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documentation/md_case.html

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<td class="markdownTableBodyRight"><code>relativity</code> </td><td class="markdownTableBodyCenter">Logical </td><td class="markdownTableBodyLeft">Enable relativistic MHD simulation </td></tr>
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<td class="markdownTableBodyRight"><code>powell</code> </td><td class="markdownTableBodyCenter">Logical </td><td class="markdownTableBodyLeft">Enable Powell's method for solenoidal constraint </td></tr>
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<td class="markdownTableBodyRight"><code>hyper_cleaning</code> </td><td class="markdownTableBodyCenter">Logical </td><td class="markdownTableBodyLeft">Enable hyperbolic (GLM) divergence cleaning for <code>div B</code> </td></tr>
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<td class="markdownTableBodyRight"><code>fd_order</code> </td><td class="markdownTableBodyCenter">Integer </td><td class="markdownTableBodyLeft">Finite difference order for Powell's method </td></tr>
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<td class="markdownTableBodyRight"><code>hyper_cleaning_speed</code> </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">Cleaning wave speed <code>c_h</code> </td></tr>
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<td class="markdownTableBodyRight"><code>Bx[y,z]</code> </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">Initial magnetic field in the x[y,z] direction </td></tr>
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<td class="markdownTableBodyRight"><code>hyper_cleaning_tau</code> </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">Cleaning damping timescale <code>tau</code> </td></tr>
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<td class="markdownTableBodyRight"><code>Bx[y,z]</code> </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">Initial magnetic field in the x[y,z] direction </td></tr>
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<td class="markdownTableBodyRight"><code>Bx0</code> </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">Constant magnetic field in the x direction (1D only) </td></tr>
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<ul>
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<li><code>mhd</code> is currently only available for single-component flows and 5-equation model. Its compatibility with most other features is work in progress.</li>
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<li><code>relativity</code> only works for <code>mhd</code> enabled and activates relativistic MHD (RMHD) simulation.</li>
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<li><code>powell</code> activates Powell's eight-wave method to impose the solenoidal constraint in the MHD simulation <a class="el" href="md_references.html">Powell (1994)</a>. It should not be used in conjunction with HLLD (<code>riemann_solver = 4</code>).</li>
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<li><code>fd_order</code> specifies the finite difference order for computing the RHS of the Powell's method. <code>fd_order = 1</code>, <code>2</code>, and <code>4</code> are allowed.</li>
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<li><code>hyper_cleaning</code> <a class="el" href="md_references.html">Dedner et al., 2002</a> only works with <code>mhd</code> in 2D/3D and reduces numerical <code>div B</code> errors by propagation and damping. Currently not compatible with HLLD (<code>riemann_solver = 4</code>).</li>
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<li><code>hyper_cleaning_speed</code> sets the propagation speed of divergence-cleaning waves.</li>
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<li><code>hyper_cleaning_tau</code> sets the decay timescale for divergence-cleaning.</li>
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<li><code>Bx0</code> is only used in 1D simulations to specify the constant magnetic field in the x direction. It must be specified in 1D simulations. <code>Bx</code> must not be used in 1D simulations.</li>
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<li><code>Bx</code>, <code>By</code>, and <code>Bz</code> are used to specify the initial magnetic field in the x, y, and z directions, respectively. They must be specified in all 1D/2D/3D MHD simulations, with the exception of <code>Bx</code> in 1D simulations.</li>
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documentation/md_case__constraints.html

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<p><b>Requirements:</b></p><ul>
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<li>relativity requires mhd to be enabled</li>
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<li>Hyperbolic cleaning requires mhd to be enabled</li>
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documentation/md_references.html

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<li><a class="anchor" id="Miyoshi05"></a>Miyoishi, T., and Kusano, K. (2005). A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics. Journal of Computational Physics, 208(1), 315-344.</li>
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<li><a class="anchor" id="Powell94"></a>Powell, K. G. (1994). An approximate Riemann solver for magnetohydrodynamics: (That works in more than one dimension). In Upwind and high-resolution schemes (pp. 570-583). Springer.</li>
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<li><a class="anchor" id="Dedner02"></a>Dedner, A., Kemm, F., Kröner, D., Munz, C. D., Schnitzer, T., &amp; Wesenberg, M. (2002). Hyperbolic divergence cleaning for the MHD equations. Journal of Computational Physics, 175(2), 645-673.</li>
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<li><a class="anchor" id="Cao19"></a>Cao, S., Zhang, Y., Liao, D., Zhong, P., and Wang, K. G. (2019). Shock-induced damage and dynamic fracture in cylindrical bodies submerged in liquid. International Journal of Solids and Structures, 169:55–71. Elsevier.</li>

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