On the numerical solution to two fluid models via a cell centered finite volume method

Ghidaglia, Jean‐Michel; Kumbaro, Anela; Coq, G. Le

doi:10.1016/s0997-7546(01)01150-5

Cited by 76 publications

(74 citation statements)

References 16 publications

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“…The main difficulty for this class of problems is not only the usual one for fluids pertaining to the free-surface flow (e.g. see [22,42,33,5,72,70,71]) but also the fluid-structure interface. Providing reliable description at the interface for a fluid-structure interaction problem is quite a challenge, since the descriptions generally used for each of the sub-problems are different: for the structure part, it is natural to follow material point motion in a Lagrangian formulation, while an Eulerian formulation is often preferred 1 for the fluid part.…”

Section: Introductionmentioning

confidence: 99%

Partitioned solution to fluid–structure interaction problem in application to free-surface flows

Kassiotis

Ibrahimbegović

Matthies

2010

European Journal of Mechanics - B/Fluids

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In this work we discuss a way to compute the impact of free-surface flow on nonlinear structures. The approach chosen rely on a partitioned strategy that allows to solve strongly coupled fluid-structure interaction problem. It is then possible to re-use existing and validated strategy for each sub-problem. The structure is formulated in a Lagrangian way and solved by the finite element method. The free-surface flow approach considers a Volume-Of-Fluid (VOF) strategy formulated in an Arbitrary Lagrangian-Eulerian (ALE) framework, and the finite volume are used to discrete and solve this problem. The software coupling is ensured in an efficient way using the Communication Template Library (CTL). Numerical examples presented herein concern 2D validations case but also 3D problems with a large number of equations to be solved.

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Section: Introductionmentioning

confidence: 99%

Partitioned solution to fluid–structure interaction problem in application to free-surface flows

Kassiotis

Ibrahimbegović

Matthies

2010

European Journal of Mechanics - B/Fluids

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“…The reconstruction procedure employed in the present study is described below. In order to discretise the advective flux f (w), we use the so-called FVCF scheme [29] …”

Section: Finite Volume Schemementioning

confidence: 99%

Modified shallow water equations for significantly varying seabeds

Dutykh

Clamond²

2016

Applied Mathematical Modelling

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Abstract. In the present study, we propose a modified version of the Nonlinear Shallow Water Equations (Saint-Venant or NSWE) for irrotational surface waves in the case when the bottom undergoes some significant variations in space and time. The model is derived from a variational principle by choosing an appropriate shallow water ansatz and imposing some constraints. Our derivation procedure does not explicitly involve any small parameter and is straightforward. The novel system is a non-dispersive non-hydrostatic extension of the classical Saint-Venant equations. A key feature of the new model is that, like the classical NSWE, it is hyperbolic and thus similar numerical methods can be used. We also propose a finite volume discretisation of the obtained hyperbolic system. Several test-cases are presented to highlight the added value of the new model. Some implications to tsunami wave modelling are also discussed.

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“…Advective and dispersive numerical fluxes. Over the last twenty years numerous numerical fluxes F have been proposed to discretize advective operators [41,25,37,23,5]. We select three quite different flux functions.…”

Section: Finite Volume Discretizationmentioning

confidence: 99%

Finite volume methods for unidirectional dispersive wave models

Dutykh

Katsaounis

Mitsotakis

2012

Numerical Methods in Fluids

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Abstract. We extend the framework of the finite volume method to dispersive unidirectional water wave propagation in one space dimension. In particular we consider a KdV-BBM type equation. Explicit and IMEX Runge-Kutta type methods are used for time discretizations. The fully discrete schemes are validated by direct comparisons to analytic solutions. Invariants conservation properties are also studied. Main applications include important nonlinear phenomena such as dispersive shock wave formation, solitary waves and their various interactions.

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On the numerical solution to two fluid models via a cell centered finite volume method

Cited by 76 publications

References 16 publications

Partitioned solution to fluid–structure interaction problem in application to free-surface flows

Partitioned solution to fluid–structure interaction problem in application to free-surface flows

Modified shallow water equations for significantly varying seabeds

Finite volume methods for unidirectional dispersive wave models

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