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In the present paper a lattice Boltzmann scheme is presented which exhibitsan increased stability and accuracy with respect to standard single- ormulti-relaxation-time (MRT) approaches. The scheme is based on asingle-relaxation-time model where a special regularization procedure isapplied. This regularization is based on the fact that, for a-thermal flows,there exists a recursive way to express the velocity distribution function atany order (in the Hermite series sense) in terms of the density, velocity, andstress tensor. A linear stability analysis is conducted which shows enhanceddispersion/dissipation relations with respect to existing models. The model isthen validated on two (one 2D and one 3D) moderately high Reynolds numbersimulations ($\mathrm{Re}\sim 1000$) at moderate Mach numbers ($\mathrm{Ma}\sim0.5$). In both cases the results are compared with an MRT model and an enhancedaccuracy and stability is shown by the present model.

Increasing stability and accuracy of the lattice Boltzmann scheme: recursivity and regularization