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<div class="" style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0);">Dear FLASH developers,</div>
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<div class="" style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0);">I am quite confident that there is a bug in the three-dimensional viscous energy fluxes for the 8 wave split solver in the public FLASH version, which we have tracked back to the original
implementation in FLASH2.2.</div>
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<div class="" style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0);">For example, in the x sweep, the z contributions to the flux are:</div>
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<div class="" style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0);"><img apple-inline="yes" id="8117A41B-318F-445A-91A2-1DA215C8C53F" class="" width="596" height="60" src="cid:3AD6848A-621A-469C-A794-136D10F8DA24"></div>
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<div class="" style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0);">which correspond to the fluxes:</div>
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<div class="" style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0);"><img apple-inline="yes" id="DB29E671-00FC-44E3-A66E-F80B9E2F9284" class="" width="596" height="102" src="cid:8A59777D-BFF6-4464-920C-09015AE37D88"></div>
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<div class="" style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0);">Where \overline{v_z \partial_z v_z} is the average along the sweep. </div>
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<div class="" style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0);">In the second term, there is a minus (highlighted in red) where there should be a plus, which computes the difference rather than the average flux on the cell face. </div>
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<div class="" style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0);">The same can be said about the z energy flux contributions to the y and z sweeps — both have terms that are differences rather than averages — resulting in incorrect viscous fluxes for the
split methods.</div>
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<div class="" style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0);">The public unsplit method has both the correct averaging and viscous energy flux terms, for comparison. </div>
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<div class="" style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0);">Thanks,</div>
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<div class="">James Beattie (he/him)<br class="">
PhD student | Deakin, Dean’s (theoretical physics) & Fulbright scholar<br class="">
University of California, Santa Cruz | Department of Astronomy and Astrophysics</div>
<div class="">Australian National University | Research School of Astronomy and Astrophysics</div>
<div class=""><a href="https://scholar.google.com/citations?user=ZIgumjQAAAAJ&hl=en" class="">GScholar</a> | <a href="https://www.researchgate.net/profile/James-Beattie-4" class="">ResearchGate</a> | <a href="https://www.mso.anu.edu.au/~beattijr/cv/AcademicCV_Beattie2022.pdf" class="">CV</a> | <a href="https://www.mso.anu.edu.au/~beattijr/" class="">Website</a></div>
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