Dividing the Reverse Rate by Kp Split 99.6% of AlO at 2500 K — The (p°/RT)^Δn Hidden in the Equilibrium Constant
Plugging Kp into kr = kf/K skews the equilibrium of any reaction with Δn≠0 by (p°/RT)^Δn. An AlO dissociation reactor reproduces the SI and CGS versions of the mistake.
Shuffling Cell Numbers Made LU-SGS 2.8× Slower — RCM Reordering and the Start Cell That Sets Sweep Direction
Shuffling cell numbers on a 576-cell grid pushed LU-SGS from 9 iterations to 25. RCM cuts bandwidth to 24, but the start corner still splits 9 from 21.
Cutting Distance Checks 574x Lost 104 Contacts — One Grain Sets the DEM Sector Size
Sector pruning in DEM neighbor search is only safe when shell·s exceeds d_max, and 2400 agglomerating grains show exactly what a shorter reach costs.
Moving refine one line below stream cost a 7.2x error — the recursive time cycle of LBM AMR
Moving refine below stream on the same LBM grid raises the L2 error from 0.657% to 4.704%, a factor of 7.2, and the excess sits on the seam.
Quadtree AMR — Letting the Mesh Grow Where It Needs To
Level-7 uniform needs 128 cells; one Gaussian keeps 41 leaves, about 32 percent. A quadtree, slope threshold tau, and a 2:1 rule decide which cells split.
When Lax–Wendroff Shook at a Step — Building a 2nd-Order TVD Advection Scheme with Flux Limiters
At CFL 0.5 and 500 steps, Lax–Wendroff overshoots a unit step by 0.181. minmod, van Leer, and MC stay at zero overshoot on the same pulse.
Choosing a CFD Linear Solver: Comparing Convergence Speeds from Jacobi to BiCGSTAB
On a 60-unknown Poisson system Jacobi is still at residual 2.11e-2 after 2000 sweeps, while CG reaches 1.87e-13 in exactly 60 steps.
Solving Wall Distance in O(N log N): Eikonal Equation and Fast Marching
Ten million cells and half a million walls mean five trillion distance checks. Fast Marching solves that wall distance as an Eikonal problem in O(N log N).