Study of free‐surface seepage problems using hypersingular equations

Chen, Jeng‐Tzong; Hsiao, Chia-Chun; Chiu, Y.P.; Lee, Ying‐Te

doi:10.1002/cnm.925

Cited by 24 publications

(26 citation statements)

References 12 publications

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“…According to Eqs. (11) and (12), the original Signorini problem (1)-(5) is reduced to the following linear problem:…”

Section: The Mfs For Signorini Problemsmentioning

confidence: 99%

“…Some applications of the BEM for Signorini problems can be found in Refs. [2,3,9,11,[14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

“…Signorini problems come up in the modeling of many realistic science and engineering applications such as the shallow dam problem [1][2][3][4], the electropaint process [3][4][5][6][7], the unilateral contact problem [8,9], the free boundary problem [10,11], and so on. Besides, in the theory of variational inequalities [12,13], a broad class of problems arising in industry, social, economics, finance, pure and applied sciences give rise to Signorini problems.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Application of the method of fundamental solutions to 2D and 3D Signorini problems

Zheng

2015

Engineering Analysis with Boundary Elements

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“…According to Eqs. (11) and (12), the original Signorini problem (1)-(5) is reduced to the following linear problem:…”

Section: The Mfs For Signorini Problemsmentioning

confidence: 99%

“…Some applications of the BEM for Signorini problems can be found in Refs. [2,3,9,11,[14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Application of the method of fundamental solutions to 2D and 3D Signorini problems

Zheng

2015

Engineering Analysis with Boundary Elements

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“…There are 132 iterations to reach the stopping criterion using the Picard scheme. The numerical solutions of free surface were then compared with those obtained from Aitchison et al [32,33]. The separation point is the intersection of the free surface and the seepage face.…”

Section: Modeling Of Subsurface Flow With Freementioning

confidence: 99%

A Novel Boundary-Type Meshless Method for Modeling Geofluid Flow in Heterogeneous Geological Media

Xiao

Liu

et al. 2018

Geofluids

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A novel boundary-type meshless method for modeling geofluid flow in heterogeneous geological media was developed. The numerical solutions of geofluid flow are approximated by a set of particular solutions of the subsurface flow equation which are expressed in terms of sources located outside the domain of the problem. This pioneering study is based on the collocation Trefftz method and provides a promising solution which integrates the T-Trefftz method and F-Trefftz method. To deal with the subsurface flow problems of heterogeneous geological media, the domain decomposition method was adopted so that flux conservation and the continuity of pressure potential at the interface between two consecutive layers can be considered in the numerical model. The validity of the model is established for a number of test problems. Application examples of subsurface flow problems with free surface in homogenous and layered heterogeneous geological media were also carried out. Numerical results demonstrate that the proposed method is highly accurate and computationally efficient. The results also reveal that it has great numerical stability for solving subsurface flow with nonlinear free surface in layered heterogeneous geological media even with large contrasts in the hydraulic conductivity.

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“…Figure 8 shows the converged configuration of the free surface from the present method. Also, the results from the BEM (Chen et al, 2007) and the MFS (Chaiyo et al, 2011) are provided in Figure 8 for comparison. We can see that there is no significant difference on the computation results between the present method and other methods.…”

Section: Double-variable Hybrid Functionalmentioning

confidence: 99%

Green's function based finite element formulations for isotropic seepage analysis with free surface

Wang

Gao

2015

Lat. Am. j. solids struct.

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A solution procedure using the Green's function based finite element method (FEM) is presented for two-dimensional nonlinear steadystate seepage analysis with the presence of free surface in isotropic dams. In the present algorithm, an iteration strategy is designed to convert the over-specified free surface problem to a regular partial differential equation problem. Then, at each iteration step, the Green's function for isotropic linear seepage partial differential equation is employed to construct the element interior water head field, while the conventional shape functions are used for the independent element frame water head field. Then these two independent fields are connected by a double-variable hybrid functional to produce the final solving equation system. By means of the physical definition of Green's function, all two-dimensional element domain integrals in the present algorithm can reduce to one-dimensional element boundary integrals, so that versatile multinode element is constructed to simplify mesh reconstruction during iteration. Finally, numerical results from the present Green's function based FEM with isotropic Green's function kernels are compared with other numerical results to verify and demonstrate the performance of the present method.

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Study of free‐surface seepage problems using hypersingular equations

Cited by 24 publications

References 12 publications

Application of the method of fundamental solutions to 2D and 3D Signorini problems

Application of the method of fundamental solutions to 2D and 3D Signorini problems

A Novel Boundary-Type Meshless Method for Modeling Geofluid Flow in Heterogeneous Geological Media

Green's function based finite element formulations for isotropic seepage analysis with free surface

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