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：在非均质多孔介质中预测水分含量动态在水文应用中具有重要意义；特别是，当存在裂缝和裂隙时，可借助近场动力学理论处理入渗问题，该理论能恰当地模拟空间非局部性。在此框架下，我们对方程中的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，所提出的谱数值格式能在适当的索伯列夫空间中给出收敛于唯一解的解。最后，我们以几种不同土壤为例进行验证，同时考虑了代表根系吸水的汇项。