[Paper Review] The Pressure Went Implicit and Δt Still Shrank 100× — the Second 1/M² Hiding in the Relative Velocity
·8 min read
In an isentropic two-phase all-Mach split, the enthalpy jump hides a second 1/M². The CFL stays tied to Mach until that term is integrated implicitly too.
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.
[Paper Review] Not Killing Sound at Low Mach — An AP IMEX Wave Scheme
·6 min read
At ε=0.01 on 64 cells the upwind amplitude falls to 1.980e-7 after 12800 steps, while the implicit AP value stays 1.00. The loss scales as 1/ε.
[Paper Review] When the Sound Speed Diverges and the Time Step Survives — Orlando–Bonaventura (2024) AP-IMEX for Non-Ideal Gases
·6 min read
An AP-IMEX-DG scheme that frees the time step from the sound speed across all Mach numbers and any EOS, reproduced in NumPy.