2010
DOI: 10.1002/nme.3087
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Stable element‐free Galerkin solution procedures for the coupled soil–pore fluid problem

Abstract: SUMMARYIt is always difficult to solve the coupled soil-pore fluid problem when the soil is saturated and impermeable, because this situation often results in intensive oscillations of the solutions. This topic has been discussed widely in the field of the finite element method but rarely by meshless methods. The ElementFree Galerkin (EFG) method has outstanding advantages of solving this problem, based on the fact that its interpolation function can be constructed flexibly by the nodes in the compact domain. … Show more

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Cited by 12 publications
(10 citation statements)
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References 157 publications
(276 reference statements)
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“…Putting (25) in the total constrained system of equations (22) and using the Newton-Raphson method, the following equations for the fully coupled formulation can be written as (26) and the unknown and residual vectors can be expressed by…”
Section: Numerical Implementationmentioning
confidence: 99%
See 1 more Smart Citation
“…Putting (25) in the total constrained system of equations (22) and using the Newton-Raphson method, the following equations for the fully coupled formulation can be written as (26) and the unknown and residual vectors can be expressed by…”
Section: Numerical Implementationmentioning
confidence: 99%
“…They also developed a novel formulation using the same methodology for partially saturated two-phase fluid flow, taking into account the hydraulic hysteresis [25]. Other important contributions in continuous porous media using mesh-free algorithms can be found in [26][27][28][29][30].On the basis of the basic concepts of generalized finite element method [31] and partition of unity finite element method [32], the local enrichment of finite element solutions for capturing of arbitrarily oriented discontinuities within a domain was proposed by Moes et al [33] and Belytschko and Black [34]. This method, now called the extended finite element method, rectifies the need for remeshing the solution domain during the propagation of discontinuities and does not require conforming the discontinuity lines with element edges [35,36].…”
mentioning
confidence: 99%
“…[40][41][42][43][44][45]), and two-phase fluid flow processes through rigid porous materials (e.g. [46][47][48]).…”
Section: Introductionmentioning
confidence: 99%
“…For example, stabilized the system by introducing a stabilization term consisting of the spatial derivatives of pore pressure to the governing equations. Reference proposed a stabilization scheme by rearranging the system matrix and taking advantage of meshfree nodal distribution.…”
Section: Introductionmentioning
confidence: 99%
“…Guidelines for appropriately choosing these parameters are proposed. Other interesting aspects include model dimensions from 1D to 2D and to 3D , loading modes from quasi‐static to dynamic loading , as well as anisotropy of hydraulic properties , just to name a few.…”
Section: Introductionmentioning
confidence: 99%