Numerical simulation models of water flow in variably saturated soils are important tools in water resource management, assessment of waterrelated disasters and agriculture. Richards equation is one of the most used models for the fluid flow simulation into porous media. It is a partial differential equation whereby analytical solutions are only possible after applying a number of restrictive assumptions. Therefore, the derivation of efficient numerical schemes for its approximated solution has to be computed by discretization methods. We propose a numerical procedure considering a simplified linearization scheme that makes it adaptable to parallel computing. A comparison in computational performances with three other numerical procedures is detailed for a large computation, including the assessment of the landslide hazard in real areas. We demonstrate the efficiency of the proposed numerical procedure by comparing the results we obtained with a parallel code.

A numerical solution of Richards equation: a simple method adaptable in parallel computing / Egidi, N.; Gioia, Eleonora; Maponi, P.; Spadoni, L.. - In: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS. - ISSN 0020-7160. - 97:1-2(2020), pp. 2-17. [10.1080/00207160.2018.1444160]

### A numerical solution of Richards equation: a simple method adaptable in parallel computing

#### Abstract

Numerical simulation models of water flow in variably saturated soils are important tools in water resource management, assessment of waterrelated disasters and agriculture. Richards equation is one of the most used models for the fluid flow simulation into porous media. It is a partial differential equation whereby analytical solutions are only possible after applying a number of restrictive assumptions. Therefore, the derivation of efficient numerical schemes for its approximated solution has to be computed by discretization methods. We propose a numerical procedure considering a simplified linearization scheme that makes it adaptable to parallel computing. A comparison in computational performances with three other numerical procedures is detailed for a large computation, including the assessment of the landslide hazard in real areas. We demonstrate the efficiency of the proposed numerical procedure by comparing the results we obtained with a parallel code.
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Descrizione: This is an Accepted Manuscript of an article published by Taylor & Francis in International Journal of Computer Mathematics on 1 February 2020, available at: https://doi.org/10.1080/00207160.2018.1444160.
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11566/269484`