Starting with the discrete lattice Boltzmann equation (also referred to as LBGK equation due to the collision operator used). We first do a 2nd-order Taylor series expansion about the left side of the LBE. This is chosen over a simpler 1st-order Taylor expansion as the discrete LBE cannot be recovered. When doing the 2nd-order Taylor series expansion, the zero derivative term and the first term on the right will cancel, leaving only the first and second derivative terms of the Taylor expansion and the collision operator: