This paper jointly addresses numerical and physical challenges related to the modeling of coalescence filtration through vertical filter cartridges, put forth in the following papers by Starnoni, M. and C. Manes:

• Starnoni, M., & Manes, C. (2021). A multiphase multicomponent flow and transport model for liquid aerosol filtration in coalescence fibrous filters. Separation and Purification Technology, 266, 118574.

• Starnoni, M., & Manes, C. (2022). On the interplay between pressure and gravitational forces in coalescence filters. Journal of Aerosol Science, 105953.

In particular, it provides the multidimensional extension of the one-dimensional model presented in Starnoni and Manes (2021) to the general case where internal gravity-induced flows play an effective role. Key to the implementation is the decomposition of the moving oil volumes along the different directions proportionally to the dimensionless number SM, a new quantity introduced in Starnoni and Manes (2022) describing the interplay between the forces dictating the oil dynamics. To validate the implementation, an experimental setup available in the literature is replicated, showing very good agreement in terms of all relevant quantities, namely saturation, pressure drop and drainage volumes. A generalized ‘Network, Channel and Film’ model is also formulated, which extends the scope of application of the original Jump and Channel model by Kampa et al. (2014) to filters with coarser fibrous microstructure. In particular, the existence of an additional flow mechanism termed ‘network’ is postulated, which is characterized by a complex multidimensional oil patterns configuration spanning the entire filter’s height and evolving, in a macroscopic sense, along the direction identified by SM.