一种基于磁通和电磁能流的磁扩散问题求解格式

针对一维磁场扩散问题设计一种显式的有限体积离散格式。格式的第一个特征是不仅将磁场的扩散表达为单元边界上的磁通流, 同时将能量方程中的欧姆加热也表达为单元边界上的电磁能量流, 该特征能够更好地保证磁场能与内能的总量守恒。格式的第二个特征是将单元边界上的磁通量和电磁能通量进行截断, 在极端电阻率存在的磁扩散问题求解过程中, 该特征能够一定程度上放宽稳定性条件对显式格式时间步长的限制。

A Finite Volume Scheme Based on Magnetic Flux and Electromagnetic Energy Flow for Magnetic Field Diffusion Problems

An explicit finite volume discrete scheme is designed for one-dimensional magnetic field diffusion problems. The first characteristic of the scheme is that, the diffusion process of magnetic field is described as magnetic flux and the ohmic heating in energy equation is presented as electromagnetic energy flow at the element boundary as well, which guarantees the conservation of the sum of electromagnetic energy and internal energy well. The second characteristic of the scheme is that it truncates magnetic flux and electromagnetic energy flux on boundary of the element. Combined with time step amplification, the truncation could break through the limitation of stability condition on explicit scheme time step to some extent in magnetic diffusion problems with extreme resistivity.