An hybrid finite volume–finite element method for variable density incompressible flows

Calgaro, Caterina; Creusé, Emmanuel; Goudon, Thierry

doi:10.1016/j.jcp.2008.01.017

Cited by 52 publications

(74 citation statements)

References 47 publications

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“…Another strategy will be to design a finite-volume method applied to a conservative formulation of the model. An idea will be to adapt the code from [3] to our problem. The latter code solves the incompressible Navier-Stokes equations.…”

Section: Resultsmentioning

confidence: 99%

Study of a low Mach nuclear core model for single-phase flows

et al. 2012

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Abstract. This paper deals with the modelling of the coolant (water) in a nuclear reactor core. This study is based on a monophasic low Mach number model (Lmnc model) coupled to the stiffened gas law for a single-phase flow. Some analytical steady and unsteady solutions are presented for the 1D case. We then introduce a numerical scheme to simulate the 1D model in order to assess its relevance. Finally, we carry out a normal mode perturbation analysis in order to approximate 2D solutions around the 1D steady solutions.Résumé. Dans cet article, nous nous intéressonsà la modélisation de l'écoulement de l'eau dans le circuit primaire d'un réacteur nucléaire. Pour cela, nous utilisons un modèle bas-Mach monophasique (modèle Lmnc) pour une loi d'état de type gaz raidi. Nous présentons des solutions analytiques 1D stationnaires et instationnaires pour certains types de données. Nous simulons ensuite le modèle afin d'évaluer sa pertinence. La dernière partie est consacréeà une analyse de pertubations en modes normaux réalisée pour approcher les solutions 2Dà partir des solutions stationnaires 1D.

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Section: Resultsmentioning

confidence: 99%

Study of a low Mach nuclear core model for single-phase flows

et al. 2012

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“…We underline that for multi-physics coupled models, a particular attention must be paid in the approximation of the continuous velocity associated to any point of ∂ C i (see [3]). In (7), ρ i j l and ρ j l i denote the density reconstructions on the segments Γ (T ) i j l , for l = 1, 2.…”

Section: Mesh Definitions and Notationsmentioning

confidence: 99%

$$L^\infty $$ -Stability of IMEX-BDF2 Finite Volume Scheme for Convection-Diffusion Equation

Calgaro

Ezzoug

2017

Springer Proceedings in Mathematics &Amp; Statistics

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In this paper, we propose a finite volume scheme for solving a twodimensional convection-diffusion equation on general meshes. This work is based on a implicit-explicit (IMEX) second order method and it is issued from the seminal paper [2]. In the framework of MUSCL methods, we will prove that the local maximum property is guaranteed under an explicit Courant-Friedrichs-Levy condition and the classical hypothesis for the triangulation of the domain.

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“…Fast and reliable numerical methods for related problems in two and three space dimensions include stable FE methods [37,49], discontinuous Galerkin methods [18], finite volume (FV) formulations [5,11], finite difference schemes [43,47], and hybrid/combined FV-FE methods [16,20,33,46]. The particular concept of FVE meth-ods (see [15]) is intermediate between finite volumes and finite elements.…”

Section: Related Workmentioning

confidence: 99%

“…Kleine and Reddy [37] study different geometries for settling tanks using a FE method, while Calgaro, Creusé, and Goudon [16] couple Taylor-Hood finite elements for the flow equations with finite volumes for a conservation law.…”

Section: Related Workmentioning

confidence: 99%

A Stabilized Finite Volume Element Formulation for Sedimentation-Consolidation Processes

Bürger¹,

Ruiz–Baier²,

Torres³

2012

SIAM J. Sci. Comput.

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Abstract.A model of sedimentation-consolidation processes in so-called clarifier-thickener units is given by a parabolic equation describing the evolution of the local solids concentration coupled with a version of the Stokes system for an incompressible fluid describing the motion of the mixture. In cylindrical coordinates, and if an axially symmetric solution is assumed, the original problem reduces to two space dimensions. This poses the difficulty that the subspaces for the construction of a numerical scheme involve weighted Sobolev spaces. A novel finite volume element method is introduced for the spatial discretization, where the velocity field and the solids concentration are discretized on two different dual meshes. The method is based on a stabilized discontinuous Galerkin formulation for the concentration field, and a multiscale stabilized pair of P 1 -P 1 elements for velocity and pressure, respectively. Numerical experiments illustrate properties of the model and the satisfactory performance of the proposed method.

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An hybrid finite volume–finite element method for variable density incompressible flows

Cited by 52 publications

References 47 publications

Study of a low Mach nuclear core model for single-phase flows

Study of a low Mach nuclear core model for single-phase flows

$$L^\infty $$ -Stability of IMEX-BDF2 Finite Volume Scheme for Convection-Diffusion Equation

A Stabilized Finite Volume Element Formulation for Sedimentation-Consolidation Processes

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