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A Lagrangian approach for solving an axisymmetric thermo-electromagnetic problem. Application to time-varying geometry processes (2403.04377v1)

Published 7 Mar 2024 in math.NA and cs.NA

Abstract: The aim of this work is to introduce a thermo-electromagnetic model for calculating the temperature and the power dissipated in cylindrical pieces whose geometry var\'ies with time and undergoes large deformations; the motion will be a known data. The work will be a first step towards building a complete thermoelectromagnetic-mechanical model suitable for simulating electrically assisted forming processes, which is the main motivation of the work. The electromagnetic model will be obtained from the time-harmonic eddy current problem with an inplane current; the source will be given in terms of currents or voltages defined at sorne parts of the boundary. Finite element methods based on a Lagrangian weak formulation will be used for the numerical solution. This approach will avoid the need to compute and remesh the thermo-electromagnetic domain along the time. The numerical tools will be implemented in FEniCS and validated by using a suitable test also solved in Eulerian coordinates.

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