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Water 2017, 9(12), 954; https://doi.org/10.3390/w9120954

Transient Modeling of Flow in Unsaturated Soils Using a Novel Collocation Meshless Method

Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung 20224, Taiwan
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Received: 1 November 2017 / Revised: 1 December 2017 / Accepted: 4 December 2017 / Published: 7 December 2017
(This article belongs to the Special Issue Soil Water Conservation: Dynamics and Impact)
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Abstract

In this paper, a novel meshless method for the transient modeling of subsurface flow in unsaturated soils was developed. A linearization process for the nonlinear Richards equation using the Gardner exponential model to analyze the transient flow in the unsaturated zone was adopted. For the transient modeling, we proposed a pioneering work using the collocation Trefftz method and utilized the coordinate system in Minkowski spacetime instead of that in the original Euclidean space. The initial value problem for transient modeling of subsurface flow in unsaturated soils can then be transformed into the inverse boundary value problem. A numerical solution obtained in the spacetime coordinate system was approximated by superpositioning Trefftz basis functions satisfying the governing equation for boundary collocation points on partial problem domain boundary in the spacetime coordinate system. As a result, the transient problems can be solved without using the traditional time-marching scheme. The validity of the proposed method is established for several test problems. Numerical results demonstrate that the proposed method is highly accurate and computationally efficient. The results also reveal that it has great numerical stability for the transient modeling of subsurface flow in unsaturated soils. View Full-Text
Keywords: unsaturated soil; Richards equation; the Trefftz method; transient; the meshless method unsaturated soil; Richards equation; the Trefftz method; transient; the meshless method
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Ku, C.-Y.; Liu, C.-Y.; Xiao, J.-E.; Yeih, W. Transient Modeling of Flow in Unsaturated Soils Using a Novel Collocation Meshless Method. Water 2017, 9, 954.

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