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A new finite volume (FV) discretisation method for the Lattice Boltzmann (LB)equation which combines high accuracy with limited computational cost ispresented. In order to assess the performance of the FV method we carry out asystematic comparison, focused on accuracy and computational performances, withthe standard $streaming$ (ST) Lattice Boltzmann equation algorithm. To ourknowledge such a systematic comparison has never been previously reported. Inparticular we aim at clarifying whether and in which conditions the proposedalgorithm, and more generally any FV algorithm, can be taken as the method ofchoice in fluid-dynamics LB simulations. For this reason the comparativeanalysis is further extended to the case of realistic flows, in particularthermally driven flows in turbulent conditions. We report the first successfulsimulation of high-Rayleigh number convective flow performed by a LatticeBoltzmann FV based algorithm with wall grid refinement.

Finite Volume $vs.$ Streaming-based Lattice Boltzmann algorithm for fluid-dynamics simulations: a one-to-one accuracy and performance study