We are carrying out a programme of non-linear time-dependent numerical calculations to study the evolution of the thermal instability driven by radiation pressure in transonic accretion discs around black holes. In our previous studies we first investigated the original version of the slim-disc model with low viscosity (parameter alpha = 0.001) for a stellar-mass (10 solar masses) 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 violently evolving shock-like feature appearing near to the sonic point. Next, we retained the original model simplifications but considered a higher value of alpha = 0.1 and demonstrated the existence of limit-cycle behaviour under suitable circumstances. The present paper describes more elaborate calculations with a more physical viscosity prescription and including a vertically integrated treatment of acceleration in the vertical direction. Limit-cycle behaviour is still found for a model with alpha = 0.1, giving a strong motivation to look for its presence in observational data.
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