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：在水文应用中，预测异质性多孔介质中含水量动态具有重要意义；特别是在存在裂缝和断层情况下处理入渗时，可以利用Peridynamic理论进行适当的建模，它允许在空间中正确地建模非局部性。在这个框架中，我们利用Chebyshev变换对方程的扩散分量进行计算，然后使用显式方法向前积分时间。我们证明了所提出的谱数值方案提供了收敛于某些适当的Sobolev空间中独特解的解决方案。我们最后在几种不同的土壤上举例说明，还考虑了代表根水吸收的汇项。