Numerical Evaluation of Fractional Vertical Soil Water Flow Equations

Significant deviations from standard Boltzmann scaling, which corresponds to normal or Fickian diffusion, have been observed in the literature for water movement porous media. However, as demonstrated by various researchers, widely used conventional Richards equation cannot mimic anomalous diffusion and ignores features of natural soils are heterogeneous. Within this framework, governing equations transient flow media fractional time multi-dimensional soil space anisotropic were recently introduced authors coupling Brooks–Corey constitutive relationships with continuity motion equations. In study, instead utilizing relationships, empirical expressions, obtained least square fits through hydraulic measurements, utilized show suitability proposed approach other relations literature. Next, a finite difference numerical method was solve The applicability investigated numerically comparison their counterparts. practice, cumulative infiltration values deviate approximation, wetting front may not be consistent traditional estimates equation. such cases, better alternative mimicking physical process they can capture sub-, super-, normal-diffusive processes during infiltration.