Characteristics method with cubic‐spline interpolation for open channel flow computation

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Abstract
In the framework of the specified‐time‐interval scheme, the accuracy of the characteristic method is greatly related to the form of the interpolation. The linear interpolation was commonly used to couple the characteristics method (LI method) in open channel flow computation. The LI method is easy to implement, but it leads to an inevitable smoothing of the solution. The characteristics method with the Hermite cubic interpolation (HP method, originally developed by Holly and Preissmann, 1977) was then proposed to largely reduce the error induced by the LI method. In this paper, the cubic‐spline interpolation on the space line or on the time line is employed to integrate with characteristics method (CS method) for unsteady flow computation in open channel. Two hypothetical examples, including gradually and rapidly varied flows, are used to examine the applicability of the CS method as compared with the LI method, the HP method, and the analytical solutions. The simulated results show that the CS method is comparable to the HP method and more accurate than the LI method. Without tackling the additional equations for spatial or temporal derivatives, the CS method is easier to implement and more efficient than the HP method. Copyright © 2004 John Wiley & Sons, Ltd.

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