Abstract. The dissolution of semi-volatile inorganic gases such as ammonia and nitric acid into the aerosol aqueous phase has an important influence on the composition, hygroscopic properties, and size distribution of atmospheric aerosol particles. The representation of dissolution in global models is challenging due to inherent issues of numerical stability and computational expense. For this reason, simplified approaches are often taken, with many models treating dissolution as an equilibrium process. In this paper we describe the new dissolution solver HyDiS-1.0, which was developed for the global size-resolved simulation of aerosol inorganic composition. The solver applies a hybrid approach, which allows for some particle size classes to establish instantaneous gas-particle equilibrium, whereas others are treated time dependently (or dynamically). Numerical accuracy at a competitive computational expense is achieved by using several tailored numerical formalisms and decision criteria, such as for the time- and size-dependent choice between the equilibrium and dynamic approaches. The new hybrid solver is shown to have numerical stability across a wide range of numerical stiffness conditions encountered within the atmosphere. For ammonia and nitric acid, HyDiS-1.0 is found to be in excellent agreement with a fully dynamic benchmark solver. In the presence of sea salt aerosol, a somewhat larger bias is found under highly polluted conditions if hydrochloric acid is represented as a third semi-volatile species. We present first results of the solver's implementation into a global aerosol microphysics and chemistry transport model. We find that (1) the new solver predicts surface concentrations of nitrate and ammonium in reasonable agreement with observations over Europe, the USA, and East Asia, (2) models that assume gas-particle equilibrium will not capture the partitioning of nitric acid and ammonia into Aitken-mode-sized particles, and thus may be missing an important pathway through which secondary particles may grow to radiation- and cloud-interacting size, and (3) the new hybrid solver's computational expense is modest, at around 10 % of total computation time in these simulations.