1987
DOI: 10.1080/00221688709499287
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Simulation of one-dimensional dam-break flows

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Cited by 100 publications
(25 citation statements)
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“…To check their applicability to the real conditions of wave propagations, the simulated results were usually compared to the analytical solutions of the shocks propagating in a 1D horizontal, frictionless channel ÿrst, then to the experimental data in a sloped, frictional channel. The numerical schemes using the ÿnite-di erence method include the Preissmann four-point scheme [2], Holly-Preissmann two-point together with the reach-back characteristics scheme [3], MacCormack scheme [4][5][6][7], Lambda scheme [7], Gabutti scheme [7], Beam-Warming scheme and its modiÿcations [8][9][10], ux di erence splitting scheme [11][12][13][14], Godunov-type upwind scheme with a Riemann solver [13; 15-19], modiÿed Godunov scheme [20], total variation diminishing (TVD) scheme [21][22][23], and semi-Lagrangian scheme [24]. Additionally, the numerical schemes using the ÿnite-element method include the Eulerian-Lagrangian linked Galerkin scheme [25], the dissipative Galerkin scheme [26][27][28], Petrov-Galerkin scheme [18; 29], Taylor-Galerkin scheme [30], and Addcollocation scheme [31].…”
Section: Introductionmentioning
confidence: 99%
“…To check their applicability to the real conditions of wave propagations, the simulated results were usually compared to the analytical solutions of the shocks propagating in a 1D horizontal, frictionless channel ÿrst, then to the experimental data in a sloped, frictional channel. The numerical schemes using the ÿnite-di erence method include the Preissmann four-point scheme [2], Holly-Preissmann two-point together with the reach-back characteristics scheme [3], MacCormack scheme [4][5][6][7], Lambda scheme [7], Gabutti scheme [7], Beam-Warming scheme and its modiÿcations [8][9][10], ux di erence splitting scheme [11][12][13][14], Godunov-type upwind scheme with a Riemann solver [13; 15-19], modiÿed Godunov scheme [20], total variation diminishing (TVD) scheme [21][22][23], and semi-Lagrangian scheme [24]. Additionally, the numerical schemes using the ÿnite-element method include the Eulerian-Lagrangian linked Galerkin scheme [25], the dissipative Galerkin scheme [26][27][28], Petrov-Galerkin scheme [18; 29], Taylor-Galerkin scheme [30], and Addcollocation scheme [31].…”
Section: Introductionmentioning
confidence: 99%
“…A very important family of the first-order schemes is the upwind methods, and the most popular upwind method is the Godunov scheme (Fennema and Chaudhry 1987). The direction of propagation of information (or waves) in this method is consistent with the spatial derivative discretization.…”
Section: First-order Finite Difference Schemesmentioning
confidence: 99%
“…Those are for example, the RoeÕs method [10], the Beam-warming scheme [9], the monotonic upstream schemes for conservation laws (MUSCL) using curve-linear coordinate [4], the Osher and Salmon scheme [36], the essentially nonoscillatory (ENO) schemes [24] and the Harten, Lax and van Leer (HLL) solver [21]. Most of these methods have the capability of shock capturing with a high level of accuracy in few computational cells, and the flux vector is determined based on the wave propagation structure.…”
Section: Introductionmentioning
confidence: 99%