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Paper: Higher Order Divergence-Free Methods for Three-Dimensional MHD Flows on Overlapping Grid
Volume: 444, 5th International Conference of Numerical Modeling of Space Plasma Flows (ASTRONUM 2010)
Page: 242
Authors: Li, S.
Abstract: We present a higher-order, divergence-free, central finite-volume method for three-dimensional magnetohydrodynamic (MHD) flows, which is an extension of the method described in [S. Li, High order central scheme on overlapping cells for MHD flows with and without constrained transport method, J. Comput. Phys. 227 (2008) 7368]. This method simultaneously advances the solutions on both original and dual overlapping grids, and can achieve any high order accuracy, depending on the order of the reconstructed polynomials. The dual overlapping grid also provides a natural way to calculate the electric field without spatial averaging for the constrained transport (CT) method, which preserves the divergence-free condition of the magnetic fields. In this paper, we describe basic components of our method implemented for 3D MHD flows. Several test problems are presented to demonstrate the accuracy and robustness of the algorithm. The high-order, low-dissipation, and divergence-free properties of this method make it an ideal tool for direct MHD turbulence simulations.
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