Book ChapterDOI
Modelling of Unsaturated Flow Through Porous Media Using Meshless Methods
Mohammad Reza Karami Mollaei
- pp 565-576
TLDR
In this paper , a method based on the localized radial basis function (RBF) and the Kirchhoff transformation technique was developed to solve the Richards equation in one and two-dimensional homogeneous medium.Abstract:
In this study, we focus on the modelling of infiltration process in porous media. We use the meshless techniques for efficiently solving the Richards equation which describes unsaturated water flow through soils. The design of approximate numerical methods for the Richards equation remains computationally challenging and requires the development of efficient numerical techniques. This difficulty is mainly due to the nonlinearity of the unsaturated hydraulic conductivity and the capillary pressure function. In this study, we develop a new method based on the localized radial basis function (RBF) and the Kirchhoff transformation technique in order to solve Richards equation in one and two-dimensional homogeneous medium. Our approach using the multiquadric radial basis function allows us to reduce the computational time and provide accurate numerical solutions. The proposed method does not require mesh generation. Picard's iterations are used to linearize the resulting nonlinear problem obtained using the Kirchhoff transformation technique. The numerical simulations show the capability of the proposed numerical techniques in predicting the dynamics of water through unsaturated soils. read more
References
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Journal ArticleDOI
A closed-form equation for predicting the hydraulic conductivity of unsaturated soils
van Genuchten,M. Th. +1 more
TL;DR: Van Genuchten et al. as mentioned in this paper proposed a closed-form analytical expression for predicting the hydraulic conductivity of unsaturated soils based on the Mualem theory, which can be used to predict the unsaturated hydraulic flow and mass transport in unsaturated zone.
Journal ArticleDOI
Capillary conduction of liquids through porous mediums
TL;DR: In this article, the authors used Darcey's law to derive the equation K∇2ψ+∇K·∇ψ +g∂K/∂z=−ρsA∆ψ/∆t for the capillary conduction of liquids in porous mediums.
Journal ArticleDOI
Some steady-state solutions of the unsaturated moisture flow equation with application to evaporation from a water table
TL;DR: Gardner as mentioned in this paper describes some STEADY-state solutions of the UNSATURATED MOISTURE FLOW EQUATION with application to EVAPORATION from a WATER TABLE.
Journal ArticleDOI
Multiquadrics--a scattered data approximation scheme with applications to computational fluid-dynamics-- ii solutions to parabolic, hyperbolic and elliptic partial differential equations
TL;DR: In this paper, the authors used MQ as the spatial approximation scheme for parabolic, hyperbolic and the elliptic Poisson's equation, and showed that MQ is not only exceptionally accurate, but is more efficient than finite difference schemes which require many more operations to achieve the same degree of accuracy.