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Performance test of high resolution schemes for 1D dam break problem
This paper describes numerical experiments of high resolution schemes applied to open-channel flow equations with discontinuities in the solution. The high resolution schemes tested are the second-order symmetric TVD scheme, the upwind TVD scheme, the upwind TVB scheme, the predictor-corrector TVD scheme, the second- and third-order ENO schemes, and the space time conservation method. The six schemes except the space time conservation method are the approximate Riemann solvers, so that they need entropy correction for the numerical solution of physical meaning. These methods are applied to 1D dam-break wave propagation over the horizontal and frictionless open-channel. The computed solutions are compared with the Stoker's solution and the solution from the first-order Roe's scheme. All schemes including the Roe's scheme are found to yield results which agree well with the analytical solution when the ratio of upstream to downstream depths is moderate such as 0.05. When the ratio is reduced to 0.0001, most schemes appear to be diffusive and to retard the shock front. It was found that the second-order upwind TVB scheme and the space time conservation scheme are very accurate but expensive regarding the computing time. The second-order ENO scheme and the second-order predictor-corrector TVD scheme appear to be moderately accurate and economical.
Performance test of high resolution schemes for 1D dam break problem
This paper describes numerical experiments of high resolution schemes applied to open-channel flow equations with discontinuities in the solution. The high resolution schemes tested are the second-order symmetric TVD scheme, the upwind TVD scheme, the upwind TVB scheme, the predictor-corrector TVD scheme, the second- and third-order ENO schemes, and the space time conservation method. The six schemes except the space time conservation method are the approximate Riemann solvers, so that they need entropy correction for the numerical solution of physical meaning. These methods are applied to 1D dam-break wave propagation over the horizontal and frictionless open-channel. The computed solutions are compared with the Stoker's solution and the solution from the first-order Roe's scheme. All schemes including the Roe's scheme are found to yield results which agree well with the analytical solution when the ratio of upstream to downstream depths is moderate such as 0.05. When the ratio is reduced to 0.0001, most schemes appear to be diffusive and to retard the shock front. It was found that the second-order upwind TVB scheme and the space time conservation scheme are very accurate but expensive regarding the computing time. The second-order ENO scheme and the second-order predictor-corrector TVD scheme appear to be moderately accurate and economical.
Performance test of high resolution schemes for 1D dam break problem
KSCE J Civ Eng
Choi, Sung-Uk (author) / Paik, Joongcheol (author)
KSCE Journal of Civil Engineering ; 5 ; 273-280
2001-09-01
8 pages
Article (Journal)
Electronic Resource
English
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