Forecasting water content dynamics in heterogeneous porous media has significant interest in hydrological applications; in particular, the treatment of infiltration when in presence of cracks and fractures can be accomplished resorting to peridynamic theory, which allows a proper modeling of non localities in space. In this framework, we make use of Chebyshev transform on the diffusive component of the equation and then we integrate forward in time using an explicit method. We prove that the proposed spectral numerical scheme provides a solution converging to the unique solution in some appropriate Sobolev space. We finally exemplify on several different soils, also considering a sink term representing the root water uptake.

翻译：预测非均匀多孔介质中水分含量动态变化在水文应用中具有重要意义；特别地，借助近场动力学理论可处理存在裂缝和裂隙时的入渗问题，该理论能够实现空间非局部性的合理建模。在此框架下，我们对方程扩散分量采用切比雪夫变换，随后使用显式方法进行时间向前积分。我们证明所提出的谱数值方案在适当的Sobolev空间中收敛至唯一解。最后，我们通过多种不同土壤实例进行验证，同时考虑了代表根系吸水的汇项。