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Lattice Boltzmann (LB) models used for the computation of fluid flowsrepresented by the Navier-Stokes (NS) equations on standard lattices can leadto non-Galilean invariant (GI) viscous stress involving cubic velocity errors.This arises from the dependence of their third order diagonal moments on thefirst order moments for standard lattices, and strategies have recently beenintroduced to restore GI without such errors using a modified collisionoperator involving either corrections to the relaxation times or to the momentequilibria. Convergence acceleration in the simulation of steady flows can beachieved by solving the preconditioned NS equations, which contain apreconditioning parameter that alleviates the numerical stiffness. In thepresent study, we present a GI formulation of the preconditioned cascadedcentral moment LB method used to solve the preconditioned NS equations, whichis free of cubic velocity errors on a standard lattice. A Chapman-Enskoganalysis reveals the structure of the spurious non-GI defect terms and it isdemonstrated that the anisotropy of the resulting viscous stress is dependenton the preconditioning parameter, in addition to the fluid velocity. It isshown that partial correction to eliminate the cubic velocity defects isachieved by scaling the cubic velocity terms in the off-diagonal third-ordermoment equilibria with the square of the preconditioning parameter.Furthermore, we develop additional corrections based on the extended momentequilibria involving gradient terms with coefficients dependent locally on thefluid velocity and the preconditioning parameter. Several conclusions are drawnfrom the analysis of the structure of the non-GI errors and the associatedcorrections, with particular emphasis on their dependence on thepreconditioning parameter. Improvements in accuracy and convergenceacceleration are demonstrated.

Galilean Invariant Preconditioned Central Moment Lattice Boltzmann Method without Cubic Velocity Errors for Efficient Steady Flow Simulations