Moment Independent Expansion for Fourth-Order Corrections in Lattice Boltzmann Methods

A expansion to fourth-order for lattice Boltzmann methods is presented. This expansion provides an easy model for finding fourth-order corrections to lattice Boltzmann methods for various physical systems. The fourth-order terms can give rise to improved results over traditional second-order lattice Boltzmann implementations. Although, this manuscript solely deals with fourth-order expansions, this expansion is easily extended to arbitrary order. We present examples of how this expansion is utilized and provide basic analysis to show how the fourth-order methods differ from lower order models for both diffusive systems and phase separating systems.