An analysis of the lattice Boltzmann (LB) method is conducted, and various conclusions are drawn on how to exploit this method for the numerical resolution of the Navier-Stokes equation. A novel LB model is introduced, first for the simulation of advection-diffusion problems, and then for the resolution of the Navier-Stokes equation. The latter model, presented under the name of "regularized lattice Boltzmann", is shown to substantially increase the stability and accuracy of LB models in numerical simulaiton. The model is furthermore found to be innovative due to the fact that it possesses an accurate dimensionless formulation in terms of macroscopic variables. Based on this observation, the regularized model is investigated to address various challenges of LB, such as the implementaiton of boundary conditions and spatially refined grids.
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Jonas Lätt (2007) studied this question.