Summary
A finite element model that solves the governing equations of a one-dimensional free-surface flow in the lagrangian form is presented. It offers the advantage of operating on a grid relating only to the initial configuration of the fluid, thus keening both trial functions and mass matrix time-independent. This technique is applied to the problem of propagation of a submersion wave on a dry river-bed.Numerical solutions are compared with analytical ones to be found in literature.
A comparison is also made,in terms of accuracy and computational effort,with a finite element model based on the eulerian formulation of the same problem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Barr D.I.H., Dass M.M. (1980). Numerical simulation of dam-burst and reflections, with verification against laboratory data. Proc. Instn. Civ. Engrs.Part 2,69 June: 359–373.
Chen C.L. (1980). Laboratory verification of a dam-break flood model, AS CE, 106, HY4: 534–556
Chervet A., Dallowes P. (1970). Calcul de l’onde de submer sion consecutive a la rupture d’un barrage, Schweizerische Baureitung, 7 Mai
Dressler R.F. (1952). Hydraulic resistance effect upon dam--break functions. Journal of Research of the National Bureau of Standards, 49, 3: 217–225.
Dressler R.F. (1954). Comparison of theories and experiments for the hydraulic dam-break wave. International Ass. of Scientific Hydrology, 3, 38: 319–328.
Lambert J.D. (1973). Computational methods in ordinary differential equations, John Wiley & Sons, London.
Mahmood K., Yevjevich V. (1975), Unsteady flow in open channels. Water Resources Publications, P.O. Box 303, Fort Collins, Colorado 80522, USA, pag. 100 Vol. I
Preissmann A., Gunge J.A. (1961). Calcul du mascaret sur machine electronique, Intumescences, So cieté Hydrotechnique de France, 15 juin.
Rajar R. (1978). Mathematical simulation of dam-break flow, Journal of the Hydraulics Division, ASCE, 104, HY 7: 1011–1025.
Richtmyer R.D., Morton K.W. (1967). Difference methods for initial value problems, Interscience, New York.
Sakkas G. J., Strelkoff T. (1973). Dam-break flood in aprisma tic dry channel, ASCE, 99, HY12: 2195–2216.
Stoker J. J. (1957). Water Waves, Interscience publishers, Inc., New York.
Strelkoff T. (1969). One-dimensional equations of open-chan nel flow. ASCE, 95, HY3: 861–876
Su S.T. (1970). Geometric and frictional effects on sudden releases. ASCE, 96, HY11: 2185–2200
Vasiliev O.F. (1970). Numerical solution of non-linear problems of unsteady flows in open channels, Proc. 2nd International Conference on numerical methods in fluid dynamics, Berkeley, Calif., September.
Whitham G. B. (1955). The effects of hydraulic resistance in the dam-break problem. Royal Society of London, Proceedings Series A, Mathematical and Physical Science Vol. 226227.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1982 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Monaco, A., Molinaro, P. (1982). Finite Element Solution of the Lagrangian Equations of Unsteady Free-Surface Flows on Dry River Beds. In: Holz, K.P., Meissner, U., Zielke, W., Brebbia, C.A., Pinder, G., Gray, W. (eds) Finite Elements in Water Resources. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02348-8_20
Download citation
DOI: https://doi.org/10.1007/978-3-662-02348-8_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-02350-1
Online ISBN: 978-3-662-02348-8
eBook Packages: Springer Book Archive