Numerical Tracking of Shallow Water Waves by the Unstructured Finite Volume WAF Approximation

Loukili, Youssef; Soulaïmani, Azzeddine

doi:10.1080/15502280601149577

Cited by 41 publications

(44 citation statements)

References 32 publications

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“…Billett and Toro considered an unsplit multidimensional WAF scheme, though for structured meshes [1,2]. Loukili and Soulaimani [8] are alone in reporting the application of the WAF scheme to an unstructured mesh. Herein, we follow on from their work on this application to improve aspects related to wetting/drying, stability and well-balancedness, in order to provide a general framework for using the WAF scheme for shallow water equations on unstructured meshes with real topography and friction.…”

Section: The Waf Scheme On Unstructured Meshesmentioning

confidence: 99%

A Weighted Average Flux (WAF) scheme applied to shallow water equations for real-life applications

Ata

Pavan

Khelladi

et al. 2013

Advances in Water Resources

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Section: The Waf Scheme On Unstructured Meshesmentioning

confidence: 99%

A Weighted Average Flux (WAF) scheme applied to shallow water equations for real-life applications

Ata

Pavan

Khelladi

et al. 2013

Advances in Water Resources

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“…They do not completely vanish as the discretization parameters are refined, and they also show up in [15] where the discretization method is quite different. In order to emphasize the three-dimensional character of the computational solver, let us extend this Stoker test case to a full three-dimensional situation, following [1,22] …”

Section: The Stoker Test Casementioning

confidence: 99%

On the modeling and simulation of non-hydrostatic dam break flows

Caboussat¹,

Boyaval²,

Masserey³

2011

Comput. Visual Sci.

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The numerical simulation of three-dimensional dam break flows is discussed. A non-hydrostatic numerical model for free-surface flows is considered, which is based on the incompressible Navier-Stokes equations coupled with a volume-of-fluid approach. The numerical results obtained for a variety of benchmark problems show the validity of the numerical approach, in comparison with other numerical models, and allow to investigate numerically the non-hydrostatic three-dimensional effects, in particular for the usual test cases where hydrostatic approximations are known analytically. The numerical experiments on actual topographies, in particular the Malpasset dam break and the (hypothetical) break of the Grande-Dixence dam in Switzerland, also illustrate the capabilities of the method for large-scale simulations and real-life visualization. Keywords: Free-surface hydrodynamical flows, Hydraulic engineering, Volume-of-fluid modeling, Three-dimensional non-hydrostatic model, Dam breaks, Finite-element method.

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“…Loukili and Soulaïmani suggested in [38] that according to a linearized stability analysis applied to the SWE, the following Courant-Friedrichs-Lewy (CFL) restriction must be respected:…”

Section: Time Integrationmentioning

confidence: 99%

The natural volume method (NVM): Presentation and application to shallow water inviscid flows

Ata

Soulaïmani

Chinesta

2008

Numerical Methods in Fluids

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SUMMARYIn this paper a fully Lagrangian formulation is used to simulate 2D shallow water inviscid flows. The natural element method (NEM), which has been used successfully with several solid and fluid mechanics applications, is used to approximate the fluxes over Voronoi cells. This particle-based method has shown huge potential in terms of handling problems involving large deformations. Its main advantage lies in the interpolant character of its shape function and consequently the ease it allows with respect to the imposition of Dirichlet boundary conditions.In this paper, we use the NEM collocationally, and in a Lagrangian kinematic description, in order to simulate shallow water flows that are boundary moving problems. This formulation is ultimately shown to constitute a finite-volume methodology requiring a flux computation on Voronoi cells rather than the standard elements, in a triangular or quadrilateral mesh. St Venant equations are used as the mathematical model. These equations have discontinuous solutions that physically represent the existence of shock waves, meaning that stabilization issues have thus been considered. An artificial viscosity deduced from an analogy with Riemann solvers is introduced to upwind the scheme and therefore stabilize the method. Some inviscid bidimensional flows were used as preliminary benchmark tests, which produced decent results, leading to well-founded hopes for the future of this method in real applications.

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Numerical Tracking of Shallow Water Waves by the Unstructured Finite Volume WAF Approximation

Cited by 41 publications

References 32 publications

A Weighted Average Flux (WAF) scheme applied to shallow water equations for real-life applications

A Weighted Average Flux (WAF) scheme applied to shallow water equations for real-life applications

On the modeling and simulation of non-hydrostatic dam break flows

The natural volume method (NVM): Presentation and application to shallow water inviscid flows

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