Note on Upwinding Constrained Transport Method for Ideal Magnetohydrodynamics 12

We describe several upwinding constrained transport (UCT) methods in this paper and compare them with the flux-CT method (Balsara & Spicer 1999). The results show that the divergence-free reconstruction is an improvement only for low-β plasma, where the pressure positivity becomes a problem. The energy-fix or pressure correction approach destroys overall conservation and leads to wrong states for some low-β MHD flows. For other problems, the flux-CT with the standard reconstruction on cell-centered values works well. This paves a way to use the dimensional splitting MHD solver for multidimensional problems.

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