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. In this study, an EFG numerical model together with a stabilization technique is proposed to obtain stable solutions, especially for the saturated and impermeable soil. Close agreement between computational results and analytical solutions for one-and two-dimensional examples shows that the proposed numerical model not only provides highly accurate solutions for the saturated soil with relatively high permeability, but also eliminates the oscillations of the solutions very effectively for the saturated and impermeable soil. Furthermore, the influences of the hydraulic anisotropy, a typical property of two-dimensional problems, on the proposed stabilization technique are discussed. It is suggested that the optimal distribution of the nodes of essential variables can be designed, according to the relative importance of the permeability in different directions.

Weak discontinuity in porous media: an enriched EFG method for fully coupled layered porous media

“…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…”

“…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].…”

A three-dimensional mesh-free model for analyzing multi-phase flow in deforming porous media

“…[40][41][42][43][44][45]), and two-phase fluid flow processes through rigid porous materials (e.g. [46][47][48]).…”

A stabilized iterative scheme for coupled hydro‐mechanical systems using reproducing kernel particle method

“…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.…”

“…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.…”