scholarly journals Assessment of water penetration problem in unsaturated soils

2009 ◽  
Vol 6 (3) ◽  
pp. 3811-3833 ◽  
Author(s):  
A. Barari ◽  
M. Omidvar ◽  
A. R. Ghotbi ◽  
D. D. Ganji
Keyword(s):  
Porous Media ◽  
Unsaturated Soils ◽  
Homotopy Perturbation Method ◽  
Unsaturated Flow ◽  
Variational Iteration Method ◽  
Environmental Engineering ◽  
Richards Equation ◽  
Proper Solution ◽  
Water Penetration ◽  
Homotopy Perturbation

Abstract. Unsaturated flow of soils in unsaturated soils is an important problem in geotechnical and geo-environmental engineering. Richards' equation is often used to model this phenomenon in porous media. Obtaining proper solution to this equation therefore provides better means to studying the infiltration into unsaturated soils. Available methods for the solution of Richards' equation mostly fall in the category of numerical methods, often having restrictions for practical cases. In this research, two analytical methods known as Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM) have been successfully utilized for solving Richards' equation. Results obtained from the two methods mentioned show a remarkably high precision in the obtained solution, compared with the existing exact solutions available.

scholarly journals Numerical analysis of Richards' problem for water penetration in unsaturated soils

2009 ◽  
Vol 6 (5) ◽  
pp. 6359-6385 ◽  
Author(s):  
A. Barari ◽  
M. Omidvar ◽  
A. R. Ghotbi ◽  
D. D. Ganji
Keyword(s):  
Porous Media ◽  
Numerical Analysis ◽  
Unsaturated Soils ◽  
Homotopy Perturbation Method ◽  
Unsaturated Flow ◽  
Variational Iteration Method ◽  
Environmental Engineering ◽  
Richards Equation ◽  
Water Penetration ◽  
Homotopy Perturbation

Abstract. Unsaturated flow of soils in unsaturated soils is an important problem in geotechnical and geo-environmental engineering. Richards' equation is often used to model this phenomenon in porous media. Obtaining appropriate solution to this equation therefore provides better means to studying the infiltration into unsaturated soils. Available methods for the solution of Richards' equation mostly fall in the category of numerical methods, often having restrictions for practical cases. In this research, two analytical methods known as Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM) have been successfully utilized for solving Richards' equation. Results obtained from the two methods mentioned show a remarkably high precision in the obtained solution, compared with the existing exact solutions available.

scholarly journals A Comparative Analysis of Fractional-Order Gas Dynamics Equations via Analytical Techniques

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1735
Author(s):  
Shuang-Shuang Zhou ◽  
Nehad Ali Shah ◽  
Ioannis Dassios ◽  
S. Saleem ◽  
Kamsing Nonlaopon
Keyword(s):  
Homotopy Perturbation Method ◽  
Graphical Representation ◽  
Analytical Techniques ◽  
Variational Iteration Method ◽  
Computational Techniques ◽  
System Of Nonlinear Equations ◽  
Gas Dynamics Equations ◽  
Homotopy Perturbation ◽  
Fractional System ◽  
Modified Forms

This article introduces two well-known computational techniques for solving the time-fractional system of nonlinear equations of unsteady flow of a polytropic gas. The methods suggested are the modified forms of the variational iteration method and the homotopy perturbation method by the Elzaki transformation. Furthermore, an illustrative scheme is introduced to verify the accuracy of the available techniques. A graphical representation of the exact and derived results is presented to show the reliability of the suggested approaches. It is also shown that the findings of the current methodology are in close harmony with the exact solutions. The comparative solution analysis via graphs also represents the higher reliability and accuracy of the current techniques.

scholarly journals MEASUREMENT OF PREFERENTIAL FLOW DURING INFILTRATION AND EVAPORATION IN POROUS MEDIA

2017 ◽  
Vol 43 (4) ◽  
pp. 1831
Author(s):  
A. Papafotiou ◽  
C. Schütz ◽  
P. Lehmann ◽  
P. Vontobel ◽  
D. Or ◽  
...  
Keyword(s):  
Porous Media ◽  
Water Distribution ◽  
Preferential Flow ◽  
Unsaturated Flow ◽  
Coupling Effect ◽  
Heterogeneous Systems ◽  
Heterogeneous Porous Media ◽  
Richards Equation ◽  
Hydraulic Coupling ◽  
Experimental Findings

Infiltration and evaporation are governing processes for water exchange between soil and atmosphere. In addition to atmospheric supply or demand, infiltration and evaporation rates are controlled by the material properties of the subsurface and the interplay between capillary, viscous and gravitational forces. This is commonly modeled with semi-empirical approaches using continuum models, such as the Richards equation for unsaturated flow. However, preferential flow phenomena often occur, limiting or even entirely suspending the applicability of continuum-based models. During infiltration, unstable fingers may form in homogeneous or heterogeneous porous media. On the other hand, the evaporation process may be driven by the hydraulic coupling of materials with different hydraulic functions found in heterogeneous systems. To analyze such preferential flow processes, water distribution was monitored in infiltration and evaporation lab experiments using neutron transmission techniques. Measurements were performed in 2D and 3D, using homogeneous and heterogeneous setups. The experimental findings demonstrate the fingering effect in infiltration and how it is influenced by the presence of fine inclusions in coarse background material. During evaporation processes, the hydraulic coupling effect is found to control the evaporation rate, limiting the modeling of water balances between soil and surface based on surface information alone.

scholarly journals Modelling Unsaturated Flow in Porous Media Using an Improved Picard Iteration Scheme

2021 ◽  
Author(s):  
S.R. Zhu ◽  
L.Z. Wu ◽  
T. Ma ◽  
S.H. Li
Keyword(s):  
Porous Media ◽  
Convergence Rate ◽  
Unsaturated Flow ◽  
Control Volume ◽  
Linear Equations ◽  
Solution Process ◽  
Coefficient Matrix ◽  
Picard Iteration ◽  
Flow In Porous Media ◽  
Richards Equation

Abstract The numerical solution of various systems of linear equations describing fluid infiltration uses the Picard iteration (PI). However, because many such systems are ill-conditioned, the solution process often has a poor convergence rate, making it very time-consuming. In this study, a control volume method based on non-uniform nodes is used to discretize the Richards equation, and adaptive relaxation is combined with a multistep preconditioner to improve the convergence rate of PI. The resulting adaptive relaxed PI with multistep preconditioner (MP(m)-ARPI) is used to simulate unsaturated flow in porous media. Three examples are used to verify the proposed schemes. The results show that MP(m)-ARPI can effectively reduce the condition number of the coefficient matrix for the system of linear equations. Compared with conventional PI, MP(m)-ARPI achieves faster convergence, higher computational efficiency, and enhanced robustness. These results demonstrate that improved scheme is an excellent prospect for simulating unsaturated flow in porous media.

scholarly journals The Approximate Solution of Fractional Fredholm Integrodifferential Equations by Variational Iteration and Homotopy Perturbation Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Abdelouahab Kadem ◽  
Adem Kilicman
Keyword(s):  
Approximate Solution ◽  
Perturbation Method ◽  
Iteration Method ◽  
Homotopy Perturbation Method ◽  
Perturbation Methods ◽  
Variational Iteration Method ◽  
Integrodifferential Equations ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
Constant Coefficients

Variational iteration method and homotopy perturbation method are used to solve the fractional Fredholm integrodifferential equations with constant coefficients. The obtained results indicate that the method is efficient and also accurate.

An Exact Solution to the Local Fractional Richards' Equation for Unsaturated Soils and Porous Fabrics

2013 ◽  
Vol 843 ◽  
pp. 97-101
Author(s):  
Zheng Biao Li ◽  
Yin Shan Yun ◽  
Hong Ying Luo
Keyword(s):  
Exact Solution ◽  
Porous Media ◽  
Water Content ◽  
Unsaturated Soils ◽  
Fractal Dimensions ◽  
Volumetric Water Content ◽  
Richards Equation ◽  
Fractional Complex Transform ◽  
Porous Soil

A local fractional Richards equation is derived by considering the soil as fractal porous media, and an exact solution is obtained by a generalized Boltzmann transform and the fractional complex transform. The new theory predicts that the volumetric water content depends on the ratio (distance)2a /(time), where a is the value of fractal dimensions of the porous soil, and its value is recommended for various soils.

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