| Abstract | 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 particular, in this framework, we introduce a suitable influence function able to provide a nonlocal interaction between material particles; moreover, 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. |
| Text | 482007 2023 10.1016/j.camwa.2023.04.032 Scopus 2 s2.0 85154567036 Richards equation Peridynamic Nonlocal model Spectral Numerical Method A numerical method for a nonlocal form of Richards equation based on peridynamic theory Berardi M.; Difonzo F.V.; Pellegrino S.F. Istituto di Ricerca sulle Acque, Consiglio Nazionale delle Ricerche, via F. de Blasio 5, Bari, 70132; Dipartimento di Matematica, Universita degli Studi di Bari Aldo Moro, Via E. Orabona, 4, Bari, 70125, Dipartimento di Matematica, Universita degli Studi di Bari Aldo Moro, Via E. Orabona, 4, Bari, 70125, Italy; Dipartimento di Ingegneria Elettrica e dell Informazione, Politecnico di Bari, Via E. Orabona, 4, Bari, 70125, Dipartimento di Ingegneria Elettrica e dell Informazione, Politecnico di Bari, Via E. Orabona, 4, Bari, 70125, Italy 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 particular, in this framework, we introduce a suitable influence function able to provide a nonlocal interaction between material particles; moreover, 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. 143 Published version http //www.scopus.com/record/display.url eid=2 s2.0 85154567036 origin=inward Articolo in rivista Pergamon Press. 0898 1221 Computers mathematics with applications 1987 Computers mathematics with applications 1987 Comput. math. appl. 1987 Computers mathematics with applications. 1987 marco.berardi BERARDI MARCO DTA.AD002.772.001 MENTOR ModElliNg waTer resOuRces |
