“Turbulence is the most important unsolved problem of classical physics.”
Field notes from a compressible multiphase CFD researcher
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Choose your first route
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.
Start this routeVerify it in OpenFOAM
Set up a backward-facing step and read the resulting recirculation region.
Start this routeTop posts this week
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Pushing the Frame to 0.2 Cut the Viscosity by 5.97% — The Missing Third Moment in LBM Equilibria
On D2Q9, Σf c³ equals ρu for any distribution you can write. The missing ρu³ breaks Galilean invariance and makes measured viscosity depend on the frame.
49.9% of the Dynamic Coefficients Came Out Negative — the Germano Identity and the Averaging Operator
Measuring the Smagorinsky coefficient with the Germano identity returns a negative value at half the grid points. Where the average is taken decides stability.
One Integral Read as 0.1406 and 56.91 — Torsion Stress Function and Duct Laminar Flow
A square bar's torsion constant and a square duct's f·Re are one Poisson solution read twice. One linear-triangle FEM run gives both handbook numbers.
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.
27 of 1,681 Voxels Flipped Inside Out — Ray Parity and Link Cutting in STL Voxelization
Turning an STL into an LBM voxel grid takes four stages: octree culling, SAT overlap tests, ray parity, and the per-link cut fraction q, verified in code.
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.
[Paper Review] Two Fragments Flew Together Instead of Pushing Apart — The 144° Equilibrium of a Mach 20 Sphere Pair
At Mach 20 two touching spheres align at one angle and generate lift together instead of repelling. A Newtonian approximation pins that angle down.
Doubling τ Left Pr at 1.0000 — The Two Constants Locked Inside Thermal LBM
A single-distribution thermal LBM ties viscosity and thermal diffusivity to one τ, locking Pr at 1. I measured on D2Q9 what a second distribution unlocks.
Where Total Pressure Dropped 1,080 Pa, Dissipation Was Zero — When the Bernoulli Constant Crosses Streamlines
Inside a spinning vortex core the total pressure falls 1,080 Pa while viscous dissipation stays exactly zero. A Rankine vortex marks where a head deficit stops meaning loss.
ρ and u Agree to the Last Digit While the Strain Rate Swells 45% — Nonequilibrium Rescaling at an LBM Refinement Interface
Copying distribution functions across an LBM AMR level interface keeps ρ and u exact but inflates the stress by up to 2x. I measured the rescale factor.
A 1% Error in Diameter Is a 4% Error in Flow Rate — Half a Cell of Wall and Poiseuille's Constant
Pipe flow rate rides on the fourth power of the diameter. The same exponent explains a mesh with the wall half a cell off and Poiseuille's 1838 glass tubes.
A 30° rigid rotation read -13% strain — conjugate stress-strain pairs in large-strain shells
Rotation alone fabricates strain in the engineering measure, and a wrong stress-strain pairing shifts the internal work rate by 5% or 54%.