Correspondence between constrained transport and vector potential methods for magnetohydrodynamics

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• 作者：Philip Mocz ^{pmocz@cfa.harvard.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Magnetohydrodynamics ; Finite difference methods ; Godunov scheme ; Numerical schemes
• 刊名：Journal of Computational Physics
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：328
• 期：Complete
• 页码：221-233
• 全文大小：1117 K

文摘

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$\mathrm{\nabla }\cdot \mathbf{B}=0$ 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.