Hydrostatic relaxation scheme for the 1D shallow water - Exner equations in bedload transport

Gunawan, P. H.; Lhébrard, Xavier

doi:10.1016/j.compfluid.2015.08.001

Cited by 22 publications

(8 citation statements)

References 23 publications

(37 reference statements)

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“…In this article, the vegetation is considered as a friction term by adding Manning friction to the governing equations directly. Following Aditya in [1] and Gunawan [10], the Manning friction is given in Equation 3. Influence of the shoreline is cosidered in the bottom topography ( ).…”

Section: Governing Equationsmentioning

confidence: 99%

Staggered Numerical Modeling for Investigating the Effectiveness of Embankment and Vegetation on the Reduction of Wave Run-up

Iryanto¹,

Mustamiin²,

Bunga³

et al. 2020

Proceedings of the Proceedings of the 7th Mathematics, Science, and Computer Science Education International Seminar, MSCEIS 20

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In this research, we develop a mathematical model to investigate the effectiveness of embankment and vegetation on the reduction of wave run-up. We solve the model numerically using a staggered conservative scheme. Wave run-up testing on a sloping beach is conducted to show the accuracy of our numerical scheme. In this case, we compare our numerical results with data of laboratory experiments of Synolakis provided in [9]. The results of the comparison show that the numerical results are in good agreement with the experimental data. Further, the results of the influence of the vegetation, embankment, and combination of both of them are presented in the article.

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Section: Governing Equationsmentioning

confidence: 99%

Staggered Numerical Modeling for Investigating the Effectiveness of Embankment and Vegetation on the Reduction of Wave Run-up

Iryanto¹,

Mustamiin²,

Bunga³

et al. 2020

Proceedings of the Proceedings of the 7th Mathematics, Science, and Computer Science Education International Seminar, MSCEIS 20

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“…From a mathematical point of view, coupling the morphodynamic model with SW equations allows us to apply a stable hyperbolic solver with a dynamic time step based on a CFL stability condition in order to avoid nonphysical oscillations and deal with geometrical discontinuities potentially formed during the bed evolution process. So far, coupled models reported in literature were only developed for unit-width formulations, hindering their application to complex 1D geometry models [4,5,[27][28][29][30][31]. Therefore, a numerical 1D coupled model able to simulate complex geometries efficiently and demonstrate its performance in realistic applications is still required.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

A 1D numerical model for the simulation of unsteady and highly erosive flows in rivers

2019

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This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights • Coupled Roe's scheme for SW-Exner equations in cross-section averaged erosive flows. • Explicit expressions for eigenvalues, eigenvectors, wave and source strengths. • A new parameter c b related to the bed change appears in the coupled Jacobian matrix. • c b depends on the erosion-deposition mechanism selected to update the cross-section. • Analytical expression for the equilibrium bed slope in variable width rectangular channels.

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“…Shallow Water Equations (SWE) is one of the hyperbolic system in conservation law which is used to solve geophysical flow problems [8], [9]. Generally, SWE is applied for water flow and gas flow.…”

Section: Shallow Water-exner Equation and Its Discretization 21 Govementioning

confidence: 99%

“…Here, Exner model is used to simulate the movement of sedimentation. Exner equation is an equation derived from conservation mass that is used to model sediment that moves because of the interaction with the flow of fluid [9]. Exner equation may be combined with SWE to model bed-load movement below the fluid current as sediment elevation , which can be affected by the velocity of water [12].…”

Section: Shallow Water-exner Equation and Its Discretization 21 Govementioning

confidence: 99%

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Shared Memory Architecture for Simulating Sediment-Fluid Flow by OpenMP

Gunawan

Utomo

2019

Jurnal Ilmu Komputer dan Informasi

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Simulation of fluid flow using Shallow water equations (SWE) and sediment movement below it using Exner equation is given. Both of the equations will be combined using splitting technique, in which SWE would be computed using Harten-Lax-van Leer and Einfeldt (HLLE) numerical flux, then Exner would be computed semi-implicitly. This paper elaborates the steps of constructing SWE-Exner model. To show the agreement of the scheme, two problems will be elaborated: (1) comparison between analytical solution and numerical solution, and (2) parallelism using OpenMP for Transcritical over a granular bump. The first problem is going to tell the discrete $L^{1}$-, $L^{2}$-, and $L^{\infty}$-norm error of the scheme, and the second one will show the simulation result, speedup, and efficiency of the scheme, which is around $56.44\%$.

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Hydrostatic relaxation scheme for the 1D shallow water - Exner equations in bedload transport

Cited by 22 publications

References 23 publications

Staggered Numerical Modeling for Investigating the Effectiveness of Embankment and Vegetation on the Reduction of Wave Run-up

Staggered Numerical Modeling for Investigating the Effectiveness of Embankment and Vegetation on the Reduction of Wave Run-up

A 1D numerical model for the simulation of unsteady and highly erosive flows in rivers

Shared Memory Architecture for Simulating Sediment-Fluid Flow by OpenMP

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