Volume 16, Issue 5
Numerical Solution of a Transient Three-Dimensional Eddy Current Model with Moving Conductors

Int. J. Numer. Anal. Mod., 16 (2019), pp. 695-717.

Published online: 2019-08

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• Abstract

The aim of this paper is to propose and analyze a numerical method to solve a time-dependent eddy current problem in a domain containing moving non magnetic conductors. To this end, we choose a formulation in terms of the magnetic field, what leads to a parabolic problem for which we prove an existence result. For space discretization, we propose a finite element method based on Nédélec edge elements on a mesh that remains fixed over the time. The curl-free constraint in the dielectric domain is relaxed by means of a penalty strategy that can be easily implemented, without the need that the mesh fits the moving conducting and dielectric domains. For time discretization, we use a backward Euler scheme. We report some numerical results. First, we solve a test problem with a known analytical solution, which allows us to assess the convergence of the method as the penalization and discretization parameters go to zero. Finally, we solve a problem with cylindrical symmetry, which allows us to compare the results with those obtained with an axisymmetric code.

65M60, 78M10

alfredo.bermudez@usc.es (Alfredo Bermúdez)

blopezr@unal.edu.co (Bibiana López-Rodríguez)

rodolfo@ing-mat.udec.cl (Rodolfo Rodríguez)

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@Article{IJNAM-16-695, author = {Bermúdez , AlfredoLópez-Rodríguez , BibianaRodríguez , Rodolfo and Salgado , Pilar}, title = {Numerical Solution of a Transient Three-Dimensional Eddy Current Model with Moving Conductors}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2019}, volume = {16}, number = {5}, pages = {695--717}, abstract = {

The aim of this paper is to propose and analyze a numerical method to solve a time-dependent eddy current problem in a domain containing moving non magnetic conductors. To this end, we choose a formulation in terms of the magnetic field, what leads to a parabolic problem for which we prove an existence result. For space discretization, we propose a finite element method based on Nédélec edge elements on a mesh that remains fixed over the time. The curl-free constraint in the dielectric domain is relaxed by means of a penalty strategy that can be easily implemented, without the need that the mesh fits the moving conducting and dielectric domains. For time discretization, we use a backward Euler scheme. We report some numerical results. First, we solve a test problem with a known analytical solution, which allows us to assess the convergence of the method as the penalization and discretization parameters go to zero. Finally, we solve a problem with cylindrical symmetry, which allows us to compare the results with those obtained with an axisymmetric code.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/13249.html} }
TY - JOUR T1 - Numerical Solution of a Transient Three-Dimensional Eddy Current Model with Moving Conductors AU - Bermúdez , Alfredo AU - López-Rodríguez , Bibiana AU - Rodríguez , Rodolfo AU - Salgado , Pilar JO - International Journal of Numerical Analysis and Modeling VL - 5 SP - 695 EP - 717 PY - 2019 DA - 2019/08 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/13249.html KW - Eddy current problems, transient electromagnetic problems, moving domains, edge finite elements, penalty formulation. AB -

The aim of this paper is to propose and analyze a numerical method to solve a time-dependent eddy current problem in a domain containing moving non magnetic conductors. To this end, we choose a formulation in terms of the magnetic field, what leads to a parabolic problem for which we prove an existence result. For space discretization, we propose a finite element method based on Nédélec edge elements on a mesh that remains fixed over the time. The curl-free constraint in the dielectric domain is relaxed by means of a penalty strategy that can be easily implemented, without the need that the mesh fits the moving conducting and dielectric domains. For time discretization, we use a backward Euler scheme. We report some numerical results. First, we solve a test problem with a known analytical solution, which allows us to assess the convergence of the method as the penalization and discretization parameters go to zero. Finally, we solve a problem with cylindrical symmetry, which allows us to compare the results with those obtained with an axisymmetric code.

Alfredo Bermúdez, Bibiana López-Rodríguez, Rodolfo Rodríguez & Pilar Salgado. (2019). Numerical Solution of a Transient Three-Dimensional Eddy Current Model with Moving Conductors. International Journal of Numerical Analysis and Modeling. 16 (5). 695-717. doi:
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