Changing One Relaxation Factor Moved the Converged Solution — Where Rhie–Chow Face Velocities Remember Under-Relaxation
In SIMPLE, cutting α_u from 0.7 to 0.3 changes the converged velocity. Standard Rhie–Chow keeps α_u on the damping term; Majumdar's face store removes it.
Upgrading Only the Viscous Term to Second Order Made the Error 1.82x Worse — Why the Semi-Implicit Gear Scheme Extrapolates Convection
Pairing BDF2 with convection at N^n drops the scheme to first order and inflates the error. The extrapolation 2N^n − N^(n−1) restores second order.
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.
A Wall the Grid Never Sees — IBM Delta Kernels and Multi-Direct Forcing
One forcing pass leaves 64% of free-stream slip on a cylinder. At Δs/h = 3 the gap slip hits 0.287, and at 0.25 the condition number reaches 1e11.
When Pressure Rings in a Checkerboard — SIMPLE and Rhie-Chow Coupling
On a 48-cell periodic line the naive stencil keeps a checkerboard of 0.80, while Rhie-Chow drives the same sawtooth down to 3.1e-16.
The Man Who Erased Pressure — Chorin's Projection Method and Fractional Step
After the predictor the divergence sits near 1e-2. One FFT projection drops it to 1e-13, and the pressure Poisson still takes most of the step.