Abstract
Abstract In astrophysical magnetohydrodynamics (MHD) and electrodynamics simulations, numerically enforcing the ∇·B= 0 constraint on the magnetic field has been difficult. We observe that for point-based discretization, as used in finite-difference type and pseudo-spectral methods, the ∇·B= 0 constraint can be satisfied entirely by a choice of interpolation used to define the derivatives of B. As an example we demonstrate a new class of finite-difference-type derivative operators on a regular grid which has the ∇·B= 0 property. This principle clarifies the nature of ∇·B≠ 0 errors. The principles and techniques demonstrated in this Letter are particularly useful for the magnetic field, but can be applied to any vector field. This Letter serves as a brief introduction to the method and demonstrates an implementation showing convergence.
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More From: Monthly Notices of the Royal Astronomical Society: Letters
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