Summary
An algorithm and essential subroutines are presented which implement a two stage finite element Galerkin method for integrating the complete two dimensional horizontal flow model. In the method a high accuracy is obtained by combining the Galerkin product with a high-order difference approximation to the derivatives in the nonlinear advection operator. The program includes the use of a weighted selective lumping scheme in the finite element method and the use of the Gauss — Seidel iterative method for solving the resulting systems of linear equations. Small scale noise is eliminated by using a shuman filter.
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References
Cullen, M. J. P., and Morton, K., K., 1980, Analysis of evolutionary error in finite element and other methods: Jour. Comput. Phys., V.34, p. 245–267.
Navon, I. M., 1982, A Numerov-Galerkin technique applied to a finite element shallow water equations model with exact conservation of integral invariants, in Kaway, T., ed. Finite element flow analysis: Univ. Tokyo Press, Tokyo, p. 75–86.
Navon, I. M., 1983, A Numerov-Galerkin technique applied to a finite element shallow water equations model with enforced conservation of integral invariants and selective lumping: Jour. Comput. Phys., V.52, No.2, p. 313–339.
Navon, I. M., 1987, A two stage, high accuracy, finite element Fortran program for solving shallow water equations: Computers & Geosciences, V.13, No. 3, p. 255–285.
Nguyen The Hung, Mathematical model of the two dimensional vertical flow, Journal of Vietnam National Science & Technology, No. 7+8, Hanoi 1990.
Nguyen The Hung, Mathematical modeling of sediment transport two dimensional horizontal, Proceedings of International Conference on Engineering Mechanics Today, Vol. 1, p. 541–548, Hanoi 1995.
Zienkiewicz, O. C., and Heinrich, J. C., 1979, A unified treatment of steady stage shallow water equations and two dimensional Navier-Stocks equations — a finite element penalty function approach: Computer Math. Appl. Mech. and Eng., V. 17/18, p. 673–688.
Zienkiewicz, O. C., Vilotte, J. P., Nakazawa, S., and Toyoshima, S., 1984, Iterative methods for constrained and mixed approximation: An inexpensive improvement of F.E.M. performance: Inst. Numerical methods in Engineering Report C/R/489/84, Swansea, United Kingdom, 20 p.
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© 2005 Springer-Verlag Berlin Heidelberg
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Hung, N.T. (2005). A Two-Stage, High-Accuracy, Finite Element Technique of the Two Dimensional Horizontal Flow Model. In: Bock, H.G., Phu, H.X., Kostina, E., Rannacher, R. (eds) Modeling, Simulation and Optimization of Complex Processes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27170-8_18
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DOI: https://doi.org/10.1007/3-540-27170-8_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23027-4
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