01 / SPH · local support

A neighborhood becomes a liquid

Drag the gold probe through a bulk region, across its free boundary, and into the thin neck. Every neighbor contributes a different amount.

Smoothing length hParticle spacing

Mint particles contribute inside the gold support circle of radius 2h. The bars rank their individual contributions. A wider kernel reduces local variation but also spreads information across finer features.

—Kernel density ρ

—Supported neighbors

—Gradient magnitude

Equations and model boundary

ρ(x) = Σⱼ mⱼ W(|x − xⱼ|, h)
∇ρ(x) = Σⱼ mⱼ ∇W(x − xⱼ, h)

The cubic spline and its 2D normalization match the native SPH kernel. This probe computes interpolation and its gradient on prescribed particle positions; it does not advance pressure, viscosity or collisions. The native codimensional branch adds a tangent-aware treatment for thin filaments.