[Paper Review] Raising β to 2 froze the interface at 14 cells and made a sine worse than first-order upwind — Tallois's compressive limiter
With a β=2 compressive limiter on the volume fraction, a slab interface stays 14 cells wide after five periods. The same limiter gives a sine wave a larger L1 error than first-order upwind.
[Paper Review] Half Water, Half Air, and Sound Crawls at 24 m/s — The K∇·u Term in the Murrone–Guillard Five-Equation Model
A 50% air–water mix carries sound at 23.6 m/s, slower than either phase. Dropping K∇·u from the five-equation model makes the same pulse run at 745 m/s.
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.
I dropped K and the water compressed 1.86x too much — an interface error that refinement does not remove
Deriving the compressibility factor K of compressible VOF straight from the isobaric closure, then measuring how much liquid volume a zeroed or sign-flipped K shaves off in a 1D compression test.
[Paper Review] The Pressure Went Implicit and Δt Still Shrank 100× — the Second 1/M² Hiding in the Relative Velocity
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.
Fewer Equations, and It Stopped Blowing Up — The Four-Equation Model and the Interface Equilibrium Condition
A uniform pressure still shakes if Γ is advected conservatively. The four-equation model moves Γ non-conservatively and the error falls to roundoff.
[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] Solve with Two Pressures, Merge to One — Saurel (2009) on Multiphase Pressure Relaxation
How a six-equation non-equilibrium model with stiff pressure relaxation routes around the failures of the five-equation diffuse-interface model.
[Paper Review] Pick the Reconstruction with Smaller Jumps — Deng (2018) MUSCL-THINC-BVD
Deng (2018) builds MUSCL and THINC in every cell, then keeps the one with the smaller jump on the two faces. The rule is called BVD.