A 1% Error in Diameter Is a 4% Error in Flow Rate — Half a Cell of Wall and Poiseuille's Constant
·8 min read
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.
Three at a wall, five at a corner — counting the populations an LBM boundary node loses
·8 min read
After streaming, empty populations at an LBM node equal the solid cells around it: three on a flat wall, five in a concave corner, one on a convex corner.
In Lattice Boltzmann, the Wall Isn't on the Node — Bounce-Back and Zou-He Boundaries
·6 min read
Half-way bounce-back puts the wall a half-cell off the node. Couette speed is U(j+1/2)/ny. Height ny-1 leaves friction bias that refinement never clears.
How to Make an Outflow Stop Reflecting Sound — Navier–Stokes Characteristic Boundary Conditions
·6 min read
A six-hour LES drifted 0.3 bar because the outlet reflected sound. NSCBC sets the incoming wave with σ near 0.25 so acoustics leave and the mean holds.