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