Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30172
Hydrodynamic Modeling of Infinite Reservoir using Finite Element Method

Authors: M. A. Ghorbani, M. Pasbani Khiavi

Abstract:

In this paper, the dam-reservoir interaction is analyzed using a finite element approach. The fluid is assumed to be incompressible, irrotational and inviscid. The assumed boundary conditions are that the interface of the dam and reservoir is vertical and the bottom of reservoir is rigid and horizontal. The governing equation for these boundary conditions is implemented in the developed finite element code considering the horizontal and vertical earthquake components. The weighted residual standard Galerkin finite element technique with 8-node elements is used to discretize the equation that produces a symmetric matrix equation for the damreservoir system. A new boundary condition is proposed for truncating surface of unbounded fluid domain to show the energy dissipation in the reservoir, through radiation in the infinite upstream direction. The Sommerfeld-s and perfect damping boundary conditions are also implemented for a truncated boundary to compare with the proposed far end boundary. The results are compared with an analytical solution to demonstrate the accuracy of the proposed formulation and other truncated boundary conditions in modeling the hydrodynamic response of an infinite reservoir.

Keywords: Reservoir, finite element, truncated boundary, hydrodynamic pressure

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1081635

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1880

References:


[1] H. M. Westergaard, "Water pressure on dams during earthquake", Transactions, ASCE, vol. 98, pp. 418-433, 1933.
[2] O. C. Zienkiewicz, B. Iron, and Nath, "Natural frequencies of complex free or submerged structures by the finite element method", Symposium on vibration in civil engineering, Butterworths, London, 1965.
[3] A. K. Chopra, "Earthquake behavior of reservoir-dam systems", Journal of engineering mechanics division, vol. 94, pp. 1475-1500, 1968.
[4] A. K. Chopra, "Earthquake response of concrete gravity dams", Journal of engineering mechanics division, vol. 96, pp. 443-454, 1970.
[5] O. C. Zienkiewicz and P. Bettess, "Dynamic fluid-structure interaction, Numerical modeling of the coupled problem", John wiley, New york, pp. 185-193, 1978.
[6] J. F. Hall and A. K. Chopra, "Two-dimensional dynamic analysis of concrete gravity and embankment dams including hydrodynamic effects", Earthquake engineering and structural dynamics, vol. 10, pp. 303-323, 1982.
[7] S. K. Sharan, "Finite element analysis of unbounded and incompressible fluid domain", International journal on numerical methods in engineering, vol. 21, pp. 1659-1669, 1985.
[8] S. K. Sharan, "Finite element modeling of infinite reservoirs", Journal of engineering mechanics, vol. 111, pp. 1457-1469, 1985.
[9] D. Maity and S. K. Bhattacharyya, "Time-domain analysis of infinite reservoir by finite element method using a novel far-boundary condition", Finite element in analysis and design, vol. 32, pp. 85-96, 1999.