Open Access

ARTICLE

A Meshless Local Petrov-Galerkin Method for Magnetic Diffusion in Non-magnetic Conductors

by J.N. Johnson¹, J.M. Owen²

1 UC Davis/LLNL, Livermore, CA, USA.
2 LLNL, Livermore, CA, USA.

Computer Modeling in Engineering & Sciences 2007, 22(3), 165-188. https://doi.org/10.3970/cmes.2007.022.165

Abstract

In this paper, we propose a Meshless Local Petrov-Galerkin method for studying the diffusion of a magnetic field within a non-magnetic (μ = μ₀) conducting medium with non-homogeneous and anisotropic electrical resistivity. We derive a local weak form for the magnetic diffusion equation and discuss the effects of different trial/test functions and nodal spacings on its solution. We then demonstrate that the method produces convergent results for several relevant one-dimensional test problems for which solutions are known. This method has the potential to be combined with other mesh-free methods such as Smoothed Particle Hydrodynamics (SPH) to solve problems in resistive magnetohydrodynamics, which has several applications in astrophysics, plasma physics, and engineering.

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