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 class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021999116304806&_mathId=si1.gif&_user=111111111&_pii=S0021999116304806&_rdoc=1&_issn=00219991&md5=5365bd8e193883742d173f0b5e1f2c66" title="Click to view the MathML source">∇⋅B=0class="mathContainer hidden">class="mathCode">$\mathrm{\nabla }\cdot \mathbf{B}=0$ 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.