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Forecasting water content dynamics in heterogeneous porous media hassignificant interest in hydrological applications; in particular, the treatmentof infiltration when in presence of cracks and fractures can be accomplishedresorting to peridynamic theory, which allows a proper modeling of nonlocalities in space. In this framework, we make use of Chebyshev transform onthe diffusive component of the equation and then we integrate forward in timeusing an explicit method. We prove that the proposed spectral numerical schemeprovides a solution converging to the unique solution in some appropriateSobolev space. We finally exemplify on several different soils, alsoconsidering a sink term representing the root water uptake.

A Numerical Method for a Nonlocal Form of Richards' Equation Based on Peridynamic Theory