FluxLab

FPS: 0

Speed 1.0x

Vector Field

P(x, y)

Q(x, y)

Parametric Curve

x(t)

y(t)

t min

t max

Enable Parameter (a)

Simulation

Particle Count 1500

Enable Grid Balancing

Resample Rate 4.0%

Substeps 1

Domain Size 5.0

Integrator

Boundary Mode

Visuals

Show Field Grid Show Particles Show Curve Show Normals Show Crossings Particle Trails Cursor Probe

How it works

Particles move according to the vector field F(x, y) = (P(x, y), Q(x, y)). Flux is the net flow across the curve C(t) = (x(t), y(t)). This is estimated based on the number of particles crossing the curve, normalized by the particle density and simulation time. The crossing direction determines whether they contribute positively or negatively to the flux.

Theoretical Flux

Φ = ∫_C F · n ds

Simulation Estimate

Φ ≈ Net Crossings / (Density × Time)

Math Expressions

Use variables x, y, t, a and constants like pi, e. Functions: sin, cos, tan, exp, log, sqrt, abs, pow, atan2.

Preset Verification

Vortex + Circle:
F = (y, -x), C = (2cos t, 2sin t)
Φ = ∮ F · n ds = 0

Source + Circle:
F = (x, y), C = (2cos t, 2sin t)
Φ = ∮ F · n ds = 8π ≈ 25.13