Modelling Fractional Advection–Diffusion Processes via the Adomian Decomposition

Alberto Antonini () and Valentina Anna Lia Salomoni
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Alberto Antonini: Department of Civil, Environmental and Architectural Engineering, University of Padua, Via F. Marzolo 9, 35131 Padova, Italy
Valentina Anna Lia Salomoni: Department of Civil, Environmental and Architectural Engineering, University of Padua, Via F. Marzolo 9, 35131 Padova, Italy

Mathematics, 2023, vol. 11, issue 12, 1-30

Abstract: When treating geomaterials, fractional derivatives are used to model anomalous dispersion or diffusion phenomena that occur when the mass transport media are anisotropic, which is generally the case. Taking into account anomalous diffusion processes, a revised Fick’s diffusion law is to be considered, where the fractional derivative order physically reflects the heterogeneity of the soil medium in which the diffusion phenomena take place. The solutions of fractional partial differential equations can be computed by using the so-called semi-analytical methods that do not require any discretization and linearization in order to obtain accurate results, e.g., the Adomian Decomposition Method (ADM). Such a method is innovatively applied for overcoming the critical issue of geometric nonlinearities in coupled saturated porous media and the potentialities of the approach are studied, as well as findings discussed.

Keywords: fractional analyses; fractor; adomian decomposition; geomaterials; geometric nonlinearity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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