NOVEL EXPANSION METHOD FOR DERIVING THE NAVIER-STOKES EQUATION FROM THE LATTICE BOLTZMANN EQUATION

This study proposes a novel expansion method for deriving the Navier-Stokes equation from the lattice Boltzmann equation. This method is used to expand the lattice Boltzmann equation with time step ±t based on the dependence of the distribution function on ±t. It is characterized by obtaining the recurrence relations for ±t that connect the expansion coefficient relationships, considerably reducing the mathematical manipulations required relative to the Chapman-Enskog expansion known for the standard expansion method. Because of its simplicity and clarity, the expansion method is suitable for deriving the lattice Boltzmann equations for complex systems such as multiphase mixtures of miscible gas phases. © 2022 by Begell House, Inc.