Spline Interpolations for Water Hammer Analysis
Publication: Journal of Hydraulic Engineering
Volume 117, Issue 10
Abstract
The method of characteristics (MOC) with spline polynomials for interpolations was investigated for numerical water hammer analysis for a frictionless horizontal pipe. A new analysis quantifies numerical errors in a systematic and dimensionless way and is used to evaluate the performance of three spline polynomials and to compare them with other numerical schemes for water hammer analysis, as well as to assess the effect of required additional interpolation boundary conditions on the overall accuracy of spline and two‐point fourth‐order Hermite schemes. For the sudden valve closure test case investigated, the overall accuracy with splines is significantly improved compared to the MOC with linear interpolations or to second‐order explicit finite difference techniques. Compared to the Hermite method, the spline scheme has about the same overall accuracy and has the advantage of offering a choice between several spline polynomials with different interpolating characteristics and of being unconditionally stable.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Branski, J. M., and Holley, E. R. (1986). “Calculation of advective transport by spline functions.” Proc. Water Forum 86, ASCE, 2, 1807–1814.
2.
Branski, J. M., Sibetheros, I. A., and Holley, E. R. (1989). “Advection error analysis with interpolation schemes.” Hydrosoft, 2(4), 186–191.
3.
Carslaw, H. S., and Jaeger, J. C. (1959). Conduction of heat in solids. 2d Ed., Oxford Press, London, United Kingdom.
4.
Chaudhry, M., and Hussaini, M. (1983). “Second‐order explicit finite‐difference methods for transient‐flow analysis.” Proc., Applied Mechanics, Bioengineering, and Fluids Engineering Conf., ASME, Houston, Tex. 9–15.
5.
de Boor, C. (1978). A practical guide to splines. Springer‐Verlag, New York, N.Y.
6.
Goldberg, D., and Wylie, E. (1983). “Characteristics method using time‐line interpolations.” J. Hydr. Div., ASCE, 109(5), 670–683.
7.
Holly, F. M., Jr., and the Preissmann, A. (1977). “Accurate calculation of transport in two directions.” J. Hydr. Engrg., ASCE, 103(11), 1259–1277.
8.
Kershaw, D. (1972). “The orders of approximation of the first derivative of cubic splines at the knots.” Math. Comput., 26(117), 191–198.
9.
Leendertse, J. J. (1967). “Aspects of a computational model for long‐period water‐wave propagation.” Memo RM‐5294‐PR, Rand Corporation, Santa Monica, Calif.
10.
Rubin, S., and Khosla, P. (1977). “Polynomial interpolation methods for viscous flow calculations.” J. Comput. Phys., 24(3), 217–244.
11.
Schol, G. A., and Holly, F. M., Jr. (1991). “Cubic‐spline interpolation in Lagrangian advection computation.” J. Hydr. Engrg., ASCE, 117(2), 248–253.
12.
Sibetheros, I. A., Holley, E. R., and Branski, J. M., (1987). “Spline interpolations for water hammer analysis.” Proc., Nat. Conf. on Hydraulic Engineering, R. M. Ragan, ed., ASCE, Williamsburg, Va., 421–426.
13.
Wiggert, D., and Sundquist, M. (1977). “Fixed‐grid characteristics for pipeline transients.” J. Hydr. Div., ASCE, 103(12), 1403–1416.
14.
Wylie, E., and Streeter, V. (1983). Fluid transients. FEB Press, Ann Arbor, Mich.
Information & Authors
Information
Published In
Copyright
Copyright © 1991 ASCE.
History
Published online: Oct 1, 1991
Published in print: Oct 1991
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.