Correspondence between constrained transport and vector potential methods for magnetohydrodynamics

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 Tóth (2000) [1] 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 ∇⋅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.