Viscous Torque & Angular Momentum Transport in an Accretion Disk

Real accretion disks are not static rings — turbulent viscosity constantly exchanges angular momentum between neighbouring orbits, spreading gas outward while draining mass inward onto the central object. This simulator solves the Lynden-Bell & Pringle viscous diffusion equation for a narrow ring of gas on a live radial grid, using the standard Shakura-Sunyaev alpha-viscosity prescription ν = α h² √(GM R). Thousands of orbiting gas parcels are advected at the exact local radial drift velocity the equation predicts, so their inward and outward motion visualises the actual solved flow field rather than a scripted animation. Adjust the turbulence strength α and disk thickness h to see how efficiently angular momentum is transported, and track the elapsed viscous time, instantaneous accretion rate, and the radius containing 90% of the disk's remaining mass as the ring spreads and drains.