Seepage analysis based on boundary-fitted coordinate transformation method

Unconfined seepage analysis in earth dams using smoothed fixed grid finite element method

“…it has poor performance in nonlinear problems and inhomogeneous materials. Finite Difference Method (FDM) 3 and Finite Volume Method (FVM) 4 have also been used in the solution of USPs. In addition to these approaches, the Finite Element Method (FEM), has been widely used to analyze the seepage problem because of its advantages in treating irregular geometries 5, 6.…”

Comparison between iteration schemes for three-dimensional coordinate-transformed saturated–unsaturated flow model

“…The coordinate transformation method has commonly been applied to the general Navier-Stokes equation in computational fluid dynamics (Hsu et al, 1998;Maliska and Raithby, 1984) and has been used for describing circulation and transport in estuaries and oceans (Chen, 2004;Murray and Reason, 2001). This method was also successfully applied to heat transport (Lakner and Plazl, 2008;Ruhaak et al, 2008), saturated groundwater flow (Koo and Leap, 1998;Jie et al, 2004;Ruhaak et al, 2008), and saturated-unsaturated flow modeling Kinouchi et al, 1991). Kinouchi et al (1991) applied a coordinate transformation method to FDM for simulating two-dimensional unsaturated flow in porous media.…”

“…However, the oft-cited disadvantage of FDMs is that they do not accurately represent all geometrically complex flow domains with a suitable resolution, especially in the case of multidimensional simulations. Usually, the representation of curvilinear domains such as a foundation fit, a lock foundation, an embarkment dam and shallow groundwater flow with a curvilinear boundary (Billstein et al, 1999;Chapman and Ong, 2006;Jie et al, 2004;Liang et al, 2009), require high-resolution grids, in which case, the FDM proves to be inefficient as compared to other numerical models that can treat non-orthogonal grids, such as FEMs.…”

“…Over the past three decades, several numerical models including finitedifference models (FDMs), finite-element models (FEMs), mixed FEMs, finite-volume models (FVMs), and the Eulerian-Lagrangian model have been developed for simulating saturated-unsaturated flow (e.g. Abdollahi-Nasab et al, 2010;An et al, 2011;Bause et al, 2004Bause et al, , 1999Boufadel, 2000;Boufadel et al, 2011;Celia et al, 1990;Clement et al, 1994;Farthing et al, 2003;Forsyth et al, 1995;Guo et al, 2010;Huang et al, 1994;Jie et al, 2004;Jones and Woodward, 2001;Boufadel, 2010, 2011;Manzini and Ferraris, 2004;Simunek et al, 1999;Tocci et al, 1997;Xia et al, 2010). FDMs, in particular, have certain advantages over other numerical models with respect to the ease of coding and understanding, owing to its simplicity of discretization; FDMs have thus been widely used for simulating saturated-unsaturated flow in porous media.…”

Locating the Free Surface Flow in Porous Media Using the Scaled Boundary Finite-Element Method

“…They analyzed a seepage flow under a dam with sheet piles to check the validity of the mathematical model. Jie et al [3] presented a finite-difference method based on boundary-fitted coordinate (BFC) to deal with the practical steady seepage in foundation pit and in lock foundation. The applications of BFC transformation method demonstrated its advantage in closely simulating the physical domain with complex geometrical boundaries.…”