A Proper Generalized Decomposition-Based Solver for Nonlinear Magnetothermal Problems
A Proper Generalized Decomposition-Based Solver for Nonlinear Magnetothermal Problems
复制标题
非线性磁热问题的一种基于广义分解的求解器
DOI：
10.1109/tmag.2015.2492462
复制
发表时间：
2016
影响因子：
2.1
通讯作者：
Z. Ren
中科院分区：
文献类型：
--
作者：
Z. Qin;H. Talleb;Z. Ren
本文研究通过适当的广义分解为基础的非增量方法求解耦合磁热问题。由于感应电流产生的焦耳热导致温度场的演化，材料的电学性质随温度的变化而发生变化，因此，磁动力学和热力学问题是强耦合的。解决耦合问题的一个挑战是电时间常数可以比热时间常数小几个数量级。通过经典的时间积分方法的解决方案需要太多的时间步长，特别是当一个长的持续时间需要模拟，从而使问题的大小太大，无法处理。该求解器克服了这一困难，通过分解未知的动态领域的空间和时间模式和解决线性化系统的空间和时间迭代，使用有限元方法。材料的非线性可以用一种简单的方式来体现。所提出的求解器的优点是证明在解决学术问题。
This paper investigates solving coupled magnetothermal problems through a proper generalized decomposition-based non-incremental approach. The magnetodynamic and thermodynamic problems are strongly coupled as the electric material property changes with the temperature while the temperature field evolves due to the Joule heat generated by induced currents. A challenge to solve the coupled problem is that the electric time constant can be several orders of magnitude smaller than the thermal one. Solution through a classical time integration approach requires too many time steps, especially when a long duration needs to be simulated, hence making the problem size too large to be handled. The proposed solver overcomes this difficulty through decomposing unknown dynamic fields into the space and time modes and solving the linearized systems in space and time iteratively, using the finite element method. The material nonlinearity can be incorporated in a straightforward way. The advantages of the proposed solver are demonstrated in solving an academic problem.