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

doi:10.19596/j.cnki.1001-246x.8430

Abstract

Abstract:

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.

Key words: nonlinear magnetic field diffusion, extreme resistivity, ohmic heating, finite volume scheme

Chun-hui YAN, Bo XIAO, Gang-hua WANG, Yu LU, Ping LI. A Finite Volume Scheme Based on Magnetic Flux and Electromagnetic Energy Flow for Magnetic Field Diffusion Problems[J]. Chinese Journal of Computational Physics, 2022, 39(4): 379-385.

Figures/Tables 7

Fig.1 Physical factors in adjacent grid cells

Fig.2 Magnetic diffusion distributions at 1 μs calculated with two discretization schemes

Table 1 Total magnetic flux and total energy at initial time and 1 μs calculated with two discretization schemes

	初始磁通量/(T·m)	1 μs时刻总磁通量/(T·m)	初始总能量/J	1 μs时刻总能量/J
节点控制体格式	0.1	0.1	3.978 87 × 10⁸	4.373 69 × 10⁸
本文计算格式	0.1	0.1	3.978 87 × 10⁸	3.978 87 × 10⁸

Fig.3 Magnetic diffusion distributions at 0.5 μs calculated with different time steps in a metal plate model of constant resistivity

Fig.4 A step-shaped resistivity model (In a simplified Burgess model, resistivity ηL is 2-5 orders of magnitude of the initial resistivity ηs.)

Fig.5 The sharp-front magnetic diffusion distributions at 0.5 μs calculated with different time steps

Fig.6 Magnetic diffusion distributions at 0.5 μs calculated with different time steps in a metal plate model with two extremely different resistivity regions

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