Compressible Multiphase

Compressible Multiphase Flow CFD: Why It's Hard, Why It Matters

Averaging gamma at a gas-liquid interface does not recover the pressure. Near half gas fraction, the mixture sound speed falls to about one hundredth.

2026.03.04

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.

2026.03.06

From the Riemann Problem to Godunov's Scheme - The Essence of Numerical Flux

Godunov flux comes from p* in a two-constant Riemann problem. Shock branches use a square-root f_K; rarefactions use an isentropic power.

2026.03.05

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.

2026.03.07

Rhie-Chow Interpolation for Compressible Multiphase Flows

At a water-air density ratio of 1000, the arithmetic mean density is 500.5 and the harmonic mean is 2.0. Filter only the driving pressure.

2026.03.10

Filling an Interface with a Fluid That Isn't There — The Ghost Fluid Method

Copy pressure across a sharp water-air interface, extrapolate density isentropically, and run a single-material solver twice. Stiffness makes it ring.

2026.06.05

Why Droplets Are Round and Water Climbs the Glass — Surface Tension and Contact Angle

A 5 µm droplet shows a 28800 Pa pressure jump, and a 0.1 mm tube at 30 degrees lifts water 127.1 mm under Jurin's law here.

2026.06.16

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.

2026.06.27

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.

2026.06.28

Why a Raindrop Is Not Tear-Shaped — The Weber Number and TAB Breakup

The TAB oscillator breaks a drop once the deformation y crosses 1. Undamped, that peak is 2·We/24, so the critical Weber number lands on 12.

2026.07.07

Why Laundry Dries at 5 °C — Diffusion-Limited Evaporation vs. Heat-Driven Boiling

Laundry dries at 5 °C because the interface vapor fraction is not zero. Boiling waits on heat, and the Lee coefficient r is a penalty, not a property.

2026.07.30

A 9% Smaller Drag Coefficient Left the Droplet 35% Slower — Where the Distortion and Vaporization Corrections Attach

Three drag-coefficient models — rigid sphere, TAB distortion, and Renksizbulut-Yuen vaporization — run on the same droplet and compared by penetration.

2026.09.08

Mobility Up 10×, Interface Width Unchanged — The Anti-Diffusion Term in Conservative Allen–Cahn

Why the anti-diffusion term cancels diffusion exactly, pinning interface width to W rather than to mobility, and where that term enters the LBM equilibrium.

2026.09.18

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.

2026.10.02

Adding a v Term to a v² Term Got Both Ends Right and Missed the Middle by 42% — Prony's Two-Term Drag Law and Re = 60

Bossut measured drag growing with v², Du Buat with v. Prony's sum a·v²+b·v hands over control at Re = 60 and overpredicts settling speed by up to 42% right there.

2026.10.20

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.

2026.10.26