A Comparative Study of Finite Volume and Finite Element on Some Transcritical Free Surface Flow Problems

Boushaba, Farid; Chaabelasri, Elmiloud; Salhi, Najim; Elmahi, I.; Benkhaldoun, Fayssal; Borthwick, Alistair G. L.

doi:10.1142/s0219876208001522

Cited by 10 publications

(5 citation statements)

References 19 publications

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“…Finite volume methods are especially powerful on coarse non uniform grids and in calculations where the mesh moves to track interfaces or shocks taking into account discontinuities, and this stems from conservative property. Another advantage of the finite volume method is the reduced efforts for computational coding even upon unstructured mesh (Boushaba et al 2008;Bouzouf et al 1999). For all these advantages, the finite volume method is widely used in fluid mechanics.…”

Section: Resultsmentioning

confidence: 99%

A comparison of finite volume method and sharp model for two dimensional saltwater intrusion modeling

BouzoufBoutaina

ChenZhi

2014

Can. J. Civ. Eng.

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Seawater intrusion in coastal aquifers is a 3-D phenomenon. However, 3-D regional aquifer models are often limited by insufficient geological and hydrological data, the large horizontal to vertical scales ratio, and by numerical constraints. A mathematical formulation and numerical implementation of the model for saltwater intrusion problems are presented in this paper. The mathematical model is based on assumption of two-phase flow between saltwater and freshwater and Dupuit approximation. Finite volume method is used as the numerical method in non-structured grids to have flexibility upon complex configuration domain and was compared to sharp model that uses finite difference method. Both models are based on the same governing mathematical equations. Finite volume method was validated using analytical test case studies with known closed form solutions, and the results showed good agreement. Both models have then been applied to the case of saltwater intrusion into a real study case. The comparison between both methods indicates that the finite volume method provides predictions closer to the observed results.Résumé : L'arrivée de l'eau de mer dans les aquifères côtières est un phénomène tridimensionnel. Toutefois, les modèles d'aquifères régionaux tridimensionnels sont souvent limités par un manque de données géologiques et hydrologiques, le grand rapport des échelles horizontales sur verticales et par des contraintes numériques. Cet article présente une formulation mathé-matique et l'implantation numérique du modèle de problèmes d'intrusion d'eau de mer. Le modèle mathématique est basé sur l'hypothèse d'un écoulement en deux phases entre l'eau salée et l'eau douce ainsi qu'une hypothèse de Dupuit. La méthode des volumes finis est la méthode numérique utilisée dans les grilles non structurées afin d'avoir une flexibilité dans le domaine de la configuration complexe; elle a été comparée au modèle de sharp, qui utilise la méthode des différences finies. Les deux modèles sont basés sur les mêmes équations mathématiques. La méthode des volumes finis a été validée au moyen d'essais analytiques avec des solutions analytiques connues et les résultats montrent une bonne corrélation. Les deux modèles ont ensuite été appliqués au cas de l'intrusion d'eau salée pour une véritable étude de cas. La comparaison entre les deux méthodes indique que la méthode des volumes finis fournit des prévisions plus près des résultats observés. [Traduit par la Rédaction] Mots-clés : modèle de sharp, méthode des volumes finis, arrivée d'eau salée, hypothèse de Dupuit.

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Section: Resultsmentioning

confidence: 99%

A comparison of finite volume method and sharp model for two dimensional saltwater intrusion modeling

BouzoufBoutaina

ChenZhi

2014

Can. J. Civ. Eng.

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“…In the current model, schemes and techniques whose robustness is widely recognized were used: especially, the Roe-MUSCL scheme for computing convective flow fluxes and Vázquez scheme for treatment of the term source. This model is initiated and developed by Elmahi et al in [12] and refined and tested in real and complex areas by Chaabelasri et al in [13][14][15][16].…”

Section: Finite Volume Methodmentioning

confidence: 99%

Effect of Coastal Waves on Hydrodynamics in One-Inlet Coastal Nador Lagoon, Morocco

Jeyar

Chaabelasri

Salhi

2015

Modelling and Simulation in Engineering

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Nador lagoon is a coastal system connected to the sea through a narrow and shallow inlet; understanding its hydraulic performance is required for its design and operation. This paper investigates the hydrodynamic impacts of the whole lagoon due to tidal waves using a numerical approach. In this study we use a two-dimensional, depth-averaged hydrodynamic model based on so-called shallow water equations solved within triangular mesh by a developed efficient finite volume method. The method was calibrated and validated against observed data and applied to analyze and predict water levels, tidal currents, and wind effects within the lagoon. Two typical idealized scenarios were investigated: tide only and tide with wind forcing. The predicted sea surface elevations and current speeds have been presented during a typical tidal period and show correct physics in different scenarios.

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“…To incorporate friction into the present numerical scheme, the friction term is discretized using an operator splitting procedure described by Boushaba et al [27], which splits the shallow water equations (2) into two equations:…”

Section: Addition Of Friction Effectsmentioning

confidence: 99%

Numerical Simulation of Dam Break Flows Using a Radial Basis Function Meshless Method with Artificial Viscosity

Chaabelasri

2018

Modelling and Simulation in Engineering

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A simple radial basis function (RBF) meshless method is used to solve the two-dimensional shallow water equations (SWEs) for simulation of dam break flows over irregular, frictional topography involving wetting and drying. At first, we construct the RBF interpolation corresponding to space derivative operators. Next, we obtain numerical schemes to solve the SWEs, by using the gradient of the interpolant to approximate the spatial derivative of the differential equation and a third-order explicit Runge-Kutta scheme to approximate the temporal derivative of the differential equation. For the problems involving shock or discontinuity solutions, we use an artificial viscosity for shock capturing. en, we apply our scheme for several theoretical twodimensional numerical experiments involving dam break flows over nonuniform beds and moving wet-dry fronts over irregular bed topography. Promising results are obtained.

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A Comparative Study of Finite Volume and Finite Element on Some Transcritical Free Surface Flow Problems

Cited by 10 publications

References 19 publications

A comparison of finite volume method and sharp model for two dimensional saltwater intrusion modeling

A comparison of finite volume method and sharp model for two dimensional saltwater intrusion modeling

Effect of Coastal Waves on Hydrodynamics in One-Inlet Coastal Nador Lagoon, Morocco

Numerical Simulation of Dam Break Flows Using a Radial Basis Function Meshless Method with Artificial Viscosity

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