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.
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.
One node pushed the error from 0.21% to 76% — local relaxation time in power-law LBM
One centreline node asks for infinite tau at n=0.6. Cap it near 4 and L2 error stays near 0.21%; leave it and that node drives the error to 76%.
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.
A 1% Error in Diameter Is a 4% Error in Flow Rate — Half a Cell of Wall and Poiseuille's Constant
Pipe flow rate rides on the fourth power of the diameter. The same exponent explains a mesh with the wall half a cell off and Poiseuille's 1838 tubes.
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.
Viscosity Is Not What Kills a Vortex — Newton's 1/r and the Lamb–Oseen Core
At r=0.5 the speed is unchanged to four decimals after 50 diffusion times. At n=1 the viscous force is zero; only a wall removes circulation.
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.