Viscous Disk Spacetime Diagram & Radial Profiles (2D)

A purely 2D companion to the 3D orbiting-particle scene: instead of rendering gas parcels drifting through a 3D disk, this model solves the same Lynden-Bell & Pringle viscous diffusion equation on an independent radial grid and draws the raw numerical solution directly. A scrolling spacetime heatmap on the left shows how the surface density Σ(R,t) rises, spreads and drains at every radius over time, while the panel on the right plots the instantaneous density, viscous torque and radial drift velocity profiles that the same alpha-viscosity prescription ν = α h² √(GM R) produces. Tune the turbulence strength α and disk thickness h to watch the torque curve reshape and the drift velocity flip sign at the radius where infall gives way to outward spreading, and track the elapsed viscous time, instantaneous accretion rate, R90 mass radius and peak torque as the ring evolves.