Velocity came out one sixth at τ=0.6 — dropping the half-force F/2 from Guo forcing
Keep the Guo source term but drop F/2 from the LBM velocity and the effective body force shrinks by (1−1/2τ). On Kolmogorov flow at τ=0.6 the amplitude is 0.166 of exact.
Changing only τ changed the density of a gas at rest — the (τ−½)² stress of Shan–Chen velocity-shift forcing
Apply the same force to a resting D1Q3 gas column and only Shan–Chen forcing gives a τ-dependent density. The shifted equilibrium velocity leaves a fake (τ−½)²F²/ρ stress.
Giving Conduction Its Own τ Left Viscous Heating Stuck at Pr = 1 — The Quasi-Equilibrium g* in Two-Population LB
In Couette flow a plain two-τ thermal LB keeps θ_max at 1.000 for every Pr. Adding the quasi-equilibrium g* recovers 0.498, 0.710, 1.000, and 1.997.
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.
At tau = 0.51 I read the viscosity 51x too high — the half step left behind by the discrete LBE
At tau=0.51 the lattice reads nu=0.00333, not 0.17. A second-order expansion drops Delta t/2 from tau: that half step is a factor of 51.
Giving every species its own tau threw the total mass off by 16.8% — correction velocity in multicomponent LBM
Different taus make Fick fluxes miss zero. Over 2000 steps a three-species LBM drops the worst mass defect from 0.168 to 0.0005.
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.
Doubling τ Left Pr at 1.0000 — The Two Constants Locked Inside Thermal LBM
A single-distribution thermal LBM ties viscosity and thermal diffusivity to one τ, locking Pr at 1. I measured on D2Q9 what a second distribution unlocks.
ρ and u Agree to the Last Digit While the Strain Rate Swells 45% — Nonequilibrium Rescaling at an LBM Refinement Interface
Copying distribution functions across an LBM AMR level interface keeps ρ and u exact but inflates the stress by up to 2x. I measured the rescale factor.
Raise the Velocity, Lose 27% of Your Diffusion — The Extra Flux in LBM Convection-Diffusion
Set D through tau in a lattice Boltzmann convection-diffusion model and it still spreads at D(1-u²/cs²). Where Chapman-Enskog drops the extra flux, and the source term that erases it.