Cubic‐Spline Interpolation in Lagrangian Advection Computation
Publication: Journal of Hydraulic Engineering
Volume 117, Issue 2
Abstract
In the computation of advection-diffusive contaminant transport, the Holly-Preissmann characteristics scheme for the advection operator is known to be quite accurate and stable. However, these qualities are obtained at the expense of having to solve an auxiliary transport problem for the concentration derivative. This paper shows that the Holly-Preissmann Hermite cubic interpolating polynomial can be replaced by a cubic-spline interpolating polynomial, thus obviating the need to solve the auxiliary problem. Although the cubic-spline approach lacks some of the intuitively appealing features of the Holly-Preissmann approach, it is nearly as accurate while offering a computational time saving of 20%–30%, with a corresponding reduction in code size. The paper outlines the computational procedure, and presents demonstrative calculations illustrating the performance of the method for the familiar test case of advective transport of a Gaussian contaminant distribution.
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References
1.
Atkinson, K. E. (1978). An introduction to numerical analysis, John Wiley and Sons, New York, N.Y.
2.
Branski, J. M., and Holley, E. R. (1986). “Advection calculations using spline schemes.” Proc. Water Forum '86, ASCE, 2, 1807–1814.
3.
Carnahan, B., Luther, H. A., and Wilkes, J. O. (1969). Applied numerical methods. John Wiley and Sons, New York, N.Y.
4.
Holly, F. M., Jr., and Rahuel, J. L. (1990). “New numerical/physical framework for mobile‐bed modelling part I—Numerical and physical principles.” J. Hydr. Res., 28(4), 401–416.
5.
Holly, F. M., Jr., and Preissmann, A. (1977). “Accurate calculation of transport in two dimensions.” J. Hydr. Div., ASCE, 103(11), 1259–1277.
6.
Komatsu, T., Holly, F. M., Jr., Nakashiki, N., and Ohgushi, K. (1985). “Numerical calculation of pollutant transport in one and two dimensions.” J. Hydroscience and Hydr. Engrg., 3(2), 15–30.
7.
Toda, K., and Holly, F. M., Jr. (1987). “Hybrid numerical method for linear advection‐diffusion.” Microsoftware for Engrs., 3(4), 199–205.
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Copyright © 1991 ASCE.
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Published online: Feb 1, 1991
Published in print: Feb 1991
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