Accretion disc outbursts: a new version of an old model
  We have developed 1D time-dependent numerical models of accretion discs, using an adaptive grid technique and an implicit numerical scheme, in which the disc size is allowed to vary with time. The code fully resolves the cooling and heating fronts propagating in the disc. We show that models in which the radius of the outer edge of the disc is fixed produce incorrect results, from which probably incorrect conclusions about the viscosity law have been inferred. In particular we show that outside-in outbursts are possible when a standard bimodal behaviour of the Shakura-Sunyaev viscosity parameter alpha is used. We also discuss to what extent insufficient grid resolutions have limited the predictive power of previous models. We find that the global properties (magnitudes, etc. ...) of transient discs can be addressed by codes using a high, but reasonable, number of fixed grid points. However, the study of the detailed physical properties of the transition fronts generally requires resolutions which are out of reach of fixed grid codes. It appears that most time-dependent models of accretion discs published in the literature have been limited by resolution effects, improper outer boundary conditions, or both. 
Jean-Marie Hameury, Kristen Menou, Guillaume Dubus, Jean-Pierre   Lasota, and Jean-Marc Hure