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

IF 1.7 3区数学 Q2 MATHEMATICS, APPLIED

Advances in Computational Mathematics Pub Date : 2024-05-08 DOI:10.1007/s10444-024-10121-y

Marta Benítez, Alfredo Bermúdez, Pedro Fontán, Iván Martínez, Pilar Salgado

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引用次数: 0

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 varies with time and undergoes large deformations; the motion will be a known data. The work will be a first step towards building a complete thermo-electromagnetic-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 in-plane current; the source will be given in terms of currents or voltages defined at some 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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解决轴对称热电磁问题的拉格朗日方法。时变几何过程的应用

这项工作的目的是引入一个热电磁模型，用于计算几何形状随时间变化并发生较大变形的圆柱形工件的温度和耗散功率；运动将是一个已知数据。这项工作将是建立一个完整的热-电磁-机械模型的第一步，该模型适用于模拟电辅助成形过程，这也是这项工作的主要动机。电磁模型将从具有平面内电流的时谐涡流问题中获得；源将以定义在边界某些部分的电流或电压的形式给出。数值求解将采用基于拉格朗日弱公式的有限元方法。这种方法可以避免计算和重新网格化热电磁域。数值工具将在 FEniCS 中实施，并通过同样以欧拉坐标求解的适当测试进行验证。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Computational Mathematics 数学-应用数学

CiteScore

3.00

自引率

5.90%

发文量

审稿时长

3 months

期刊介绍： Advances in Computational Mathematics publishes high quality, accessible and original articles at the forefront of computational and applied mathematics, with a clear potential for impact across the sciences. The journal emphasizes three core areas: approximation theory and computational geometry; numerical analysis, modelling and simulation; imaging, signal processing and data analysis. This journal welcomes papers that are accessible to a broad audience in the mathematical sciences and that show either an advance in computational methodology or a novel scientific application area, or both. Methods papers should rely on rigorous analysis and/or convincing numerical studies.