  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.
