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

Abstract

Fully coupled flow-deformation analysis of deformable multiphase porous media saturated by several immiscible fluids has attracted the attention of researchers in widely different fields of engineering. This paper presents a new numerical tool to simulate the complicated process of two-phase fluid flow through deforming porous materials using a mesh-free technique, called element-free Galerkin (EFG) method. The numerical treatment of the governing partial differential equations involving the equilibrium and continuity equations of pore fluids is based on Galerkin's weighted residual approach and employing the penalty method to introduce the essential boundary conditions into the weak forms. The resulting constrained Galerkin formulation is discretized in space using the same EFG shape functions for the displacements and pore fluid pressures which are taken as the primary unknowns. Temporal discretization is achieved by utilizing a fully implicit scheme to guarantee no spurious oscillatory response. The validity of the developed EFG code is assessed via conducting a series of simulations. According to the obtained numerical results, adopting the appropriate values for the EFG numerical factors can warrant the satisfactory application of the proposed mesh-free model for coupled hydro-mechanical analysis of applied engineering problems such as unsaturated soil consolidation and infiltration of contaminant into subsurface soil layers.

A hydromechanical EFG-based Model for Numerical Simulation of Land Subsidence Induced by Groundwater Extraction in Anisotropic Aquifers

“…Assuming constant temperature, full fluid occupancy in the solid skeleton's voids, and minimal interphase mass transfer, the equations for a porous medium with two viscous fluids are stated as follows (Samimi & Pak, 2014Thomas, 2000): ulus of the solid phase and fluid phase, respectively. For a hydromechanical study of multiphase systems, the above nonlinear equations need to be supplemented with auxiliary functions, such as saturation degree as a function of capillary pressure, permeability coefficient as a function of saturation degree of wetting and non-wetting phases, and constitutive law of the solid phase (Samimi & Pak, 2016).…”

“…demonstrates the temporal derivative. Each term in Equation 9 is either a matrix or a vector, assembled from the nodal matrices or vectors, and is detailed in Appendix C. Comprehensive derivation of Equation 9 is beyond the scope of this article, and it is thoroughly provided in Samimi and Pak (Samimi & Pak, 2016). The derived system of equations (Equation 9) is discretized in the time domain, adopting a fully implicit approach with the finite difference method (Samimi & Pak, 2014.…”

“…Due to EFG's mesh-free nature, it can offer higher accuracy and convergence by utilizing a higher order of interpolation functions and improves handling of domain discontinuities. Despite the utilization of the EFG method in analyzing multiphase flow in deforming porous media (Samimi & Pak, 2016) or in groundwater modeling studies (Pathania et al, 2019(Pathania et al, , 2020Pathania & Rastogi, 2017), application of this technique for coupled hydromechanical modeling in the context of land subsidence in aquifers remains unexplored. This study applies the EFG method to coupled hydromechanical modeling, specifically focusing on land subsidence phenomena and considering unsaturated effects in aquifers.…”

A fully coupled element‐free Galerkin model for hydro‐mechanical analysis of advancement of fluid‐driven fractures in porous media

“…For selection of the numerical factors derived from the EFG discretization of the governing field equations of soil–water interaction problems in geo‐materials with penalty method, Oliaei et al have proposed some guidelines. These recommendations after a slight adjustment have been used by Samimi and Pak , and then extended to two‐phase flow systems by Samimi and Pak . Herein, the penalty factors and the radius of the nodal domain of influence are chosen on this basis, namely, α pu = 10 6 × E , , and the scale factor of the influence domain is 1.5.…”

Fully coupled elastoplastic hydro‐mechanical analysis of unsaturated porous media using a meshfree method

“…Modaressi and Aubert 40 were first to apply a MM (ie, EFGM) to model coupled flow deformation in saturated porous media. Since then, many MMs have been employed for coupled flow-deformation analysis of multiphase porous media, including the SPH, [52][53][54] EFGM, [55][56][57] PFEM, [58][59][60] RPIM, [61][62][63] MPM, [64][65][66][67] and SPIM, [68][69][70] just to mention a few. SPH uses point-wise integration and hence is free from any background mesh; however, it suffers from spatial instabilities.…”