OBSERVATION CONTRACT
Density, not decorative smoke
Every square stores an Eulerian density ρ. Conservative face fluxes carry it across the periodic cell domain. The canvas shows the field; the readouts certify mass, bounds, and finite values.
OBSERVATION CHAMBER / ACTIVE
Volumetric Advection Field
Observe a conserved 2D density field as a divergence-free velocity carries it through diffusion and decay.
flow / advection
Observation Model
DENSITY / CONSERVATIVE TRANSPORT
A density field carried by a closed velocity field
Start the field and watch cell density move while the diagnostics stay visible.
Each cell stores ρ. The velocity is derived from a stream function, so its discrete divergence is checked rather than drawn as smoke.
The field is ready. Press START or STEP to advance it.
- Mass ρ dA
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- Centroid x · y
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- Variance
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- Max ρ
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Canvas 2D is required for this observation. The numerical contract remains available through the model API.
Conservation and numerical health
FINITE- Advective flux
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- Diffusive flux
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- Vorticity RMS
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- Dissipation
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- Divergence RMS
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- CFL / Fourier / λdt
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- Applied source ΔM
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- Clipped source
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WHAT TO WATCH
One update has several signatures
- Advection changes shape while closed-face mass stays fixed.
- Diffusion widens the field; decay lowers mass with slope
−λ. - Vorticity belongs to
u; dissipation belongs to the density gradients and decay.
MODEL NOTE
Finite-volume balance
∂tρ + ∇·(uρ) = κ∇²ρ − λρ + s
u = ∇⊥ψ with a periodic stream function, so ∇·u = 0. Source clipping is reported separately when ρ reaches its upper bound.
OBSERVATION POLICY
This chamber runs a deterministic finite-volume density model in your browser. The field, settings, calculations, and images stay local. It does not measure visitors, devices, or physical fluids.
Route
This chamber belongs to Fields in Motion.
FIELD Back to Fields in Motion Route.