Stirling engine regenerators are sometimes fabricated by stacking screens of randomly distributed wires within a duct. Such regenerators are modeled as porous media with a high void volume. Gaps may appear between the porous medium and duct walls due to radial expansion of duct walls or compression of the porous medium. In this paper, a model to characterize steady flow through three different porous media geometries is presented: no gap, with a gap that runs over the upstream half of the regenerator length, and with a gap over the downstream half of the regenerator length. Our objective is to describe the influence of axial location of the gap on the flow through the regenerator by documenting the evolution of velocity and turbulence fields in the regenerator and the gap. Mean flow is assumed to be two-dimensional and axisymmetric, based on previous measurements from our lab taken under identical conditions. The resistance created by the presence of solid obstacles in the porous medium is captured using a sink term in the momentum equation. This sink term is provided by the Darcy-Forchheimer model, which is applied for flow components in both the axial and radial directions. Within the matrix, the computed Reynolds numbers based on hydraulic diameter and Darcy velocity indicate inertia-dominated flow having many of the characteristics of turbulent flow. To account for eddy transport within the pores, a uniform eddy transport model for dispersion within the matrix is used. This model has the same value for axial and radial direction eddy transport coefficients. In the gap, when Reynolds numbers based on gap height correspond to turbulent flow, the Shear Stress Transport (SST) k-ω turbulence closure model is employed. At the interface between the porous medium and the gap, velocity gradients remain continuous. The computation was carried out using the commercial finite volume code FLUENT and the dispersion model was handled via FLUENT User Defined Functions (UDF). The computational model is validated by comparing the computed velocity profiles at the exit plane to measured exit plane velocity profiles for the three gap geometries. Measurements of velocities and turbulence quantities inside the porous medium and gap are unavailable. For the no-gap and the downstream gap cases, the model shows good agreement with the measured exit plane velocity profiles. The computed exit plane velocity profile for the upstream gap case does not match well with the measured velocity profile. In the upstream gap case, the computation shows that the velocity in the gap is high and the fluid decelerates rapidly as it leaves the gap and enters the matrix. Under such conditions, it is conjectured that the closure model employed in the present computation fails to capture all features of the flow. Recommendations for future work on improving these computations are proposed.