Staggered scheme for the Exner–shallow water equations

Gunawan, P. H.; Eymard, Robert; Pudjaprasetya, S. R.

doi:10.1007/s10596-015-9533-4

Cited by 19 publications

(5 citation statements)

References 27 publications

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“…We would like to emphasize that, in fact, they only conclude to the bad behavior of 1 possible way to perform the splitting approach, not of the splitting approach itself. First attempts to introduce stable splitting approaches were performed recently in related works,() where the authors proposed what they call a weak coupling approach for the SWExner system by introducing a slight modification in the discretization of the Exner Equation (1c) and in the work of Gunawan et al, where the authors dealt with staggered grids.…”

Section: Introductionmentioning

confidence: 99%

A simple three‐wave approximate Riemann solver for the Saint‐Venant‐Exner equations

Audusse

Chalons

Ung

2018

Numerical Methods in Fluids

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Erosion and sediments transport processes have a great impact on industrial structures and on water quality. Despite its limitations, the Saint-Venant-Exner system is still (and for sure for some years) widely used in industrial codes to model the bedload sediment transport. In practice, its numerical resolution is mostly handled by a splitting technic that allows a weak coupling between hydraulic and morphodynamic distinct softwares but may suffer from important stability issues. In recent works, many authors proposed alternative methods based on a strong coupling that cure this problem but are not so trivial to implement in an industrial context. In this work, we then pursue two objectives. First we propose a very simple scheme based on an approximate Riemann solver, respecting the strong coupling framework, and we demonstrate its stability and accuracy through a number of numerical test cases. But, second, we reinterpret our scheme as a splitting technic and we extend the purpose to propose what should be the minimal coupling that ensures the stability of the global numerical process in industrial codes, at least when dealing with collocated finite volume method. The resulting splitting method is, up to our knowledge, the only one for which stability properties are fully demonstrated.

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Section: Introductionmentioning

confidence: 99%

A simple three‐wave approximate Riemann solver for the Saint‐Venant‐Exner equations

Audusse

Chalons

Ung

2018

Numerical Methods in Fluids

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“…Note that, this Exner equation uses the Grass formula [13] as the bed load function. See references [9], [14] for more detail about other bed load functions.…”

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

confidence: 99%

“…It means that the value of +1 not only needs , it also needs +1 that is found earlier from SWE (see Figure 3). Exner equation can be discretized as follows [14].…”

Section: February 2019mentioning

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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“…Different from the collocated finite volume, here we implement the staggered finite volume method to approximate the rotating shallow water equations (1) to (3). This scheme is chosen because it is efficient, relatively simple, and robust, see Doyen and Gunawan (2014), Stelling and Duinmeijer (2003), Pudjaprasetya and Magdalena (2014) and Gunawan et al (2015) for thorough discussions about this method. Moreover, thorough study in Doyen and Gunawan (2014) has shown the staggered scheme produce nicely comparable results with the collocation method counterparts.…”

Section: Introductionmentioning

confidence: 99%

Explicit staggered grid scheme for rotating shallow water equations on geostrophic flows

Gunawan

Pudjaprasetya

2018

PCFD

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This paper is devoted to the description of an explicit staggered grid scheme for the rotating shallow water equations in one and two-dimension. The shallow water equations is approximated using the momentum conservative scheme, and the Coriolis terms is calculated using the Crank-Nicolson method. The resulting scheme is implemented for simulating various rotating phenomena, such as, the interior gravity wave, oscillation in a paraboloid, coastal and equatorial Kelvin waves. Comparison with exact solution or other collocated scheme (Suliciu or HLLC scheme) give good agreement. The discrete L 1 error and the convergence rate of the scheme are shown to be satisfied. Moreover, our numerical experiments satisfy entropy stability. Except from adjustment for the initial and boundary conditions, no special treatment are required for all simulations above. And these indicate the robustness of our explicit staggered grid scheme.

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Staggered scheme for the Exner–shallow water equations

Cited by 19 publications

References 27 publications

A simple three‐wave approximate Riemann solver for the Saint‐Venant‐Exner equations

A simple three‐wave approximate Riemann solver for the Saint‐Venant‐Exner equations

Shared Memory Architecture for Simulating Sediment-Fluid Flow by OpenMP

Explicit staggered grid scheme for rotating shallow water equations on geostrophic flows

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