Finite element/volume solution to axisymmetric conservation laws

Guardone, Alberto; Vigevano, Luigi

doi:10.1016/j.jcp.2006.08.018

Cited by 24 publications

(28 citation statements)

References 43 publications

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“…Contributions more closely related to the present paper include the work of Guardone and Vigevano [35], who present a "node-pair" FE method and make the link with the FV approximation for axially symmetric scalar conservation laws. 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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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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“…The axisymmetric approximation and its application to conservation laws is discussed in Guardone and Vigevano [51]. The axisymmetric form of the conservation laws, (2.1)-(2.3), is given by…”

Section: Axisymmetric Formulationmentioning

confidence: 99%

A Cell-Centered Multiphase ALE Scheme With Structural Coupling

Dunn

2012

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“…The first step is a simple Laplace-type differential equation that can be solved with standard finite element techniques, see, for instance, [32]. The second step can be treated with finite volume techniques, in particular we have used the one described in [54,55] and we have used a Roe-type Riemann solver adapted to reacting gas mixtures, for details see [50]. Problem (10) can be formulated as a standard ordinary differential equation in fact, since in the second step ρ and m are constant, we get…”

Section: The Numerical Schemementioning

confidence: 99%

A multiscale technique for the validation of a numerical code for predicting the pressure field induced by a high-power spark

Villa¹,

Malgesini²,

Barbieri³

2011

J. Phys. D: Appl. Phys.

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A more precise knowledge of the pressure field induced by a high-power spark is essential to estimate the mechanical damage that a lightning strike can induce near the impact point. In this work we propose a multiscale approach to validate a numerical magnetohydro-dynamic model that can predict the pressure field when a very high-power discharge is considered. Two simplified models for the arc resistance are considered and their respective results are compared. A brief analysis regarding the numerical issues involved in the solution of a very high temperature gas is included. The numerical code has been validated against the experimental data of a short-arc discharge using a current waveform prescribed by the aeronautical standards. Our study shows that a strong shock wave is generated in the first power peak and this travels away from the arc column maintaining a relatively high strength a few tens of centimetres away. The pressure in the arc region remains high for the whole discharge period.

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Finite element/volume solution to axisymmetric conservation laws

Cited by 24 publications

References 43 publications

A Stabilized Finite Volume Element Formulation for Sedimentation-Consolidation Processes

A Stabilized Finite Volume Element Formulation for Sedimentation-Consolidation Processes

A Cell-Centered Multiphase ALE Scheme With Structural Coupling

A multiscale technique for the validation of a numerical code for predicting the pressure field induced by a high-power spark

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