Comparison of the temperature and population distributions obtained by two versions of the MURaM code. The left column shows results from the previous version, while the right column presents results from the updated version. The first row displays the temperature distribution, while the second, third, fourth, and fifth rows show the population fractions of level 1, level 2, level 3, and protons, respectively, where n_p is the proton number density and n_H is the total hydrogen number density. To compare the extended height of the incompletely ionized region, a reference line is provided in panels (c), (d), (i) and (j). The previous version assumes R_lu = R_ul = 0 for the Lyman series and computes radiative cooling using an empirical recipe, whereas the updated version calculates the Lyman-α and β lines rate coefficients and the associated radiative heating and cooling through solving the RT equation. The time corresponding to the simulated data is t = 20 s