall demonstrate thes e conditions by discussing (1) pure diffusion equation and (2) hydrodynamic equations. While the fact that diffusion equation allows the higher-order dynamics can be shown easily, we will illustrate that care must be taken wh en deriving Burnett-like equations for lattice-based hydrodynamics models u sing the Chapman-Enskog method.