ADER schemes for the shallow water equations in channel with irregular bottom elevation

Vignoli, Gianluca; Титарев, В. А.; Toro, Eleuterio F.

doi:10.1016/j.jcp.2007.11.006

Cited by 35 publications

(25 citation statements)

References 27 publications

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“…The discharge solutions, however, have some oscillations as also observed in other methods [14,41,13,31,20,21] with a comparable magnitude. We also observe that the numerical oscillations in the discharge of the steady flows presented here are slightly larger than those in [41].…”

Section: Steady Flow Over a Bumpsupporting

confidence: 75%

“…This type of tests have been used to examine if the numerical solution can converge to the steady state under the effect of bottom topography in literature [14,41,13,31,20,21] Depending on the boundary conditions at the two ends of the domain, different regimes of the final steady state can be obtained. Same as in [32,41], we consider the following three cases by imposing different boundary conditions.…”

Section: Steady Flow Over a Bumpmentioning

confidence: 99%

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A multi-moment finite volume formulation for shallow water equations on unstructured mesh

Akoh

Satoshi

Xiao

2010

Journal of Computational Physics

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Section: Steady Flow Over a Bumpsupporting

confidence: 75%

Section: Steady Flow Over a Bumpmentioning

confidence: 99%

A multi-moment finite volume formulation for shallow water equations on unstructured mesh

Akoh

Satoshi

Xiao

2010

Journal of Computational Physics

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“…The ADER is a finite-volume Godunov-type approach that allows to obtain schemes with arbitrary order of accuracy, involving the use of data reconstruction and a first order flux solver. We can also find the extension of ADER to the multidimensional case [24,37,27,36] and to the non-homogeneous case [36,39,34].…”

Section: Introductionmentioning

confidence: 94%

Extension of WAF Type Methods to Non-Homogeneous Shallow Water Equations with Pollutant

Fernández-Nieto

Narbona-Reina

2008

J Sci Comput

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This paper deals with the extension of the WAF method to discretize Shallow Water Equations with pollutants. We consider two different versions of the WAF method, by approximating the intermediate waves using the flux of HLL or the direct approach of HLLC solver. It is seen that both versions can be written under the same form with different definitions for the approximation of the velocity waves. We also propose an extension of the method to non-homogeneous systems. In the case of homogeneous systems it is seen that we can rewrite the third component of the numerical flux in terms of an intermediate wave speed approximation. We conclude that -in order to have the same relation for non-homogeneous systems -the approximation of the intermediate wave speed must be modified. The proposed extension of the WAF method preserves all stationary solutions, up to second order accuracy, and water at rest in an exact way, even with arbitrary pollutant concentration. Finally, we perform several numerical tests, by comparing it with HLLC solver, reference solutions and analytical solutions.Short title : the WAF method for non-homogeneous SWE with pollutant.

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“…In fact, the expression of the elevation and the discharge, similar to that of [25], are the following:…”

Section: Numerical Test With Analytical Solutionmentioning

confidence: 99%

Shallow Water 1D Model for Pollution River Study

Jotsa¹

2017

PAMJ

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Abstract:In this paper a finite element 1D model for shallow water flows with distribution of chemical substances is presented. The deterministic model, based on unsteady flow and convection-diffusion-decay of the pollutants, allows for evaluating in any point of the space-time domain the concentration values of the chemical compounds. The numerical approach followed is computationally cost-effectiveness respect both the stability and the accuracy, and by means of it is possible to foresee the evolution of the concentrations.

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ADER schemes for the shallow water equations in channel with irregular bottom elevation

Cited by 35 publications

References 27 publications

A multi-moment finite volume formulation for shallow water equations on unstructured mesh

A multi-moment finite volume formulation for shallow water equations on unstructured mesh

Extension of WAF Type Methods to Non-Homogeneous Shallow Water Equations with Pollutant

Shallow Water 1D Model for Pollution River Study

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