A Two-Cell Interface Loses 39% of Its Surface Tension — The Anisotropy of the Korteweg Stress
Across a flat liquid–vapor interface the normal pressure stays constant and only the tangential pressure dips. That dip is surface tension, and a dz=1 lattice loses up to 39% of it.
[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.
I asked for σ₁₂ = 1.00 and got 0.78 — where an absent phase leaks into the interface in three-component Allen–Cahn
Fixing Σc = 1 with a mean projection in three-component Allen–Cahn lets the absent phase leak into the interface and cuts the realized surface tension by 21.9%. A triple-well penalty closes the gap.
[Paper Review] The Same Point Read 0.544 Apart Along Two Paths — Curl Involutions on a Staggered Grid
A staggered grid holds interface curl near 1e-12 for 400 steps. The collocated Rusanov run on the same shear opens a path gap of 0.544.
Pressure Jumped 21% in a Problem Where Nothing Should Happen — The Abgrall Criterion and the Nonconservative Term
Uniform pressure and velocity stop staying uniform because of the nonconservative term, not the flux. I remeasured Re-Abgrall's H_u operator on one grid.
Raise the Velocity, Lose 27% of Your Diffusion — The Extra Flux in LBM Convection-Diffusion
Set D through tau in a lattice Boltzmann convection-diffusion model and it still spreads at D(1-u²/cs²). Where Chapman-Enskog drops the extra flux, and the source term that erases it.
Un-smearing the Interface Every Step — Implementing Anti-Diffusion Sharpening (IST)
After 200 steps a helium bubble edge grows from 6 cells to 20. IST post-processing then locks that smeared thickness to the ratio of ε/a.
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.
Giving Each Phase Its Own Equations — The Baer–Nunziato Seven-Equation Model
The printed 324 bar is the 1.2 percent left after two huge stiffened-gas terms cancel. The first relaxation step is what pushes that leftover.
Why a Shout Above Water Never Reaches Below — Acoustics Across a Diffuse Interface
Near an air–water impedance ratio of 3600, about 99.9% of the sound reflects. The 13.4 degree critical angle is checked in a 1D tube.
[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.
5-Equation Model Implementation Guide: Building a Multiphase Flow Solver in Python
At volume fraction 0.5 the mixture sound speed is about 24 m/s. The same initial air is near 374 m/s and the water near 1625 m/s.
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.