Mass Is Conserved Exactly, Yet the Density Is Negative — The Positivity-Preserving Flux Limiter
·9 min read
At CFL 0.45 a limiter-off double rarefaction dies at step 2: density 0.37, pressure -0.163. One θ per face blends LF and the high-order flux.
The Mach Number Goes to Zero, the Time Step Doesn't Budge — Reproducing an IMEX TVD Scheme
·11 min read
At Mach 10^{-4} the time step stays on the convective CFL. Pure second-order IMEX overshoots by about 0.4 unless theta is held to sqrt(2)-1 or below.
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.