The effect of nonzero \(\bigtriangledown\cdot B\) on the numerical solution of the magnetohydrodynamic equations
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Publication:1137932
DOI10.1016/0021-9991(80)90079-0zbMath0429.76079OpenAlexW1999105805MaRDI QIDQ1137932
D. C. Barnes, Jeremiah U. Brackbill
Publication date: 1980
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0021-9991(80)90079-0
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Cites Work
