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Computational magnetohydrodynamics
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<h2 id="open-source-mhd-software">Open-source MHD software</h2> <ul><li><a href="/facts/Pencil_Code/5IpemmNR">Pencil Code</a>Compressible resistive MHD, intrinsically divergence free, embedded particles module, finite-difference explicit scheme, high-order derivatives, Fortran95 and C, parallelized up to hundreds of thousands cores. <a href="http://pencil-code.nordita.org/download.php">Source code</a> is available.</li> <li><a href="http://www.ics.uzh.ch/~teyssier/ramses/RAMSES.html">RAMSES</a> RAMSES is an open source program to model astrophysical systems, featuring self-gravitating, magnetised, compressible, radiative fluid flows. It is based on the <a href="/facts/Adaptive_Mesh_Refinement/5FHW0UbQ">Adaptive Mesh Refinement</a> (AMR) technique on a fully threaded graded octree. RAMSES is written in Fortran 90 and is making intensive use of the <a href="/facts/Message_Passing_Interface/BEuBgDpm">Message Passing Interface</a> (MPI) library.<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a><a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a> <a href="https://bitbucket.org/rteyssie/ramses">Source code</a> is available.</li> <li><a href="http://www.maisondelasimulation.fr/projects/RAMSES-GPU/html/index.html">RamsesGPU</a> RamsesGPU is an MHD program written in C++, based on the original <a href="http://www.ics.uzh.ch/~teyssier/ramses/RAMSES.html">RAMSES</a> but only for regular grid (no <a href="/facts/Adaptive_Mesh_Refinement/5FHW0UbQ">AMR</a>). The code has been designed to run on large clusters of <a href="/facts/Graphics_processing_unit/PTK1RQVp">GPU</a> (<a href="/facts/NVIDIA/8QfCgqbu">NVIDIA</a> graphics processors), so parallelization relies on <a href="/facts/Message_Passing_Interface/BEuBgDpm">MPI</a> for distributed memory processing, as well as the programing language CUDA for efficient usage of <a href="/facts/Graphics_processing_unit/PTK1RQVp">GPU</a> resources. Static Gravity Fields are supported. Different finite volume methods are implemented. <a href="https://github.com/pkestene/ramsesGPU">Source code</a> is available.</li> <li><a href="https://trac.princeton.edu/Athena/">Athena</a>Athena is a grid-based program for astrophysical magnetohydrodynamics (MHD). It was developed primarily for studies of the interstellar medium, star formation, and accretion flows.<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a> <a href="https://trac.princeton.edu/Athena/">Source code</a> is available.</li> <li><a href="https://eof-library.com/">EOF-Library</a> EOF-Library is a software that couples <a href="/facts/Elmer_FEM_solver/Vf5y5ShF">Elmer FEM</a> and <a href="/facts/OpenFOAM/juBSzlRz">OpenFOAM</a> simulation packages. It enables efficient internal field interpolation and communication between the <a href="/facts/Finite_element_method/eUcfP1vn">finite element</a> and the <a href="/facts/Finite_volume_method/6JfQMucX">finite volume</a> frameworks. Potential applications are MHD, convective cooling of electrical devices, industrial <a href="/facts/Plasma_(physics)/1d3btMVU">plasma physics</a> and <a href="/facts/Dielectric_heating/LvxNcysf">microwave heating</a> of liquids.<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a></li></ul> <h2 id="closed-source-mhd-software">Closed-source MHD software</h2> <ul><li><a href="http://www.txcorp.com/">USim</a></li> <li><a href="http://www.numerex-llc.com/m2.htm">MACH2</a></li> <li><a href="https://www.plm.automation.siemens.com/global/de/products/simcenter/STAR-CCM.html">STAR-CCM+</a></li></ul> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/Magnetohydrodynamic_turbulence/IH5etefV">Magnetohydrodynamic turbulence</a></li> <li><a href="/facts/Magnetic_flow_meter/UsMnWSA0">Magnetic flow meter</a></li> <li><a href="/facts/Plasma_modeling/7zJNCUzD">Plasma modeling</a></li></ul> <ul><li>Brio, M., Wu, C. C.(1988), "An upwind differencing scheme for the equations of ideal magnetohydrodynamics", <i>Journal of Computational Physics</i>, 75, 400–422.</li> <li>Henri-Marie Damevin and Klaus A. Hoffmann(2002), "Development of a Runge-Kutta Scheme with TVD for Magnetogasdynamics", <i>Journal of Spacecraft and Rockets</i>, 34, No.4, 624–632.</li> <li>Robert W. MacCormack(1999), "An upwind conservation form method for ideal magnetohydrodynamics equations", <i>AIAA-99-3609</i>.</li> <li>Robert W. MacCormack(2001), "A conservation form method for magneto-fluid dynamics", <i>AIAA-2001-0195</i>.</li></ul> <h2 id="further-reading">Further reading</h2> <ul><li>Toro, E. F. (1999), <i>Riemann Solvers and Numerical Methods for Fluid Dynamics</i>, Springer-Verlag.</li> <li>Ledvina, S. A.; Y.-J. Ma; E. Kallio (2008). "Modeling and Simulating Flowing Plasmas and Related Phenomena". <i>Space Science Reviews</i>. 139 (1–4): 143–189. <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/2008SSRv..139..143L">2008SSRv..139..143L</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2Fs11214-008-9384-6">10.1007/s11214-008-9384-6</a>. <a href="/facts/S2CID_(identifier)/ldJsHa2Y">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:121999061">121999061</a>.</li></ul> <h2 id="external-links">External links</h2> <ul><li><a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC392293/">NCBI</a></li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Teyssier, R (2002). "Cosmological hydrodynamics with adaptive mesh refinement. A new high resolution program called RAMSES". Astronomy and Astrophysics. 385: 337–364. arXiv:astro-ph/0111367. Bibcode:2002A&A...385..337T. doi:10.1051/0004-6361:20011817. S2CID 5504247. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Gheller, C; Wang, P; Vazza, F; Teyssier, R (28 September 2015). "Numerical cosmology on the GPU with Enzo and Ramses". Journal of Physics: Conference Series. 640 (1): 012058. arXiv:1412.0934. Bibcode:2015JPhCS.640a2058G. doi:10.1088/1742-6596/640/1/012058. S2CID 118194615. Retrieved 1 July 2016. <a href="http://stacks.iop.org/1742-6596/640/i=1/a=012058" target="_blank">http://stacks.iop.org/1742-6596/640/i=1/a=012058</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Stone, James M.; Gardiner, Thomas A.; Teuben, Peter; Hawley, John F.; Simon, Jacob B. (September 2008). "Athena: A New Code for Astrophysical MHD". The Astrophysical Journal Supplement Series. 178 (1): 137–177. arXiv:0804.0402. Bibcode:2008ApJS..178..137S. doi:10.1086/588755. S2CID 10934839. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Vencels, Juris; Råback, Peter; Geža, Vadims (2019-01-01). "EOF-Library: Open-source Elmer FEM and OpenFOAM coupler for electromagnetics and fluid dynamics". SoftwareX. 9: 68–72. Bibcode:2019SoftX...9...68V. doi:10.1016/j.softx.2019.01.007. ISSN 2352-7110. <a href="https://doi.org/10.1016%2Fj.softx.2019.01.007" target="_blank">https://doi.org/10.1016%2Fj.softx.2019.01.007</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> </ol>