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：预测非均质多孔介质中的水分动态在水文应用中具有重要研究价值；特别是采用近场动力学理论处理存在裂缝和裂隙时的入渗问题，该理论能够有效模拟空间非局部性。在此框架下，我们对方程中的扩散分量采用切比雪夫变换，随后利用显式方法进行时间向前积分。我们证明了该谱数值格式能在特定Sobolev空间中收敛至唯一解。最后以多种不同土壤为例进行数值验证，同时考虑了代表根系吸水的汇项。