Drainage of circular foam films is much more rapid when it is asymmetric than when it is axisymmetric. Asymmetric drainage stems from a hydrodynamic instability produced by surface-tension-driven flow. It is opposed by surface viscosity, surface diffusivity, and system dimensions, which stabilize perturbations having short wavelengths. Numerical simulation of this instability is carried out. The results(1) clarify the conditions for applicability of a simplified linear stability analysis derived previously, (2) show clearly the circulating surface convection patterns that arise, and (3)confirm the rapid increase in drainage rate. The same instability is responsible for periodic convection patterns known as "marginal regeneration" in vertical soap films that also lead to rapid drainage.