Degree six returned 9 where 15 was required — the three Hermite roots that fixed D2Q9
Where c_s² = 1/3 and the weights 4/9, 1/9, 1/36 actually come from, traced all the way back to the degree of a Gauss–Hermite quadrature rule.
Deriving μ and k from One Formula Put Pr Off by 1.98× — the 9/4 Behind a 123.5 K Wall Temperature
Deriving μ and k from one mean free path pins air's Pr at γ = 1.400 against a measured 0.707. Eucken's 9/4 drops the Couette wall gap from 123.5 K.
Filling the Third Moment Honestly Made the Error 2.8x Worse — What a Forcing Term Actually Owes
On D2Q9, filling the force third moment raises error from 0.053% to 0.150%. The lattice locks half the tensor, and it arrives only at Burnett order.
Pushing the Frame to 0.2 Cut the Viscosity by 5.97% — The Missing Third Moment in LBM Equilibria
On D2Q9, Σf c³ equals ρu for any distribution you can write. The missing ρu³ breaks Galilean invariance and makes measured viscosity depend on the frame.
Nine Arrows of Maxwell–Boltzmann — Why LBM's Equilibrium Is a Polynomial
Cutting Maxwell–Boltzmann at Hermite order two builds the D2Q9 polynomial, and that same cut leaves the Mach 0.3 ceiling in place.
The Paramecium Swims Through Honey — Where Viscosity Comes From and Why Fourier and Fick Wrote the Same Line
At 1 atm the mean free path is about 68 nm and the mean speed about 470 m/s. One flux, μ ≃ ρ c̄ ℓ / 3, is the line Fourier and Fick used for heat and mass.