Changing only τ changed the density of a gas at rest — the (τ−½)² stress of Shan–Chen velocity-shift forcing
·6 min read
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.
Where Half the Force Goes in LBM — Four Forcing Schemes and 1−1/(2τ)
·10 min read
Steady Poiseuille gives the same error for five LBM forcing schemes. At τ=0.6, the half-shift alone inflates the amplitude by a factor of 1.83.