Divergence-free interpolation of vector fields from point values - exact ∇·B= 0 in numerical simulations
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.
- Publication:
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Monthly Notices of the Royal Astronomical Society
- Pub Date:
- May 2011
- DOI:
- 10.1111/j.1745-3933.2011.01037.x
- arXiv:
- arXiv:1102.4852
- Bibcode:
- 2011MNRAS.413L..76M
- Keywords:
-
- magnetic fields;
- magnetohydrodynamics (MHD);
- methods: numerical;
- Astrophysics - Instrumentation and Methods for Astrophysics
- E-Print:
- MNRAS Letters accepted. 5 figures and 1 table