Raise the Velocity, Lose 27% of Your Diffusion — The Extra Flux in LBM Convection-Diffusion
·7 min read
Set D through tau in a lattice Boltzmann convection-diffusion model and it still spreads at D(1-u²/cs²). Where Chapman-Enskog drops the extra flux, and the source term that erases it.
Advecting Without Splitting Directions — The Bell-Colella-Glaz Unsplit Upwind Scheme
·7 min read
Directional splitting twists a diagonal scalar. Bell-Colella-Glaz keeps the rotating disk's peak with a (1-CFL) slope weight plus a transverse correction.
When FTCS Trembles, Upwind Goes Numb — First-Order Advection, Artificial Viscosity, and the CFL Trade
·4 min read
At c=0.8 the worst FTCS mode grows by about 1.28 each step. Upwind artificial viscosity drops to zero only when c equals 1.
When Lax–Wendroff Shook at a Step — Building a 2nd-Order TVD Advection Scheme with Flux Limiters
·6 min read
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.