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.
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.
I Dropped the −1/2 and the Viscosity Came Back Six Times Too Large — the Δt/2 Left Behind by LBM's Discretisation
One trapezoidal step and one change of variables leave a Δt/2 in viscosity, velocity, and stress. A scalar ODE and a D2Q9 lattice measure all three.
I Plugged in Pressure Directly and a Still Interface Started to Shiver — Two Forms of Nonideal LBM Forcing
Pressure-form and chemical-potential forcing agree for van der Waals in the continuum, then split on the lattice where the Gibbs-Duhem defect lives.
Where Half the Force Goes in LBM — Four Forcing Schemes and 1−1/(2τ)
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.