Three-step explicit finite element computation of shallow water flows on a massively parallel computer. (English) Zbl 0861.76044

Summary: Massively parallel finite element strategies for large-scale computations of shallow water flows and contaminant transport are presented. The finite element discretizations, carried out on unstructured grids, are based on a three-step explicit formulation both for the shallow water equations and for the advection-diffusion equation governing the contaminant transport. Parallel implementations of these unstructured-grid-based formulations are carried out on the Army High Performance Computing Research Center Connection Machine CM-5. It is demonstrated with numerical examples that the strategies presented are applicable to large-scale computations of various shallow water flow problems.


76M10 Finite element methods applied to problems in fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
65Y05 Parallel numerical computation
86A05 Hydrology, hydrography, oceanography
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[1] , and , ’Computation of unsteady incompressible flows with the stabilized finite element methods–space-time formulations, iterative strategies and massively parallel implementations’, in , and (eds), New Methods in Transient Analysis, AMD Vol. 143, ASME, New York, 1992, pp. 7-24.
[2] Behr, Comput. Methods Appl. Mech. Eng. 112 pp 3– (1994)
[3] Johan, Comput. Methods Appl. Mech. Eng. 113 pp 363– (1994)
[4] Kawahara, Int. j. numer. methods fluids 2 pp 89– (1982)
[5] Kawahara, Int. j. numer. methods fluids 4 pp 71– (1984)
[6] Brooks, Comput. Methods Appl. Mech. Eng. 32 pp 199– (1982)
[7] and , ’Finite element formulations for convection dominated flows with particular emphasis on the Euler equations’, AIAA Paper 83-0125, 1983.
[8] Jiang, Comput. Fluid Dyn. J. 1 pp 443– (1993)
[9] Personal communication, 1994.
[10] , and , ’An observation and simulation of tidal currents of Tokyo Bay’, Proc. 27th Natl. Conf. of Coastal Engineering, JSCE, 1980, pp. 448-452.
[11] ’Numerical simulation of tidal currents by means of finite element method’, Tech. Note of Port and Harbor Research Institute (Ministry of Transport, Japan), No. 404, 1981 (in Japanese).
[12] Kodama, Proc. JSCE 446 pp 89– (1992)
[13] Kashiyama, Int. j. numer. methods fluids 15 pp 1037– (1992)
[14] Kashiyama, Comput. Methods Appl. Mech. Eng. 112 pp 185– (1994)
[15] Martime Chart of Tokyo Datum, No. 90, Marine Safety Agency, 1984.
[16] Harmonic Constant Table, Marine Safety Agency, 1989.
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