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Paper: Magnetic Flux Conservation in Constrained Transport Adaptive Mesh MHD Codes Without Refluxing
Volume: 385, Numerical Modeling of Space Plasma Flows: Astronum-2007
Page: 158
Authors: Loring, B.; Raeder, J.
Abstract: The key property of constrained transport (CT) methods on fixed grids is that by design the equation ∇ · B = 0 is satisfied to within machine precision. However, when adaptive grids are introduced a naive treatment of magnetic flux conservation across the coarse–fine grid interface will lead to ∇ · B ≠ 0 in coarse cells adjacent to refined regions. In this report we review the CT method for solving Faraday’s law and present a new method for conserving magnetic flux across the coarse–fine grid interface. We show how magnetic flux can be conserved across the grid interface without a refluxing step. We then show a validation of our method, obtained with a new Adaptive Mesh Refinement (AMR) magnetohydrodynamic (MHD) code implemented with the CHOMBO AMR C++ classes.
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