Application of Differential Transform Method for Solving Free-Surface Seepage Problem of One-Dimensional Porous Media

مهندسی عمران فردوسی

Article 1, Volume 37, Issue 1 - Serial Number 45, April 2024, Pages 1-18   

Document Type: Original Article

DOI: 10.22067/jfcei.2024.82170.1226

Authors

Mohammad Saleh Baradaran¹; Ahmad Aftabi Sani^{* 2}; Saeed abrishami²

¹Department of Civil Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran

²Department of Civil Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

Abstract

Several numerical methods, such as finite difference, finite volume, finite element, and so on, have been utilized to solve the problem of the free surface seepage in one-dimensional and two-dimensional domains. The governing equation of the seepage problem in porous media is the well-known Laplace equation. The finite difference and finite element methods are based on meshing the desired surface and obtaining the head values at this level; and repeating this process until convergence is reached. In this paper, a new method is proposed to solve the one-dimensional free-surface seepage problem in one-dimensional water column based on the Taylor-series expansion, entitled Differential Transform Method (DTM). It should be mentioned, up to now, DTM is employed to solve the various form of differential equations, but it has not been used in seepage problems. For some verification purposes, the obtained results are compared with the well-known finite difference method, and the good agreement is observed. Moreover, the analytical solution of the problem is attained by the use of mathematical techniques and it is reported in the paper as an appendix.

Keywords

Differential transform method; porous media; Laplace equation; free surface seepage; extended pressure method

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