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A New Second Order Scheme for Solving Saint Venant Equations

Author(s): Wenxue Chen; Yihong Wu; Zhiping Liu; Xiaochen Guo

Linked Author(s): Wenxue Chen, Zhiping Liu, Yihong WU

Keywords: Saint Venant equations; Numerical simulation; FVM; Flux split; Dam break

Abstract: A new second order scheme for solving Saint Venant equations is presented in this paper. The unsteady conservative equations are integrated by means of the predictor-corrector method, and are discretized in the form of Finite Volume Method (FVM). The fluxes on the control surface are split into negative and positive parts. Then the split fluxes are expanded based on the Taylor series, and the first derivatives are reserved and calculated by means of Minmod scheme. This new scheme is a kind of second order scheme and has merits as numerical stability and automatic up-wind on the characteristic directions. Therefore, the scheme can not only calculate the continuous solution, but also discontinuous solutions of Saint Venant equations. Two numerical experimentations are described, one is an unsteady subcritical flow and the other is one-dimensional dam break problem. The numerical results are in good agreement with that of Preissmann method for the subcritical flow and the theoretical results for the dam break problem.


Year: 2009

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