A Steady-State Preconditioner Inside a Dual-Time Loop Took 19× More Inner Iterations — A Low-Mach Acoustic Pulse Test
Put a Weiss–Smith preconditioner into physical time and the acoustic pulse freezes in place. Put it inside dual time and the answer returns, but inner iterations jump from 16 to 305.
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.
At acoustic CFL 10 the preconditioner multiplied the error by 100 every sweep — the one arrow a block preconditioner throws away
Block Gauss-Seidel discards a pressure-velocity feedback whose gain is exactly the acoustic CFL squared. A 1D acoustic model measures the cost.
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.
Letting Sound and Matter Flow Separately — Acoustic-Convective Splitting (Lagrange-Projection)
At M=0.02 the acoustic band stays 2c wide while convection crawls. Feeding R back into the upwind step holds the momentum error at 2.2e-16.
[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] Why Roe breaks at low Mach — Hope–Collins (2022) and three artificial-diffusion scalings
At Mach 0.01 the convective scaling leaves amplitude 0.018. Acoustic and mixed scalings still hold 0.974 and 0.971 after one acoustic period.
[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.