A computationally efficient hybrid magnetic field correction for the magnetohydrodynamic equations

Abstract

During the simulations of the magnetohydrodynamic equations, numerical errors might cause the formation of non-physical divergence components in the magnetic field. This divergence compromises the stability and accuracy of the simulations. In order to overcome this problem, several methodologies, called divergence cleaning methods, are proposed. Besides many comparative works between these methods, the construction of the best approach is still an open problem. A popular divergence cleaning strategy is the parabolic-hyperbolic approach due to its easy implementation and low computational cost in CPU time, however this approach just transports and diffuses the divergence components instead of eliminating them globally. On the other hand, the elliptic approach, also known as the projection method, uses a Poisson equation to eliminate the divergence effectively at a huge computational cost. This work proposes a successful combination of these approaches in order to create a new divergence cleaning methodology that incorporates the advantages provided by both methods, a small CPU time and a good accuracy.

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ORCID for Ralf Deiterding: orcid.org/0000-0003-4776-8183

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