Summary
A simple novel approach to preserve the divergence-free condition with adaptive mesh refinement is presented. The new approach uses only reconstructions on the coarse faces and the divergence-free condition to reconstruct the field values on the internal fine faces, and does not construct a global interpolation polynomial over a whole coarse cell. Therefore it can be easily applied to any refinement ratio. It is implemented via a directionally split approach in a directional splitting manner so that it can be applied to any kind of grids in any dimensions. Implementation is presented in the Cartesian, cylindrical and spherical geometries. It is shown by several 2D magneto-hydrodynamic simulations that such a method can keep the divergence-free error of magnetic fields at the round-off level.
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© 2005 Springer-Verlag Berlin Heidelberg
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Li, S., Li, H. (2005). Dimensional Split Divergence-Free Reconstruction and Prolongation for Adaptive Mesh Refinement. In: Plewa, T., Linde, T., Gregory Weirs, V. (eds) Adaptive Mesh Refinement - Theory and Applications. Lecture Notes in Computational Science and Engineering, vol 41. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27039-6_9
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DOI: https://doi.org/10.1007/3-540-27039-6_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21147-1
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