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.
Water's 1625 m/s Sound Speed Became 18 m/s in the Pressure Subsystem — Where Toro–Vázquez Splitting Moves the Stiffness
At 1 bar, water's split wave speed A is 18.44 m/s, not the 1624.9 m/s sound speed. A/c is 0.011, so the stiffness now sits between the two IMEX steps.
The bill for a 1001x larger time step — why a semi-implicit pressure scheme is not L∞ stable
A semi-implicit pressure scheme drops sound speed from the CFL limit and gains a 1001x step at M = 0.001. The discontinuity oscillation does not decay.
The Mach Number Goes to Zero, the Time Step Doesn't Budge — Reproducing an IMEX TVD Scheme
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
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] Stop letting sound speed swallow your CFL — Peluchon (2017) acoustic-transport IMEX
Liquid at 1500 m/s and flow at 5 m/s force a 0.67 μs explicit step on a 1 mm cell. The acoustic split leaves the outer CFL on flow speed.
[Paper Review] When the Sound Speed Diverges and the Time Step Survives — Orlando–Bonaventura (2024) AP-IMEX for Non-Ideal Gases
An AP-IMEX-DG scheme that frees the time step from the sound speed across all Mach numbers and any EOS, reproduced in NumPy.