and electrons have separate temperatures and instead only using a single temperature. I have tested this simplification by rerunning the model for the modern Earth’s upper atmosphere and find good agreement with the models presented in @Johnstone18. Another difference to the model is the chemical network which I have changed in two ways. Firstly, all chemical reactions and species that contain elements other than hydrogen and oxygen have been removed since I assume a purely H$_2$O gas at the lower boundary. Secondly, I have added chemical reactions and species involving deuterium; the reactions included in the model are taken from @LiangYung09 and @GarciaMunoz07, with additional XUV photoreactions taken from the PHIDRATES database (@HuebnerMukherjee15).

The model starts from a set of arbitrary initial conditions and evolves the state of the system forward in time by a large number of small timesteps until it reaches a steady state. The basic set of equations describing the evolution of the atmospheric properties is $$\label{eqn:main_speciescontinuity}
\frac{\partial n_j}{ \partial t} 
+ \frac{1}{r^2} \frac{\partial \left[ r^2 ( n_j v + \Phi_{\mathrm{d},j}) \right] }{\partial r} 
=
S_j ,$$ $$\label{eqn:main_momentum}
\frac{\partial ( \rho v ) }{ \partial t} 
+ \frac{1}{r^2} \frac{\partial \left[ r^2 \left( \rho v^2 + p \right) 