The science
Cars are conserved, so the density ρ(x,t) obeys a conservation law with flux q = ρ v(ρ):
∂ρ/∂t + ∂q/∂x = 0
Greenshields: v = v_max (1 - ρ/ρ_max)
q = v_max ρ (1 - ρ/ρ_max), q_max = v_max ρ_max / 4
Disturbances travel at c = dq/dρ = vmax(1 - 2ρ/ρmax), which turns negative above ρmax/2, so a jam front moves backwards against the traffic. A step ρL → ρR (ρL < ρR) forms a shock with the Rankine-Hugoniot speed s = (qR - qL)/(ρR - ρL); a drop forms a rarefaction fan with exact profile ρ = ρmax(1 - x/(vmaxt))/2. The checks above run the same solver against both exact solutions and against vehicle conservation on the ring.
Scheme: first-order Godunov (demand/supply fluxes), CFL 0.9, periodic ring of 300 cells over 3 km. Honest limits: shocks are smeared over a few cells; there are no lanes, reaction times or stop-and-go instability (that needs a car-following model). The 60 cars are probes moving at the local speed, not to scale; the road is drawn about 16 m per scene unit, the cars are enlarged.
Compare: 2D twin of this page · straight-motorway shockwave lab · autonomous highway (car-following IDM) · on-ramp bottleneck and ramp metering. This page differs by using a closed ring, a 3D space-time wall and exact-solution validation.