In this paper, an analytical model was proposed to describe the filtration process applicable to a base soil-filter system. The Navier-Stokes equation for porous media was used to capture the hydrodynamic behavior, while numerically a new algorithm has been proposed to solve the Navier-Stokes equation in non-linear form. The various mixtures of base particles eroded and water flow within the system was computed using the work-energy principle incorporating the constriction size of the filter. The model can assess the filtration process through the flow rate, and the accumulation and erosion of base soil within the filter. By discretising the base soil and filter domains into discrete elements, the model can predict the time dependent particle gradation of the filter for each element. Laboratory tests reported in other studies and those conducted by the Authors have verified the validity of the model, in relation to other available models.