Does hydroxyl radical chemistry in air quality models create numerical stability problems?
The hydroxyl radical chemistry is not modeled explicitly in air quality models, so numerical stability is not an issue.  Instead, OH is held in pseudo-steady-state.  For instance, see CMAQ's documentation which states:


  In CMAQ's gas phase, OH is assumed to be in pseudo-steady state, and it is not a transported species.  This is because hydroxyl radical reactions tend to be catalytic (e.g., consumption and production). In the aqueous phase chemistry, OH is absorbed by cloud water and in an open cloud model (i.e., the design approach currently employed), absorbed species (e.g., OH) would be replenished via gas-to-cloud partitioning. However, due to operator splitting, aqueous and gas-phase chemistry are not solved simultaneously. To account for this and other uncertainties in predicted OH aqueous phase concentrations (e.g., neglect of production reactions (H2O2 + hv -> 2 OH) not currently implemented in aqchem), a steady-state assumption for OH is adopted in the aqueous chemistry routine.


Typically, if you are trying to model something like the hydroxyl radical, you would use a box-model like MECCA, not a chemical transport model.