Non-linear evolution of thermally unstable slim accretion discs with a diffusive form of viscosity

We are carrying out a programme of non-linear, time-dependent numerical cal culations to study the evolution of the thermal instability driven by radia tion pressure in transonic accretion discs around black holes. In our previ ous studies we first investigated the original version of the slim-disc mod el with low viscosity (alpha = 0.001) for a stellar-mass (10 M.) black hole , comparing the behaviour seen with results from local stability analysis ( which were broadly confirmed). In some of the unstable models, we saw a vio lently evolving shock-like feature appearing near to the sonic point. Next, we retained the original model simplifications but considered a higher val ue of alpha (=0.1), and demonstrated the existence of limit-cycle behaviour under suitable circumstances. The present paper describes more elaborate c alculations with a more physical viscosity prescription and including a ver tically integrated treatment of acceleration in the vertical direction. Lim it-cycle behaviour is still found for a model with alpha = 0.1, giving a st rong motivation to look for its presence in observational data.