The MOOD method for the non-conservative shallow-water system

Clain, Stéphane; Figueiredo, Joana

doi:10.1016/j.compfluid.2016.11.013

Cited by 18 publications

(17 citation statements)

References 60 publications

(98 reference statements)

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“…To the extent of our knowledge, there is no such solution referenced. We turn to a two-dimensional experiment, by considering the steady vortex (see [52]), to assess the order of accuracy of the scheme. Indeed, the scheme is exact for all the steady states in the x and y directions, but the question of the preservation of a fully 2D steady state arises.…”

Section: D Steady Vortexmentioning

confidence: 99%

A well-balanced scheme for the shallow-water equations with topography

Michel-Dansac¹,

Berthon²,

Clain³

et al. 2016

Computers & Mathematics with Applications

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International audienceA non-negativity preserving and well-balanced scheme that exactly preserves all the smooth steady states of the shallow water system, including the moving ones, is proposed. In addition, the scheme must deal with vanishing water heights and transitions between wet and dry areas. A Godunov-type method is derived by using a relevant average of the source terms within the scheme, in order to enforce the required well-balance property. A second-order well-balanced MUSCL extension is also designed. Numerical experiments are carried out to check the properties of the scheme and assess the ability to exactly preserve all the steady states

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Section: D Steady Vortexmentioning

confidence: 99%

A well-balanced scheme for the shallow-water equations with topography

Michel-Dansac¹,

Berthon²,

Clain³

et al. 2016

Computers & Mathematics with Applications

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“…Another point is the capacity of the method to directly take into account the physics of the problem (positivity, entropy production, etc.). The MOOD paradigm has been developed for non-stationary hyperbolic system [51,29,14] and we aim at demonstrating that the methodology is adapted to steady-state situations. The key point is the introduction of an additional unknown vector which represents the maximum admissible polynomial degree on each cell.…”

mentioning

confidence: 99%

a posteriori stabilized sixth-order finite volume scheme for one-dimensional steady-state hyperbolic equations

2017

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To cite this version:Stéphane Clain, Raphaël Loubère, Gaspar Machado. a posteriori stabilized sixth-order finite volume scheme for one-dimensional steady-state hyperbolic equations. 2016. a posteriori stabilized sixth-order finite volume scheme for one-dimensional steady-state hyperbolic equationsWe propose a new family of finite volume high-accurate numerical schemes devoted to solve one-dimensional steady-state hyperbolic systems. High-accuracy (up to the sixth-order presently) is achieved thanks to polynomial reconstructions while stability is provided with an a posteriori MOOD method which control the cell polynomial degree for eliminating non-physical oscillations in the vicinity of discontinuities. Such a procedure demands the determination of a chain detector to discriminate between troubled and valid cells, a cascade of polynomial degrees to be successively tested when oscillations are detected, and a parachute scheme corresponding to the last, viscous, and robust scheme of the cascade. Experimented on linear, Burgers', and Euler equations, we demonstrate that the schemes manage to retrieve smooth solutions with optimal order of accuracy but also irregular solutions without spurious oscillations.

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“…Next, we focus on a partial dam-break (see for instance [42,18]). This experiment concerns a dam that has partially broken, leaving a corridor where the water flows.…”

Section: Partial Dam-breakmentioning

confidence: 99%

A well-balanced scheme for the shallow-water equations with topography or Manning friction

Michel-Dansac

Berthon

Clain

et al. 2017

Journal of Computational Physics

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International audienceWe consider the shallow-water equations with Manning friction and topography source terms. The main purpose of this work concerns the derivation of a non-negativity preserving and well-balanced scheme that approximates solutions of the system and preserves the associated steady states, including the moving ones. In addition, the scheme has to deal with vanishing water heights and transitions between wet and dry areas. To address such issues, a particular attention is paid to the study of the steady states related to the friction source term. Then, a Godunov-type scheme is obtained by using a relevant average of the source terms in order to enforce the required well-balance property. An implicit treatment of both topography and friction source terms is also exhibited to improve the scheme while dealing with vanishing water heights. A second-order well-balanced MUSCL extension is designed, as well as an extension for the two-dimensional case. Numerical experiments are performed in order to highlight the properties of the scheme

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The MOOD method for the non-conservative shallow-water system

Cited by 18 publications

References 60 publications

A well-balanced scheme for the shallow-water equations with topography

A well-balanced scheme for the shallow-water equations with topography

a posteriori stabilized sixth-order finite volume scheme for one-dimensional steady-state hyperbolic equations

A well-balanced scheme for the shallow-water equations with topography or Manning friction

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