  Context. A crucial step in the numerical investigation of small-scale dynamos
in the solar atmosphere consists of an accurate determination of the magnetic
Prandtl number, Prm, stemming from radiative magneto-hydrodynamic (MHD)
simulations. Aims. The aims are to provide a reliable methodology for
estimating the effective Reynolds and magnetic Reynolds numbers, Re and Rem,
and their ratio Prm=Rem/Re (the magnetic Prandlt number), that characterise MHD
simulations and to categorise small-scale dynamo simulations in terms of these
dimensionless parameters. Methods. The methodology proposed for computing Re
and Rem is based on the method of projection on proper elements and it relies
on a post-processing step carried out using higher order accurate numerical
operators than the ones in the simulation code. A number of radiative MHD
simulations with different effective viscosities and plasma resistivities were
carried out with the CO5BOLD code, and the resulting growth rate of the
magnetic energy and saturated magnetic field strengths were characterised in
terms of Re and Rem. Results. Overall, the proposed methodology provides a
solid estimate of the dissipation coefficients affecting the momentum and
induction equations of MHD simulation codes, and consequently also a reliable
evaluation of the magnetic Prandtl number characterising the numerical results.
Additionally, it is found that small-scale dynamos are active and can amplify a
small seed magnetic field up to significant values in CO5BOLD simulations with
a grid spacing smaller than h=12 km, even at Prm=0.65. However, it is also
evident that it is difficult to categorise dynamo simulations in terms of Prm
alone, because it is not only important to estimate the amplitude of the
dissipation coefficients, but also at which scales energy dissipation takes
place.
