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Keywords: shallow-water equations, least-squares finite-element, standing wave, solitary wave, dam-break, vortex shedding.

Summary

A two-dimensional shallow-water model based on solving the non-conservative, depth-averaged shallow-water equations is presented. The least-squares finite-element formulation and theta-time-integration is employed. Advantages of the model include:

source terms, such as bottom slope and bed frictions, can be handled easily without any special treatment;
an upwind scheme is not required;
a single approximation space is used for all variables, and its choice is not subjected to the Ladyzhenskaya-Babuska-Brezzi (LBB) condition [1]; and
the resulting system of equations is symmetric and positive-definite (SPD) which can be solved efficiently with the preconditioned conjugate gradient method [2,3].

The model is verified with the one-dimensional standing wave in a slope channel, one-dimensional solitary wave in a flat channel, and two-dimensional dam-break. Computed results are compared with the exact solution and other numerical solutions, and show good agreement. The model is then applied to simulate flow past a vertical circular cylinder. Salient characteristics, such as wave reflection and diffraction, and the variations of water surface around the cylinder and vortex shedding behind the cylinder, were well predicted. Computed results compared favourably with the experiment data and other numerical solutions.

References

1: V. Girault, P. Raviart, "Finite Element Methods for Navier-Stokes Equations: Theory and Algorithm", Springer, Berlin, 1986.
2: M.D. Gunzburger, "Finite Element Methods for Viscous Incompressible Flows", Academic Press, Boston, 1989.
3: B.N. Jiang, "The Least-Squares Finite Element Method", Springer, Berlin, 1998.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 89 PROCEEDINGS OF THE SIXTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: M. Papadrakakis and B.H.V. Topping Paper 97 Numerical Simulation of Wave-Structure Interactions Using the Least-Squares Finite Element Method S.J. Liang Department of Marine Environmental Informatics, National Taiwan Ocean University, Keelung, Taiwan doi:10.4203/ccp.89.97 purchase the full-text of this paper Full Bibliographic Reference for this paper S.J. Liang, "Numerical Simulation of Wave-Structure Interactions Using the Least-Squares Finite Element Method", in M. Papadrakakis, B.H.V. Topping, (Editors), "Proceedings of the Sixth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 97, 2008. doi:10.4203/ccp.89.97 Keywords: shallow-water equations, least-squares finite-element, standing wave, solitary wave, dam-break, vortex shedding. Summary A two-dimensional shallow-water model based on solving the non-conservative, depth-averaged shallow-water equations is presented. The least-squares finite-element formulation and theta-time-integration is employed. Advantages of the model include: source terms, such as bottom slope and bed frictions, can be handled easily without any special treatment; an upwind scheme is not required; a single approximation space is used for all variables, and its choice is not subjected to the Ladyzhenskaya-Babuska-Brezzi (LBB) condition [1]; and the resulting system of equations is symmetric and positive-definite (SPD) which can be solved efficiently with the preconditioned conjugate gradient method [2,3]. The model is verified with the one-dimensional standing wave in a slope channel, one-dimensional solitary wave in a flat channel, and two-dimensional dam-break. Computed results are compared with the exact solution and other numerical solutions, and show good agreement. The model is then applied to simulate flow past a vertical circular cylinder. Salient characteristics, such as wave reflection and diffraction, and the variations of water surface around the cylinder and vortex shedding behind the cylinder, were well predicted. Computed results compared favourably with the experiment data and other numerical solutions. References 1 V. Girault, P. Raviart, "Finite Element Methods for Navier-Stokes Equations: Theory and Algorithm", Springer, Berlin, 1986. 2 M.D. Gunzburger, "Finite Element Methods for Viscous Incompressible Flows", Academic Press, Boston, 1989. 3 B.N. Jiang, "The Least-Squares Finite Element Method", Springer, Berlin, 1998. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £95 +P&P)
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