The characteristics-based ssolution. It is easy to verify thatectional method (CBSM) offers an Eulerian description of an internally mixed aerosol. It was shown to be robust and capable of exact preservation of lower order moments, allowing for highly skewed sectional droplet size distributions. In this paper we apply CBSM to a spatially varying flow, by incorporating the fractional step method. In this way an accurate time integration of the spatial terms in the transport equations for the velocity, mass fractions and sectional droplet concentrations is achieved. Integrating CBSM into the compressible PISO (Pressure-Implicit with Splitting of Operators) algorithm allows for phase change and corresponding changes in pressure. We apply CBSM to a lid-driven cavity flow. First, the steady state isothermal flow solution is validated against published data. Next, by releasing a saturated vapor into the cavity while cooling the walls, we simulate the formation of aerosol. The accuracy of the solution is studied, as well as the performance of the CBSM scheme in the spatially varying context. The solution of the velocity is shown to be accurate, even at CFL (Courant-Friedrichs-Lewy) numbers of unity. The feasibility of the developed method is demonstrated in a 3D complex geometry studying the aerosol generation via nucleation of hot vapors cooled by a dilution stream of cold air in a double-mixing tee system. The sectional approach delivers detailed information about the aerosol formation and size distribution of the droplets in the domain.