Research on the suspension-feeding apparatus of fishes has led recently to the identification of novel filtration mechanisms involving vortices. Structures inside fish mouths form a series of ‘backward-facing steps' by protruding medially into the mouth cavity. In paddlefish and basking shark mouths, porous gill rakers lie inside ‘slots’ between the protruding branchial arches. Vortical flows inside the slots of physical models have been shown to be important for the filtration process, but the complex flow patterns have not been visualised fully. Here we resolve the three-dimensional hydrodynamics by computational fluid dynamics simulation of a simplified mouth cavity including realistic flow dynamics at the porous layer. We developed and validated a modelling protocol in ANSYS Fluent software that combines a porous media model and permeability direction vector mapping. We found that vortex shape and confinement to the medial side of the gill rakers result from flow resistance by the porous gill raker surfaces. Anteriorly directed vortical flow shears the porous layer in the centre of slots. Flow patterns also indicate that slot entrances should remain unblocked, except for the posterior-most slot. This new modelling approach will enable future design exploration of fish-inspired filters.