Analysis of a finite-volume-finite-element scheme for a nuclear transport model

Choquet, Catherine; Zimmermann, Sebastien

doi:10.1093/imanum/drp029

Cited by 2 publications

(2 citation statements)

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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%

“…Models similar to (1.1) also arise in other applications, including so-called timedependent natural convection flows, in which the Navier-Stokes equations are coupled with a transport equation for temperature [21], thermal convection flows [52], the melting of glaciers [36], aluminum production [31], petroleum reservoir engineering [50], and nuclear waste contamination [20]. The present numerical method should therefore be of interest in these applications.…”

Section: Related Workmentioning

confidence: 99%

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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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