| [1] | Terzaghi, K. T., Theoretical soil mechanics (1943), INC |
| [2] | Biot, Maurice A., General theory of three-dimensional consolidation, J Appl Phys, 12, 2, 155-164 (1941) ·JFM 67.0837.01 |
| [3] | Biot, M. A., General solutions of equations of elasticity and consolidation for a porous material, J Appl Phys, 23, 91-96 (1956) ·Zbl 0074.19101 |
| [4] | Van den Hoek, P. J.; Kooijman, A. P.; Bree, P. D., Horizontal-wellbore stability and sand production in weakly consolidated sandstones, J SPE Drill Complet, V15, 4, 274-283 (2000) |
| [5] | Xueqing, TENG; Mian, CHEN; Yan, JIN; Yunhu, LU; Yang, XIA, Poroelastic dynamics mechanisms of wellbore instability in tight formations, Pet Sci Bull, 2, 4, 478-489 (2017) |
| [6] | Michael, S.; Bruno, Geomechanical and decision analyses for mitigating compaction-related casing damage, SPE Drill Complet, V17, 3, 179-188 (2002) |
| [7] | Xiaorong, L.; Chenwang, G.; Yongcun, F.; Zechen, D., Numerical study of shear deformation of casings during hydraulic fracturing considering wellbore loading history, Pet Sci Bull, 02, 245-261 (2021) |
| [8] | Fredrich, J. T.; Arguello, J. G.; Deitrick, G. L., Geomechanical modeling of reservoir compaction, surface subsidence, and casing damage at the Belridge Diatomite Field, SPE Reserv Eval Eng, V3, 4, 348-359 (2000) |
| [9] | Schutjens, P. M.T. M.; Hanssen, T. H.; Hettema, M. H.H., Compaction-induced porosity/permeability reduction in sandstone reservoirs: data and model for elasticity-dominated deformation, SPE Reserv Eval Eng, V7, 3, 202-214 (2004) |
| [10] | Cook, C. C.; Andersen, M. A.; Halle, G., An approach to simulating the effects of water-induced compaction in a north sea reservoir, SPE Reserv Eval Eng, V4, 2, 121-127 (2001) |
| [11] | tran, David; Settari, A.; Nghiem, Long, New iterative coupling between a reservoir simulator and a geomechanics module, SPE J, V9, 3, 362-369 (2004) |
| [12] | Vaziri, H. H., Coupled fluid flow and stress analysis of oil sands subject to heating, J Can Pet Technol, 27, 5, 84-91 (1988) |
| [13] | Lewis, R. W.; Sukirman, Y., Finite element modelling of three-phase flow in deforming saturated oil reservoirs, Int J Numer Anal Methods Geomech, 17, 577-598 (1993) ·Zbl 0785.76042 |
| [14] | Fung, LSK., Coupled geomechanical-thermal simulation for deforming heavy-oil reservoirs, JCPT, 4, 22-28 (1994) |
| [15] | Heffer, K. J.; Fox, R. J.; McGill, C. A., Novel techniques show links between reservoir flow directionality, earth stress, fault structure and geomechanical changes in mature waterfloods, SPE J, V2, 2, 91-98 (1997) |
| [16] | Osorio, J. G.; Her-Yuan, C.; Lawrence, W. T., Numerical simulation of the impact of flow-induced geomechanical response on the production of stress-sensitive reservoirs, Proceedings of the SPE reservoir simulation symposium. OnePetro, 51929 (1999) |
| [17] | Fanchi, J. R., Estimating geomechanical properties using an integrated flow model, SPE Reserv Eval Eng, 6, 2, 108-116 (2003) |
| [18] | Collins, P. M., Geomechanical effects on the SAGD process, SPE Reserv Eval Eng, 10, 4, 367-375 (2007) |
| [19] | Dean, R. H.; Gai, X.; Stone, C. M., A comparison of techniques for coupling porous flow and geomechanics, Spe J, 11, 1, 132-140 (2006) |
| [20] | Kanj, M. Y.; Abousleiman, Y. N., Taming complexities of coupled geomechanics in rock testing: from assessing reservoir compaction to analyzing stability of expandable sand screens and solid tubulars, J Graph Tool, 12, 3, 293-304 (2007) |
| [21] | Bear, J., & Bachmat, Y. (1990). Introduction to modeling of transport phenomena in porous media. Vol. 4. Springer Science & Business Media, 2012. ·Zbl 0743.76003 |
| [22] | Zhou, J.; Zhang, Y.; Chen, J. K., Numerical simulation of compressible gas flow and heat transfer in a microchannel surrounded by solid media, Int J Heat Fluid Flow, 28, 6, 1484-1491 (2007) |
| [23] | Lewis, R. W.; Roberts, P. J.; Schrefler, B. A., Finite element modeling of two-phase heat and fluid flow in deforming porous media, Transp Porous Media, 4, 4, 319-334 (1989) |
| [24] | Wu, Y. S.; Pruess, K., Numerical simulation of non-isothermal multiphase tracer transport in heterogeneous fractured porous media, Adv Water Res, 23, 7, 699-723 (2000) |
| [25] | Liu, G. R.; Gu, Y. T., An introduction to meshfree methods and their programming (2005), Springer Science & Business Media |
| [26] | Liu, G. R., Meshfree methods: moving beyond the finite element method (2009), CRC press |
| [27] | Zhang, Y.; Shao, K. R.; Guo, Y.; Zhu, J.; Xie, D. X.; Lavers, J. D., An improved multiquadric collocation method for 3-D electromagnetic problems, IEEE Trans Magn, 43, 4, 1509-1512 (2007) |
| [28] | Chantasiriwan, S. (2007). Multiquadric collocation method for time-dependent heat conduction problems with temperature-dependent thermal properties, 109-113. |
| [29] | Zerroukat, M.; Power, H.; Chen, C., A numerical method for heat transfer problems using collocation and radial basis functions, Int J Numer Methods Eng, 42, 7, 1263-1278 (1998) ·Zbl 0907.65095 |
| [30] | Chantasiriwan, S., Performance of multiquadric collocation method in solving lid-driven cavity flow problem with low Reynolds number, Comput Model Eng Sci, 15, 3, 137 (2006) |
| [31] | Łarler, B. (2003). MESH œ FREE COMPUTATIONAL FLUID DYNAMICS: A RADIAL BASIS FUNCTION COLLOCATION METHOD APPROACH. |
| [32] | Shu, C.; Ding, H.; Yeo, K. S., Computation of incompressible Navier-Stokes equations by local RBF-based differential quadrature method, CMES, 7, 2, 195-206 (2005) ·Zbl 1106.76427 |
| [33] | Wang, L.; Qian, Z.; Zhou, Y.; Peng, Y., A weighted meshfree collocation method for incompressible flows using radial basis functions, J Comput Phys, 401, Article 108964 pp. (2020) ·Zbl 1453.65364 |
| [34] | Nuss, W. A.; Titley, D. W., Use of multiquadric interpolation for meteorological objective analysis, Mon Weather Rev, 122, 7, 1611-1631 (1994) |
| [35] | Benito, J. J.; Urena, F.; Gavete, L., Influence of several factors in the generalized finite difference method, Appl Math Modell, 25, 12, 1039-1053 (2001) ·Zbl 0994.65111 |
| [36] | Tadeusz, Liszka., An interpolation method for an irregular net of nodes, Int J Numer Method Eng, 20, 9, 1599-1612 (1984), 32 ·Zbl 0544.65006 |
| [37] | Liszka, T.; Orkisz, J., The finite difference method at arbitrary irregular grids and its application in applied mechanics, Comput Struct, 11, 1-2, 83-95 (1980) ·Zbl 0427.73077 |
| [38] | Benito, J. J.; Urena, F.; Gavete, L.; Alvarez, R., An h-adaptive method in the generalized finite differences, Comput Methods Appl Mech Eng, 192, 5-6, 735-759 (2003) ·Zbl 1024.65099 |
| [39] | Gavete, L.; Gavete, M. L.; Benito, J., Improvements of generalized finite difference method and comparison with other meshless methods, Appl Math Modell, 27, 10, 831-847 (2003) ·Zbl 1046.65085 |
| [40] | Li, P. W.; Fan, C. M., Generalized finite difference method for two-dimensional shallow water equations, Eng Anal Boundary Elem, 80, 58-71 (2017) ·Zbl 1403.76133 |
| [41] | Ureña, F.; Salete, E.; Benito, J. J.; Gavete, L., Solving third-and fourth-order partial differential equations using GFDM: application to solve problems of plates, Int J Comput Math, 89, 3, 366-376 (2012) ·Zbl 1242.65217 |
| [42] | Fu, Z. J.; Tang, Z. C.; Zhao, H. T.; Li, P. W.; Rabczuk, T., Numerical solutions of the coupled unsteady nonlinear convection-diffusion equations based on generalized finite difference method, Eur Phys J Plus, 134, 6, 1-20 (2019) |
| [43] | Gu, Y.; Sun, H., A meshless method for solving three-dimensional time fractional diffusion equation with variable-order derivatives, Appl Math Modell, 78, 539-549 (2020) ·Zbl 1481.65130 |
| [44] | Gu, Y.; Qu, W.; Chen, W.; Song, L.; Zhang, C., The generalized finite difference method for long-time dynamic modeling of three-dimensional coupled thermoelasticity problems, J Comput Phys, 384, 42-59 (2019) ·Zbl 1451.74215 |
| [45] | Qu, W.; He, H., A spatial-temporal GFDM with an additional condition for transient heat conduction analysis of FGMs, Appl Math Lett, 110, Article 106579 pp. (2020) ·Zbl 1452.80005 |
| [46] | Benito, J. J.; Ureña, F.; Gavete, L.; Salete, E.; Ureña, M., Implementations with generalized finite differences of the displacements and velocity-stress formulations of seismic wave propagation problem, Appl Math Modell, 52, 1-14 (2017) ·Zbl 1480.65203 |
| [47] | Wang, Y.; Gu, Y.; Fan, C. M.; Chen, W.; Zhang, C., Domain-decomposition generalized finite difference method for stress analysis in multi-layered elastic materials, Eng Anal Bound Elem, 94, 94-102 (2018) ·Zbl 1403.74282 |
| [48] | Fan, C. M.; Li, P. W., Generalized finite difference method for solving two-dimensional Burgers’ equations, Procedia Eng, 79, 55-60 (2014) |
| [49] | Li, P. W., Space-time generalized finite difference nonlinear model for solving unsteady Burgers’ equations, Appl Math Lett, 114, Article 106896 pp. (2021) ·Zbl 1458.65110 |
| [50] | Chavez-Negrete, C.; Dominguez-Mota, F. J.; Santana-Quinteros, D., Numerical solution of Richards’ equation of water flow by generalized finite differences, Comput Geotech, 101, 168-175 (2018), SEP. |
| [51] | Tinoco-Guerrero, G.; Dominguez-Mota, F. J.; Gaona-Arias, A., A stability analysis for a generalized finite-difference scheme applied to the pure advection equation, Math Comput Simul, 147, may, 293-300 (2018) ·Zbl 1540.65336 |
| [52] | Tinoco-Guerrero, G.; Domínguez-Mota, FJ; Tinoco-Ruiz, J. G., A study of the stability for a generalized finite-difference scheme applied to the advection-diffusion equation, Math Comput Simul (MATCOM), 176 (2020) ·Zbl 1510.76115 |
| [53] | Fu, Z. J.; Xie, Z. Y.; Ji, S. Y.; Tsai, C. C.; Li, A. L., Meshless generalized finite difference method for water wave interactions with multiple-bottom-seated-cylinder-array structures, Ocean Eng, 195, Article 106736 pp. (2020) |
| [54] | Gu, Y.; Wang, L.; Chen, W.; Zhang, C.; He, X., Application of the meshless generalized finite difference method to inverse heat source problems, Int J Heat Mass Transf, 108, 721-729 (2017) |
| [55] | Zhan, W.; Rao, X.; Zhao, H., Generalized finite difference method (GFDM) based analysis for subsurface flow problems in anisotropic formation, Eng Anal Bound Elem, 140, 48-58 (2022) ·Zbl 1521.76609 |
| [56] | Chen, S. Y.; Hsu, K. C.; Fan, C. M., Improvement of generalized finite difference method for stochastic subsurface flow modeling, J Comput Phys, 429, Article 110002 pp. (2021) ·Zbl 07500737 |
| [57] | Saucedo-Zendejo, F. R.; Reséndiz-Flores, E. O.; Kuhnert, J., Three-dimensional flow prediction in mould filling processes using a GFDM, Comput Part Mech, 6, 3, 411-425 (2019) |
| [58] | Atluri, S. N.; Shen, S., The Meshless Local Petrov-Galerkin (MLPG) method: a simple & less-costly alternative to the finite element and boundary element methods, Comput Model Eng Sci, 3, 1, 11-52 (2002) ·Zbl 0996.65116 |
| [59] | Cheng, M.; Liu, G. R., A novel finite point method for flow simulation, Int J Numer Methods Fluids, 39, 12, 1161-1178 (2002) ·Zbl 1053.76056 |
| [60] | Li, P. W.; Fan, C. M.; Grabski, J. K., A meshless generalized finite difference method for solving shallow water equations with the flux limiter technique, Eng Anal Bound Elem, 131, 159-173 (2021) ·Zbl 1521.76556 |
| [61] | Rao, X., An upwind generalized finite difference method (GFDM) for meshless analysis of heat and mass transfer in porous media, Comp Part Mech (2022) |
| [62] | Rao, X.; Liu, Y.; Zhao, H., An upwind generalized finite difference method for meshless solution of two-phase porous flow equations, Eng Anal Bound Elem, 137, 105-118 (2022) ·Zbl 1521.76577 |
| [63] | Biot, M. A., General theory of three-dimensional consolidation, J Appl Phys, 12, 2, 155-164 (1941) ·JFM 67.0837.01 |
| [64] | Rao, X., A novel meshless method based on the virtual construction of node control domains for porous flow problems (2022), arXiv preprint, arXiv:2206.05531 |
| [65] | Milewski, S., Meshless finite difference method with higher order approximation—applications in mechanics, Arch Comput Meth Eng, 19, 1, 1-49 (2012) ·Zbl 1354.74313 |
| [66] | Brandt, A., MacCormick, S., & Ruge, J. (1983). Algebraic multigrid (AMG) for automatic multigrid solution with application to geodetic computations. |
| [67] | Ruge, J. W.; Stüben, K., Algebraic multigrid, Multigrid methods, 73-130 (1987), Society for Industrial and Applied Mathematics ·Zbl 0659.65094 |
| [68] | Saad, Y., ILUT: A dual threshold incomplete LU factorization, Numer Linear Algebr Appl, 1, 387-402 (1994) ·Zbl 0838.65026 |
| [69] | Benzi, M., Preconditioning techniques for large linear systems: a survey, J Comput Phys, 182, 418-477 (2002) ·Zbl 1015.65018 |
| [70] | Saad, Y.; Schultz, M. H., GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J Sci Stat Comput, 7, 856-869 (1986) ·Zbl 0599.65018 |
