A comparison of modeling approaches for steady-state unconfined flow

The Dupuit-Forchheimer, the fully saturated flow, and the variably saturated flow models, are compared for problems involving steady-state, unconfined how through porous media. The variably saturated flow model is the most comprehensive of the three and requires more parameters. The performances of the three models are compared for different soil properties, problem dimensions, and how geometries. There are certain types of problems where the simpler models may yield satisfactory results. For soils with large pores and/or broad pore-size-density functions, the variably saturated how model solutions to steady-state problems approach those of the fully saturated flow model, owing to the manner in which the soil-water retention curve and relative permeability function, respectively, affect the variably saturated flow model solutions. For problems of significant size, the fully saturated how model may be sufficient, as the effects of the vadose zone are relatively diminished. For problems with radial symmetry (e.g. steady flow to a well), the fully saturated flow model performs well because the variably saturated flow model is relatively insensitive to the parameters describing the soil properties, as the amount of vadose zone how, compared with the total flow, is relatively insignificant in such problems.