[Paper Review] MSTACS with Slope 3 Blew Up After 255 Steps at Co=0.5 — Compressive Differencing and the Courant Limit
We ran the compressive scheme of MSTACS eq. (18) on a 1D slab. Without redistribution it diverges above Co=0.44. The culprit is the product of the NVD slope k and the Courant number.
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.
Raising the time step 5x ran 1.9x faster; 10x ran no faster at all — the window implicit surface tension opens
At density ratio 1000, raising the capillary step 5x ran 1.9x faster. Pushing to 10x did not. Janodet et al. (2025) measured both walls.
[Paper Review] The Capillary Shackle Came Off and CFL 0.05 Was Still There — The Real Ceiling on VOF Interface Advection
Implicit surface tension breaks the capillary time-step limit, yet the compressive scheme carrying the color function caps the time step at CFL 0.05.
Why Droplet Simulations Get Trapped by Δt — Solving Surface Tension Implicitly
From N=64 to N=256, dt_sigma falls by 8. omega*dt_sigma stays 2.221 on every mesh, and explicit integration breaks past about 0.9 dt_sigma.
[Paper Review] Two-Phase Flow Without a Poisson Solver — Coupling the General Pressure Equation with MSTACS
Raising artificial sound speed from 5 to 15 cuts the stable step by three. OS-MSTACS lists a volume error E_G of 6.57e-8, four orders under OS-CICSAM.
Interface Capturing Methods: VOF vs Level Set vs Diffuse Interface
A conservative alpha update rings the pressure at a contact. The five-equation model leaves only alpha advection non-conservative, and equilibrium holds.