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Simulation of Hydraulic Shock Waves by Hybrid Flux-Splitting Schemes in Finite Volume Method

Published online by Cambridge University Press:  05 May 2011

J.-S. Lai ,
G.-F. Lin  and
W.-D. Guo
J.-S. Lai*
Affiliation:
Hydrotech Research Institute, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
G.-F. Lin*
Affiliation:
Department of Civil Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
W.-D. Guo*
Affiliation:
Department of Civil Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
*
*Assistant Research Fellow
**Professor
***Postdoctoral Researcher
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Abstract

In the framework of the finite volume method, a robust and easily implemented hybrid flux-splitting finite-volume (HFF) scheme is proposed for simulating hydraulic shock waves in shallow water flows. The hybrid flux-splitting algorithm without Jacobian matrix operation is established by applying the advection upstream splitting method to estimate the cell-interface fluxes. The scheme is extended to be second-order accurate in space and time using the predictor-corrector approach with monotonic upstream scheme for conservation laws. The proposed HFF scheme and its second-order extension are verified through simulations of the 1D idealized dam-break problem, the 2D oblique hydraulic shock-wave problem, and the 2D dam-break experiments with channel contraction as well as wet/dry beds. Comparisons of the HFF and several well-known first-order upwind schemes are made to evaluate numerical performances. It is demonstrated that the HFF scheme captures the discontinuities accurately and produces no entropy-violating solutions. The HFF scheme and its second-order extension are proven to achieve the numerical benefits combining the efficiency of flux-vector splitting scheme and the accuracy of flux-difference splitting scheme for the simulation of hydraulic shock waves.

Keywords

Hybrid flux-splitting finite-volume schemeShallow water flowsFlux-vector splittingFlux-difference splitting
Type
Articles
Information
Journal of Mechanics , Volume 21 , Issue 2 , June 2005 , pp. 85 - 101
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2005

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