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Lattice Boltzmann (LB) models used for the computation of fluid flows represented by the Navier-Stokes (NS) equations on standard lattices can lead to non-Galilean invariant (GI) viscous stress involving cubic velocity errors. This arises from the dependence of their third order diagonal moments on the first order moments for standard lattices, and strategies have recently been introduced to restore GI without such errors using a modified collision operator involving either corrections to the relaxation times or to the moment equilibria. Convergence acceleration in the simulation of steady flows can be achieved by solving the preconditioned NS equations, which contain a preconditioning parameter that alleviates the numerical stiffness. In the present study, we present a GI formulation of the preconditioned cascaded central moment LB method used to solve the preconditioned NS equations, which is free of cubic velocity errors on a standard lattice. A Chapman-Enskog analysis reveals the structure of the spurious non-GI defect terms and it is demonstrated that the anisotropy of the resulting viscous stress is dependent on the preconditioning parameter, in addition to the fluid velocity. It is shown that partial correction to eliminate the cubic velocity defects is achieved by scaling the cubic velocity terms in the off-diagonal third-order moment equilibria with the square of the preconditioning parameter. Furthermore, we develop additional corrections based on the extended moment equilibria involving gradient terms with coefficients dependent locally on the fluid velocity and the preconditioning parameter. Several conclusions are drawn from the analysis of the structure of the non-GI errors and the associated corrections, with particular emphasis on their dependence on the preconditioning parameter. Improvements in accuracy and convergence acceleration are demonstrated.
Simulating inhomogeneous flows with different characteristic scales in different coordinate directions using the collide-and-stream based lattice Boltzmann methods (LBM) can be accomplished efficiently using rectangular lattice grids. We develop and
It is well-known that the original lattice Boltzmann (LB) equation deviates from the Navier-Stokes equations due to an unphysical velocity dependent viscosity. This unphysical dependency violates the Galilean invariance and limits the validation doma
Lattice Boltzmann Method(LBM) has achieved considerable success on simulating complex flows. However, how to impose correct boundary conditions on the fluid-solid interface with complex geometries is still an open question. Here we proposed a velocit
We present a multi-scale lattice Boltzmann scheme, which adaptively refines particles velocity space. Different velocity sets, i.e., higher- and lower-order lattices, are consistently and efficiently coupled, allowing us to use the higher-order latti
In recent years, the lattice Boltzmann (LB) method has been widely employed to simulate boiling phenomena [A. Markus and G. Hazi, Phys. Rev. E 83, 046705 (2011); Biferale et al., Phys. Rev. Lett. 108, 104502 (2012); Li et al., Phys. Rev. E 96, 063303