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Correspondence between constrained transport and vector potential methods for magnetohydrodynamics. (English) Zbl 1406.76090
Summary: We show that one can formulate second-order field- and flux-interpolated constrained transport/central difference (CT/CD) type methods as cell-centered magnetic vector potential schemes. We introduce four vector potential CTA/CDA schemes – three of which correspond to CT/CD methods of G. Tóth [ibied. 161, No. 2, 605–652 (2000; Zbl 0980.76051)] and one of which is a new simple flux-CT-like scheme – where the centroidal vector potential is the primal update variable. These algorithms conserve a discretization of the \(\nabla \cdot \mathbf{B} = 0\) condition to machine precision and may be combined with shock-capturing Godunov type base schemes for magnetohydrodynamics. Recasting CT in terms of a centroidal vector potential allows for some simple generalizations of divergence-preserving methods to unstructured meshes, and potentially new directions to generalize CT schemes to higher-order.

MSC:
76W05 Magnetohydrodynamics and electrohydrodynamics
76M20 Finite difference methods applied to problems in fluid mechanics
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