“Turbulence is the most important unsolved problem of classical physics.”
Field notes from a compressible multiphase CFD researcher
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Three clear entry points for a first visit: foundations, compressible flow, or a hands-on case.
FDM, FEM and FVM compared
See what each discretization approximates, and what each method is built to preserve.
Start this routeRiemann problems and fluxes
Build from the origin of shock-wave calculations to the logic behind Godunov-type solvers.
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Set up a backward-facing step and read the resulting recirculation region.
Start this routeTop posts this week
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Velocity came out one sixth at τ=0.6 — dropping the half-force F/2 from Guo forcing
Keep the Guo source term but drop F/2 from the LBM velocity and the effective body force shrinks by (1−1/2τ). On Kolmogorov flow at τ=0.6 the amplitude is 0.166 of exact.
A Small Wobble in Mixture Fraction Drops the Mean Flame Temperature by 964 K — Presumed β-PDF and the Infinity at Z=0
At stoichiometric mean Z, the β-PDF mean temperature sits 964 K below T(Z̄). When a<1, a 100-cell uniform-grid integral also overshoots by 115 K. Here is why, with code.
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] 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.
[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.
Changing only τ changed the density of a gas at rest — the (τ−½)² stress of Shan–Chen velocity-shift forcing
Apply the same force to a resting D1Q3 gas column and only Shan–Chen forcing gives a τ-dependent density. The shifted equilibrium velocity leaves a fake (τ−½)²F²/ρ stress.
Dividing the Reverse Rate by Kp Split 99.6% of AlO at 2500 K — The (p°/RT)^Δn Hidden in the Equilibrium Constant
Plugging Kp into kr = kf/K skews the equilibrium of any reaction with Δn≠0 by (p°/RT)^Δn. An AlO dissociation reactor reproduces the SI and CGS versions of the mistake.
Halving the Grid Spacing Tripled the Error — What an Increment-Based Stopping Rule Hides in Jacobi Iteration
Stop Jacobi when the update drops below a tolerance and the error left behind grows as 1/(1-ρ) on finer grids. A 2D heat-conduction plate compares Jacobi, SOR and optimal ω.
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.
Giving Conduction Its Own τ Left Viscous Heating Stuck at Pr = 1 — The Quasi-Equilibrium g* in Two-Population LB
In Couette flow a plain two-τ thermal LB keeps θ_max at 1.000 for every Pr. Adding the quasi-equilibrium g* recovers 0.498, 0.710, 1.000, and 1.997.
[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.
[Paper Review] The Tetrahedron That Led With One Sphere Never Broke Apart — A Bluntness Index for Mach 20 Fragment Clusters
Four spheres at Mach 20 separate by tetrahedron attitude. Bluntness B and asymmetry A on 40,000 orientations show which number sets the split.