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Lattice Boltzmann simulations of three-dimensional, isothermal hydrodynamicsoften use either the D3Q19 or the D3Q27 velocity sets. While both modelscorrectly approximate Navier-Stokes in the continuum limit, the D3Q19 model iscomputationally less expensive but has some known deficiencies regardingGalilean invariance, especially for high Reynolds number flows. In this work wepresent a novel methodology to construct lattice Boltzmann equilibria forhydrodynamics directly from the continuous Maxwellian equilibrium. While ournew approach reproduces the well known LBM equilibrium for D2Q9 and D3Q27lattice models, it yields a different equilibrium formulation for the D3Q19stencil. This newly proposed formulation is shown to be more accurate than thewidely used second order equilibrium, while having the same computation costs.We present a steady state Chapman-Enskog analysis of the standard and theimproved D3Q19 model and conduct numerical experiments that demonstrate thesuperior accuracy of our newly developed D3Q19 equilibrium.

An improved lattice Boltzmann D3Q19 method based on an alternative equilibrium discretization