关键词: 非线性磁扩散, 极端电阻率, 欧姆加热, 有限体积法

Abstract: The magnetic field diffusion problem is the coupling of the magnetic diffusion equation and the ohmic heating energy equation. In this paper, an explicit finite volume discrete scheme is designed for one dimensional magnetic field diffusion problem. The first characteristic of this scheme is that, not only the diffusion process of magnetic field is described as the magnetic flux but the ohmic heating in energy equation is also presented as electromagnetic energy flow at the element boundary, which can guarantee the conservation of the sum of the electromagnetic energy and internal energy better. The second characteristic of the scheme is that it truncates the magnetic flux and electromagnetic energy flux on the boundary of the element. Combined with the time step amplification, the truncation can break through the limitation of the stability condition on the explicit scheme time step to some extent, in the magnetic diffusion problems with extreme resistivity.

Key words:  Nonlinear magnetic field diffusion, extreme resistivity, Ohmic heating, finite volume scheme