to a much more unstable disc between $R_0 = 0-14.47$ kpc (dotted curve in Fig. \[Q\]).\
To form gravitationally bound clumps, an efficient cooling is needed [@Gammie:2001hv; @Dekel:2009bn]. This is ensured by the isothermal EoS, which keeps the temperature at $10^4$ K at all densities.

Numerical considerations {#subsec:Numerical considerations}
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To avoid artificial fragmentation in gravitationally collapsing gas, the Jeans length has to be resolved by at least four cells $N_{\mathrm{J}} = 4$ [@1997ApJ...489L.179T]. @Ceverino:2010eh found convergence in their simulations in clump numbers and masses by resolving the Jeans length with at least seven elements, $N_{\mathrm{J}} = 7$, at each refinement level.\
Furthermore, it is also crucial to resolve the mid-plane sufficiently, where the structures in the disc form first. Too low resolution cannot represent the higher densities there, which can lead to an unreasonable structure formation. Due to the Jeans length refinement and the density distribution of the disc, the initial AMR grid has a resolution gradient, with smaller cells in the galactic centre and larger ones at larger radius and height. The scaleheight is represented with at most two cells for $N_{\mathrm{J}} = 7$, and by increasing the number in test simulations, we found, that the ring-like structures 