An implicit numerical model for solving free-surface seepage problems

References

• Ahmadi, H., Namin, M.M., and Kilanehei, F. 2016. “Development a numerical model of flow and contaminant transport in layered soils.” Adv. Environ. Res., 5(4), 263–282. doi: 10.12989/aer.2016.5.4.263
   Google Scholar
• Angermann, L. (2000). “Node-centered finite volume schemes and primal-dual mixed formulations.”
   Google Scholar
• Bardet, J.P., and Tobita, T. 2002. “A practical method for solving free-surface seepage problems.” Comput. Geotech., 29(6), 451–475. doi: 10.1016/S0266-352X(02)00003-4
   Web of Science ®Google Scholar
• Bekele, Y.W., Kvamsdal, T., Kvarving, A.M., and Nordal, S. 2016. “Adaptive isogeometric finite element analysis of steady‐state groundwater flow.” Int. J. Numer. Anal. Methods Geomech., 40(5), 738–765. doi: 10.1002/nag.2425
   Web of Science ®Google Scholar
• Borja, R.I., and Kishnani, S.S. 1991. “On the solution of elliptic free-boundary problems via Newton’s method.” Comput. Methods Appl. Mech. Eng., 88(3), 341–361. doi: 10.1016/0045-7825(91)90094-M
   Web of Science ®Google Scholar
• Castro-Orgaz, O. 2011. “A new model for soil–water drainage problems.” Environ. Fluid Mech., 11(4), 427–435. doi: 10.1007/s10652-010-9196-6
   Web of Science ®Google Scholar
• Darbandi, M., Torabi, S.O., Saadat, M., Daghighi, Y., and Jarrahbashi, D. 2007. “A moving‐mesh finite‐volume method to solve free‐surface seepage problem in arbitrary geometries.” Int. J. Numer. Anal. Methods Geomech., 31(14), 1609–1629. doi: 10.1002/nag.611
   Web of Science ®Google Scholar
• Darcy, H.P.G. (1856). Les Fontaines publiques de la ville de Dijon. “Exposition et application des principes à suivre et des formules à employer dans les questions de distribution d’eau.” etc. V. Dalamont.
   Google Scholar
• Freitas, C.J. 2002. “The issue of numerical uncertainty.” Appl. Math. Model., 26(2), 237–248. 10.1016/S0307-904X(01)00058-0
   Web of Science ®Google Scholar
• Fu, J.F., and Sheng, J.I.N. 2009. “A study on unsteady seepage flow through dam.” J Hydrodynam B, 21(4), 499–504. doi: 10.1016/S1001-6058(08)60176-6
   Web of Science ®Google Scholar
• Fukuchi, T. 2014. “Finite difference method and algebraic polynomial interpolation for numerically solving Poisson’s equation over arbitrary domains.” AIP Adv., 4(6), 060701. doi: 10.1063/1.4885555
   Web of Science ®Google Scholar
• Fukuchi, T. 2016. “Numerical analyses of steady-state seepage problems using the interpolation finite difference method.” Soils Found., 56(4), 608–626. doi: 10.1016/j.sandf.2016.07.003
   Web of Science ®Google Scholar
• Govindarajan, S.K., and Rakesh, T.V. 2018. “Numerical modeling of hyperbolic dominant transient fluid flow in saturated fractured rocks using Darcian approach.” Groundwater Sustainable Dev., 7, 56–72. doi: 10.1016/j.gsd.2018.03.006
   Google Scholar
• Gupta, R.D., and Alam, J. 2004. “An experimental study of the seepage and strength characteristics of dadri fly-ash mixed with cement and lime.” ISH J. Hydraul. Eng., 10(2), 49–57. doi: 10.1080/09715010.2004.10514753
   Google Scholar
• Jiang, Q.H., Deng, S.S., Zhou, C.B., and Lu, W.B. 2010. “Modeling unconfined seepage flow using three-dimensional numerical manifold method.” J. Hydrodyn., 22(4), 554–561. doi: 10.1016/S1001-6058(09)60088-3
   Web of Science ®Google Scholar
• Kacimov, A.R., Al-Maktoumi, A., and Obnosov, Y.V. 2019. “Seepage through earth dam with clay core and toe drain: The Casagrande–Numerov analytical legacy revisited.” ISH J. Hydraul. Eng., 1–9. doi: 10.1080/09715010.2019.1633694
   Google Scholar
• Kermani, F.E., and Barani, G.A. 2012. “Seepage analysis through earth dam based on finite difference method.” J. Basic Appl. Sci. Res., 2(11), 11621–11625.
   Google Scholar
• Kochina, P., 1962. “Theory of ground water movement.”
   Google Scholar
• Ku, C.Y., Xiao, J.E., and Liu, C.Y. 2019. “On solving nonlinear moving boundary problems with heterogeneity using the collocation meshless method.” Water, 11(4), 835. doi: 10.3390/w11040835
   Web of Science ®Google Scholar
• Lacy, S.J., and Prevost, J.H. 1987. “Flow through porous media: A procedure for locating the free surface.” Int. J. Numer. Anal. Methods Geomech., 11(6), 585–601. doi: 10.1002/nag.1610110605
   Web of Science ®Google Scholar
• Leontiev, A., and Huacasi, W. 2001. “Mathematical programming approach for unconfined seepage flow problem.” Eng. Anal. Bound. Elem., 25(1), 49–56. doi: 10.1016/S0955-7997(00)00067-9
   Web of Science ®Google Scholar
• Li, M.C., Guo, X.Y., Shi, J., and Zhu, Z.B. 2015. “Seepage and stress analysis of anti-seepage structures constructed with different concrete materials in an RCC gravity dam.” Water Sci. Eng., 8(4), 326–334. doi: 10.1016/j.wse.2015.10.001
   Web of Science ®Google Scholar
• Meenal, M., and Eldho, T.I. 2011. “Meshless point collocation method for 1D and 2D groundwater flow simulation.” ISH J. Hydraul. Eng., 17(1), 71–87. doi: 10.1080/09715010.2011.10515034
   Google Scholar
• Mohsenian, A.R., Sedghi-Asl, M., and Rahimi, H. 2019. “An analytical solution for confined seepage problem beneath hydraulic structures.” Iran. J. Sci. Technol. Trans. Civ. Eng., 43(2), 361–369. doi: 10.1007/s40996-018-0146-8
   Web of Science ®Google Scholar
• Namin, M., Lin, B., and Falconer, R.A. 2004. “Modelling estuarine and coastal flows using an unstructured triangular finite volume algorithm.” Adv. Water Resour., 27(12), 1179–1197. doi: 10.1016/j.advwatres.2004.08.012
   Web of Science ®Google Scholar
• Navas, P., López‐Querol, S., Yu, R.C., and Li, B. 2016. “B‐bar based algorithm applied to meshfree numerical schemes to solve unconfined seepage problems through porous media.” Int. J. Numer. Anal. Methods Geomech., 40(6), 962–984. doi: 10.1002/nag.2472
   Web of Science ®Google Scholar
• Oden, J.T., and Kikuchi, N. 1980. “Theory of variational inequalities with applications to problems of flow through porous media.” Int. J. Eng. Sci., 18(10), 1173–1284. doi: 10.1016/0020-7225(80)90111-1
   Web of Science ®Google Scholar
• Pham-Van, S., Hinkelmann, R., Nehrig, M., and Martinez, I. 2011. “A comparison of model concepts and experiments for seepage processes through a dike with a fault zone.” Eng. Appl. Comput. Fluid Mech., 5(1), 149–158. doi: 10.1080/19942060.2011.11015359
   Google Scholar
• Sanayei, H.R.Z., and Javdanian, H. 2020. “Assessment of steady-state seepage through dams with nonsymmetric boundary conditions: Analytical approach.” Environ. Monit. Assess., 192(1), 3. doi: 10.1007/s10661-019-7973-3
   Web of Science ®Google Scholar
• Swathi, B., and Eldho, T.I. 2013. “Groundwater flow simulation in confined aquifers using meshless local Petrov-Galerkin (MLPG) method.” ISH J. Hydraul. Eng., 19(3), 335–348. doi: 10.1080/09715010.2013.819707
   Google Scholar
• Tang, Y., Zhou, J., Yang, P., Yan, J., and Zhou, N. 2017. Groundwater engineering. Springer Singapore.
   Google Scholar
• Tayfur, G., Swiatek, D., Wita, A., and Singh, V.P. 2005. “Case study: Finite element method and artificial neural network models for flow through Jeziorsko earthfill dam in Poland.” J. Hydraul. Eng., 131(6), 431–440. doi: 10.1061/(ASCE)0733-9429(2005)131:6(431)
   Web of Science ®Google Scholar
• Tracy, F.T. 2016. “Using analytic solution methods on unsaturated seepage flow computations.” Procedia Comput. Sci., 80, 554–564. doi: 10.1016/j.procs.2016.05.335
   Google Scholar
• Zhang, T., Fang, F., and Feng, P. 2017. “Simulation of dam/levee-break hydrodynamics with a three-dimensional implicit unstructured-mesh finite element model.” Environ. Fluid Mech., 17(5), 959–979. doi: 10.1007/s10652-017-9530-3
   Web of Science ®Google Scholar