<p>Foam injection in porous media is a promising technique for enhanced recovery and other industrial applications, but its modeling is complicated by instabilities in the computed foam apparent viscosity. This study investigates oscillations observed during foam displacement simulations. Mesh refinement demonstrates that increasing discretization reduces the amplitude of global oscillations in the average apparent viscosity; however, sharp local peaks persist at shock fronts and may intensify over time. These instabilities are not solely numerical artifacts but are linked to the mathematical structure of the foam model, particularly the presence of steep saturation fronts. We show that numerical diffusion, unavoidable in simulation frameworks, can amplify such effects. To address this issue, we introduce a filtering technique that reconstructs the water saturation profile in the vicinity of the shock without affecting convergence. The method effectively suppresses viscosity oscillations while maintaining physical accuracy near discontinuities.</p>