Details

Autor(en) / Beteiligte

• Freitas, Amauri A.
• Alfaro Vigo, Daniel G.
• Teixeira, Marcello G.
• Vasconcellos, Carlos A.B. de

Titel

Horizontal water flow in unsaturated porous media using a fractional integral method with an adaptive time step

Ist Teil von

• Applied Mathematical Modelling, 2017-08, Vol.48, p.584-592

Ort / Verlag

New York: Elsevier Inc

Erscheinungsjahr

2017

Quelle

Psychology & Behavioral Sciences Collection

Beschreibungen/Notizen

• •A new numerical scheme to solve the problem of horizontal infiltration is proposed.•The numerical results are consistent with experimental data.•This new scheme is 900% faster in some examples.•A comparison between our scheme, the fractional integral scheme and experimental data. Predicting the horizontal groundwater flow in unsaturated porous media is a challenge in many areas of science and engineering. The governing equation associated with this phenomenon is a nonlinear partial differential equation known as the Richards equation. However, the numerical results obtained using this equation can differ substantially from the experimental results. In order to overcome this difficulty, a new version of the Richards equation was proposed recently that considers a time derivative of fractional order. In this study, we present a numerical method for solving this fractional Richards equation. Our method comprises an adaptive time marching scheme that uses Picard iterations to solve the corresponding nonlinear equations. A computational code was implemented for the proposed method using the Scilab programming language. We performed numerical simulations of the anomalous diffusion of water in a white siliceous brick and showed that the numerical results were consistent with the available experimental data.