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On the Use of Temporal Reachout Technique for Characteristics Method with Time-Line Cubic Spline Interpolation

Published online by Cambridge University Press:  16 June 2011

T.-L. Tsai  and
J.-Y. Chen
T.-L. Tsai*
Affiliation:
Department of Civil and Water Resources Engineering, National Chiayi University, Chiayi City, Taiwan 60004, R.O.C.
J.-Y. Chen
Affiliation:
Department of Civil and Water Resources Engineering, National Chiayi University, Chiayi City, Taiwan 60004, R.O.C.
*
*Assistant Professor, corresponding author
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Abstract

The study had indicated that the computational performances of the characteristics method with the time-line cubic spline interpolation are related to the endpoint constraint, especially for large Courant number in which the foot of the characteristic trajectory is located near the endpoint. The first derivative endpoint constraint with higher-order central difference approximation provides better simulation results among various endpoint constraints, but it still induces some degree of numerical error. In this study, by locating the foot of the characteristic trajectory away from the endpoint, the temporal reachout technique is proposed to avoid the effect of endpoint constraint on the time-line cubic spline interpolation. Modeling the transport of a Gaussian concentration distribution in a uniform flow with constant diffusion coefficient and the viscous Burgers equation is used to examine the temporal reachout technique. The outcomes show that the temporal reachout technique yields much better simulation results than the first derivative endpoint constraint with higher-order central difference approximation. The effect of endpoint constraint on the time-line cubic spline interpolation can be greatly diminished by the use of the temporal reachout technique.

Keywords

Characteristics methodCubic spline interpolationTemporal reachout techniqueTime-line interpolation
Type
Technical Note
Information
Journal of Mechanics , Volume 27 , Issue 2 , June 2011 , pp. N5 - N11
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2011

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