Abstract
Explicit methods of solution, of the Saint Venant equations for open channel flow, have not been favoured for use in practice by some engineers. The reason, given for this disfavour, is that the observance of the so called Courant condition for stability imposes a severe restriction on the size of the time step used at each stage of the computation, even though the acceptable accuracy may not warrant the use of such small time steps, and that this in turn results in large computation times. The limitation, on the size of the time steps seems, to the writer, to stem indirectly from an assumption that is implicit in the procedure normally used. This assumption seems to be that in the computation of the dependent variables at a grid point on the new time level, its domain of dependence should lie within the adjoining cells of the grid used. This paper shows how, when this assumption is relaxed, it is possible to use arbitrary time steps without violating the essence of the Courant condition.
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
Liggett J.A., (Aug 1968) Mathematical Flow Determination in Open Channels, Journal of the Eng. Mech. Div. ASCE, EM4, 947–963.
Sivaloganathan K., (Jun 1980) Numerical Computation of Flows in Storm Water Sewers, PhD Thesis, University of London, 53–58.
Sivaloganathan K., (Jul 1979) Channel Flow Computations Using Characteristics, Journal of Hyd.r. Div. ASCE, RY7, Vol 105, 899–910.
Strelkoff T., (May 1969) One Dimensional Equations of Open Channel Flow, Journal of the Uydr. Div. ASCE, RY3, Vol 95, 861–876.
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
Sivaloganathan, K. (1982). On the Use of Explicit Methods of Solution of the Saint Venant Equations for open Channel Flow. 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_22
Download citation
DOI: https://doi.org/10.1007/978-3-662-02348-8_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-02350-1
Online ISBN: 978-3-662-02348-8
eBook Packages: Springer Book Archive