A non-reflecting boundary condition for the finite element modeling of infinite reservoir with layered sediment

Gogoi, Indrani; Maity, Damodar

doi:10.1016/j.advwatres.2005.11.004

Cited by 27 publications

(16 citation statements)

References 15 publications

(25 reference statements)

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“…Each element at Interface 2 represents a sub-domain (i.e. sub-semi-infinite layered medium), so that the whole far-field domain is represented by an assemblage of elements at Interface 2 and its dynamic characteristics is described by the following SBFEM formulation (7) where the superscript n denotes the instant at time…”

Section: Sbfem-fem Coupling Formulation For Near Fieldmentioning

confidence: 99%

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Coupled Finite Element - Scaled Boundary Finite Element Method for Transient Analysis of Dam-Reservoir Interaction

2011

Computational Science and Its Applications - ICCSA 2011

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Abstract.The scaled boundary finite element method (SBFEM) was extended to solve dam-reservoir interaction problems in the time domain, where dams were flexible and the fluid in reservoir was semi-infinite and compressible. Transient responses of dam-reservoir systems subjected to horizontal ground motions were analyzed based on the SBFEM and finite element method (FEM) coupling method. A dam was modeled by FEM, while the whole fluid in reservoir was modeled by the SBFEM alone or a combination of FEM and SBFEM. Two benchmark examples were considered to check the accuracy of the SBFEM-FEM coupling method. For a vertical dam-reservoir system, the semi-infinite fluid with a uniform cross section was modeled by the SBFEM alone. For non-vertical dam-reservoir systems, the fluid was divided into a nearfield FEM domain and a far-field SBFEM domain. The geometry of near field is arbitrary, and the far field is a semi-infinite prism. Their numerical results obtained through the presented method were compared with those from analytical or substructure methods and good agreements were found.

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Section: Sbfem-fem Coupling Formulation For Near Fieldmentioning

confidence: 99%

“…An efficient semi-analytical TBC [3] and later, its application [4] exhibited good results, but it required the full eigen-modes of the nearto-far-field interface. Other types of TBC were also developed [5][6][7]. Except for the TBC, boundary element method (BEM) was often adopted to model a semi-infinite reservoir [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Coupled Finite Element - Scaled Boundary Finite Element Method for Transient Analysis of Dam-Reservoir Interaction

2011

Computational Science and Its Applications - ICCSA 2011

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“…To assess dam safety, there are different methods developed to evaluate the dynamic analysis [1][2][3][4][5][6][7][8][9]. Owing to the fact that analytical methods are not readily available for systems in which geometries of dam and reservoir are arbitrary, numerical methods have been developed.…”

Section: Introductionmentioning

confidence: 99%

Diagonalization procedure for scaled boundary finite element method in modeling semi‐infinite reservoir with uniform cross‐section

2009

Numerical Meth Engineering

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SUMMARYTo improve the ability of the scaled boundary finite element method (SBFEM) in the dynamic analysis of dam-reservoir interaction problems in the time domain, a diagonalization procedure was proposed, in which the SBFEM was used to model the reservoir with uniform cross-section. First, SBFEM formulations in the full matrix form in the frequency and time domains were outlined to describe the semi-infinite reservoir. No sediments and the reservoir bottom absorption were considered. Second, a generalized eigenproblem consisting of coefficient matrices of the SBFEM was constructed and analyzed to obtain corresponding eigenvalues and eigenvectors. Finally, using these eigenvalues and eigenvectors to normalize the SBFEM formulations yielded diagonal SBFEM formulations. A diagonal dynamic stiffness matrix and a diagonal dynamic mass matrix were derived. An efficient method was presented to evaluate them. In this method, no Riccati equation and Lyapunov equations needed solving and no Schur decomposition was required, which resulted in great computational costs saving. The correctness and efficiency of the diagonalization procedure were verified by numerical examples in the frequency and time domains, but the diagonalization procedure is only applicable for the SBFEM formulation whose scaling center is located at infinity.

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“…Practical FEM modeling requires the virtual truncation of large extent or infinite fluid domains at a finite distance from the studied structure. In this case, a Transmitting Boundary Condition (TBC) has to be applied at the boundary between the near and far fields to ensure adequate energy radiation [5,6]. These special boundary conditions and the truncation distance should be defined appropriately to prevent reflection of spurious waves back towards the structure.…”

Section: Introductionmentioning

confidence: 99%

An error estimator for transmitting boundary conditions in fluid-structure interaction problems

Bouaanani¹,

Miquel²

2011

WIT Transactions on the Built Environment

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This paper proposes error estimators to validate Transmitting Boundary Conditions (TBCs) in fluid-structure interaction problems. The error estimators are based on a new formulation of the dynamic response of fluid-structure systems including TBCs. The mathematical background is briefly discussed and the obtained equations are solved numerically to assess the accuracy of a given TBC and determine the associated error independently of FEM or BEM modeling of the fluid domain. The error estimators take account of : (i) structure's flexibility, (ii) fluid compressibility, (iii) energy dissipation at fluid boundaries, (iv) fluid domain truncation length, and (v) excitation frequency. An illustrative example consisting of a dam-reservoir system is presented where an error estimator is used to evaluate the effects of various TBCs on the hydrodynamic pressure acting on the dam upstream face. The proposed formulation can be programmed easily and used efficiently for rigorous assessment of classical or newly-developed TBCs for vibrating fluid-structure systems.

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A non-reflecting boundary condition for the finite element modeling of infinite reservoir with layered sediment

Cited by 27 publications

References 15 publications

Coupled Finite Element - Scaled Boundary Finite Element Method for Transient Analysis of Dam-Reservoir Interaction

Coupled Finite Element - Scaled Boundary Finite Element Method for Transient Analysis of Dam-Reservoir Interaction

Diagonalization procedure for scaled boundary finite element method in modeling semi‐infinite reservoir with uniform cross‐section

An error estimator for transmitting boundary conditions in fluid-structure interaction problems

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