References

• Anninos, W. Y., & Norman, M. L. 1994, ApJ, 429, 434
• Aparicio, J. M. 1998, ApJS, 117, 627
• Atzeni, S. and Meyer-Ter-Vehn, J. 2004, The Physics of Inertial Fusion: Beam Plasma Interaction, Hydrodynamics, Hot Dense Matter (Oxford Science Publications)
• Armfield, S. & Street, R. 2002, Int. J. Numer. Meth. Fluids, 38, 255-282
• Bader, G. & Deuflhard, P. 1983, NuMat, 41, 373
• Balsara, D. S., 2001, JCP, 174, 614
• Balsara, D. S. 2004, ApJS, 151, 149
• Balsara, D. S., & Spicer, D. S. 1999, JCP, 149, 270
• Bardeen, J. M., Bond, J. R., Kaiser, N., & Szalay, A. S. 1986, ApJ, 304, 15
• Barnes, J. & Hut, P. 1986, Nature, 324, 446
• Berger, M. J. & Collela, P. 1989, JCP, 82, 64
• Berger, M. J. & Oliger, J. 1984, JCP, 53, 484
• Blinnikov, S. I., Dunina-Barkovskaya, N. V., & Nadyozhin, D. K. 1996, ApJS, 106, 171
• Boris, J. P. & Book, D. L. 1973, JCP, 11, 38
• Bonnor, W. B. 1956, MNRAS, 116, 351
• Brackbill, J. & Barnes, D. C. 1980 JCP, 35, 426
• Braginskii, S. I. 1965 Rev. Plasma Phys., 1, 205
• Brandt, A. 1977, Math. Comp., 31, 333
• Brio, M. & Wu, C. C. 1988 JCP, 75, 400
• Brown, P. N., Byrne, G. D., & Hindmarsh, A. C. 1989, SIAM J. Sci. Stat. Comput., 10, 1038
• Brysk, H., Campbell, P.M., Hammerling, P. 1974, Plasma Physics, 17, 473
• Bunn, E. F. & White, M. 1997, ApJ, 480, 6
• Burgers, J. M. 1969, Flow Equations for Composite Gases (New York: Academic)
• Nakamura, K. et al. 2010, J. Phys., G 37, 075021 (also http://pdg.lbl.gov/2010/reviews/contents_sports.html)
• Caughlan, G. R. & Fowler, W. A. 1988, Atomic Data and Nuclear Data Tables, 40, 283
• Chandrasekhar, S. 1961, Hydrodynamic and Hydromagnetic Stability (Oxford: Clarendon)
• Chandrasekhar, S. 1939, An Introduction to the Study of Stellar Structure (Toronto: Dover)
• Chandrasekhar, S. 1987, Ellipsoidal Figures of Equilibrium (New York: Dover)
• Chapman, D. L. 1899, Philos. Mag., 47, 90
• Chapman, S. & Cowling, T. G. 1970, The Mathematical Theory of Non-uniform Gases (Cambridge: CUP)
• Chatzopoulos, E. & Weide, K. 2017, arXiv:1712.10091
• Christy, R. F. 1966, ApJ, 144, 108
• Cohen, E. R. & Taylor, B. N. 1987, Rev.Mod.Phys., 59, 1121
• Colella, P. & Glaz, H. M. 1985, JCP, 59, 264
• Colella, P. & Woodward, P. 1984, JCP, 54, 174
• Colgate, S. A., & White, R. H. 1966, ApJ, 143, 626
• Colin, O. & Ducros, F. & Veynante, D. & Poinsot, T. 2000, Physics of Fluids, 12, 7, 1843
• Couch, S. M., Graziani, C. & Flocke, N. 2013, ApJ, 778, 181
• Decyk, V. K., Norton, C. D., & Szymanski, B. K. 1997, ACM Fortran Forum, 16 (also
  http://www.cs.rpi.edu/~szymansk/oof90.html)
• A. Dedner, F. Kemm, D. Kröner, C.-D. Munz, T. Schnitzer, and M. Wesenberg, “Hyperbolic Divergence Cleaning for the MHD Equations,” Journal of Computational Physics, vol. 175, no. 2, pp. 645–673, Jan. 2002, doi: 10.1006/jcph.2001.6961.
• DeZeeuw, D. & Powell, K. G. 1993, JCP, 104, 56
• Doring, W. 1943, Ann. Phys., 43, 421
• Dubey, A., Daley, C., ZuHone, J., Ricker, P. M., Weide, K. & Graziani, C. 2012, ApJS, 201, 27
• Duff, I. S., Erisman, A. M., & Reid, J. K. 1986, Direct Methods for Sparse Matrices (Oxford: Clarendon Press)
• Einfeldt, B., Munz, C. D., Roe, P. L., & Sjögreen, B. 1991, JCP, 92, 273-295
• Emery, A. F. 1968, JCP, 2, 306
• Epperlein, E. M. & Haines, M. G. 1986, Phys. Fluids, 29, 1029
• Eswaran, V. and Pope, S. B. 1988, Computers & Fluids, 16, 257-278
• Evans, C. R. & Hawley, J. F. 1988, ApJ, 332, 659
• Ewald, P. P. 1921, Ann. Phys., 64, 253
• Federrath, C., Banerjee, R., Clark, P. C. & Klessen, R. S. 2010, ApJ 713, 269
• Federrath, C., Roman-Duval, J., Klessen, R. S., Schmidt, W., Mac Low, M.-M. 2010, A&A, 512, A81
• Ferguson, J. W., Alexander, D. R., Allard, F., Barman, T., Bodnarik, J. G., Hauschildt, P. H., Heffner-Wong, A., & Tamanai, A. 2005, ApJ, 623, 585
• Fletcher, C. A. J. 1991, Computational Techniques for Fluid Dynamics, 2d ed. (Berlin: Springer)
• Flocke, N. 2015, ACM Transactions on Mathematical Software, 41, Article 30
• Forester, C. K. 1977, JCP, 23, 1
• Foster, P. N., & Chevalier, R. A. 1993, ApJ, 416, 303
• Froula, D. H., Glenzer, S. H., Luhmann Jr., N. C., & Sheffield, J. 2011, Plasma Scattering of Electromagnetic Radiation, 2d ed. (Elsevier: AP)
• Fryxell, B. A., Müller, E., & Arnett, D. 1989, in Numerical Methods in Astrophysics, ed. P. R. Woodward (New York: Academic)
• Fryxell, B., Olson, K., Ricker, P., Timmes, F. X., Zingale, M., Lamb, D. Q., MacNeice, P., Rosner, R., Truran, J. W., & Tufo, H. 2000, ApJS, 131, 273
• Gardiner, T., & Stone, J. 2005, JCP, 205, 509
• Gittings, M., et al. 2008, Computational Science and Discovery, 1, 015005
• Godunov, S. K. 1959, Mat. Sbornik, 47, 271
• Grevesse, N., & Sauval, A. J. 1998, Space Science Reviews, 85, 161
• Harten, A. 1983, JCP, 49, 357-393
• Hawley, J. F. 2000, ApJ, 528, 462
• Holmström, M., Fatemi, S., Futaana, Y., & Nilsson, H. 2012, The interaction between the Moon and the solar wind. Earth, Planets and Space, 74, 237-245
• Holmström, M. 2013, Handling vacuum regions in a hybrid plasma solver. Numerical modeling of space plasma flows (ASTRONUM-2012), ASP Conference Series, vol. 474, 202-207. arXiv:1301.0272
• Hu, W. & Sugiyama, N. 1996, ApJ, 471, 542
• Huang, J. & Greengard, L. 2000, SIAM. J. Sci. Comput., 21, 1551
• Huba, J.D. 2009, NRL Plasma Formulary (NRL/PU/6790-11-551).
• Huba, J.D. 2003, Space Plasma Simulation, 615
• Iben, I. Jr. 1975, ApJ, 196, 525
• Itoh, N., Hayashi, H., Nishikawa, A., & Kohyama, Y. 1996, ApJS, 102, 411
• Jackson, A. P. & Townsley, D. M. & Calder, A. C. 2014, ApJ, 784, 174
• James, R. A. 1977, JCP, 25, 71
• Jeans, J. H. 1902, Phil. Trans. Roy. Soc. (London), 199, 1
• Jouguet, E. 1905, J. Math. Pure Appl., 1, 347
• Kaiser, T. B. 2000, Phys. Rev. E, 61, 895
• Khokhlov, A. M. 1997, Naval Research Lab memo 6406-97-7950
• Krumholz, M., Klein, R., McKee, C., & Bolstad, J. 2007, ApJ, 667, 626
• Kurganov, A., Noelle, S., & Petrova, G. 2001, SIAM. J. 23, 707
• Kurganov, A., & Tadmor, E. 2000, JCP, 160, 241
• Lacey, C. G. & Cole, S. 1993, MNRAS, 262, 627
• Ledvina, S., Ma, Y.-J., and Kallio, E., Modeling and Simulating Flowing Plasmas and Related Phenomena, Space Sci. Rev., 143-189, 2008.
• Lee, D. 2006, Ph.D. Dissertation, Univ. of Maryland
• Lee, D. & Deane, A. 2009, JCP, 228, 952
• Lee, D. 2013, JCP, 243, 269-292, doi:10.1016/j.jcp.2013.02.049
• Lee, Y. T. & More, R. M. 1984, Phys. Fluids, 27, 1273
• Li, S., & Li, H. 2004, JCP, 199, 1
• Li, S. 2005, JCP, 203, 344-357
• Löhner, R. 1987, Comp. Meth. App. Mech. Eng., 61, 323
• LeVeque, R. J. 1992, Numerical Methods for Conservation Laws, Birkhäuser.
• LeVeque, R. J. 1997, JCP, 131, 327
• LeVeque, R. J. 1998, “Nonlinear Convservation Laws and Finite Volume Methods”, LeVeque, R. J., Mihalas, D., Dorfi, E. A., Mueller, E. (ed.), Computational Methods for Astrophysical Fluid Flow, Springer.
• Lowrie, R. 2008, Shock Waves, 18, 129
• MacLaurin, C. 1801, A Treatise on Fluxions, (W. Baynes), Available on http://books.google.com
• MacNeice, P., Olson, K. M., Mobarry, C., de Fainchtein, R., & Packer, C. 1999, CPC, 126, 3
• Marder, B. 1987, JCP, 68, 48
• Martií, J. M., Müller, E., 2003, Living Rev. Relativ., 6, 7, .
• Martin, D. & Cartwright, K., “Solving Poisson's Equation using Adaptive Mesh Refinement.” (http://seesar.lbl.gov/anag/staff/martin/AMRPoisson.html)
• Martin, D., & Cartwright, K. 1996, “Solving Poisson's Equation using Adaptive Mesh Refinement”, Technical Report No. UCB/ERL M96/66
• Matthews, A. P., Current Advance Method and Cyclic Leapfrog for 2D Multispecies Hybrid Plasma Simulations, Journal of Computational Physics, 112, 102-116, 1994.
• Mignone, A., Plewa, T., Bodo, G. 2005, ApJ, 160, 199
• Mignone, A., Bodo, G., Massaglia, S., Matsakos, T., Tesileanu, O., Zanni, C., & Ferrari, A. 2007, ApJS, 170, 228.
• Miller, G. H. & Puckett, E. G. 1996 JCP, 128, 134-164
• Miyoshi, T. & Kusano K. 2005, JCP, 208, 315-344
• Mönchmeyer, R., & Müller, E. 1989, A&A, 217, 351
• Morozova, V., Piro, A. L., Renzo, M., Ott, C. D., Clausen, D., Couch, S. M., Ellis, J., &Roberts, L. F. 2015, ApJ, 814, 63
• Müller, E., & Steinmetz, M. 1995, Comp. Phys. Comm., 89, 45
• Munz, C. D., Omnes, P., Schneider, R., Sonnendrücker, & Voß, U. 2000, JCP, 161, 484
• Nadyozhin, D. K. 1974, Nauchnye informatsii Astron, Sov. USSR, 32, 33
• Noh, W. F. 1987, JCP, 72, 78
• Orszag, S. A., Tang, C.-M., 1979, JFM, 90, 129
• Ostriker, J.P., ed. 1992, Selected Works of Yakov Borisovich Zeldovich (Princeton Univ. Press)
• Paczynsky B., & Wiita, P. J. 1980, A&A, 88, 23.
• Parashar M., 1999, private communication (http://www.caip.rutgers.edu/~parashar/DAGH)
• Paxton, B., Bildsten, L., Dotter, A., Herwig, F., Lesaffre, P., & Timmes, F. 2011, ApJS, 192, 3
• Paxton, B., Cantiello, M., Arras, P., Bildsten, L., Brown, E. F., Dotter, A., Mankovich, C., Montgomery, M. H., Stello, D., Timmes, F. X., & Townsend, R. 2013, ApJS, 208, 4
• Paxton, B., Marchant, P., Schwab, J., Bauer, E. B., Bildsten, L., Cantiello, M., Dessart, L., Farmer, R., Hu, H., Langer, N., Townsend, R. H. D., Townsley, D. M. & Timmes, F. X. 2015, ApJS, 220, 15
• Pert, G.J., 1977, J. Plasma Physics, vol.18, part 2, pp. 227-241
• Plewa, T. & Müller, E. 1999, A&A, 342, 179.
• Potekhin, A. Y., Chabrier, G., & Yakovlev, D. G. 1997, A&A323, 415
• Powell, K. G., Roe, P. L., Linde, T. J. , Gombosi, T. I., & DeZeeuw, D. L. 1999, JCP, 154, 284
• Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. 1992, Numerical Recipes in Fortran, 2d ed. (Cambridge: CUP)
• Price, D. J. & Federrath, C. 2010, MNRAS, 406, 1659
• Pritchett, Philip L., Particle-in-cell Simulations of Magnetosphere Electrodynamics, IEEE Transactions on Plasma Science, 28, 6, 1976-1990, 2000.
• Quirk, J. J., in Upwind and High-Resolution Schemes, ed. M. Yousuff Hussaini, Bram van Leer, and John Van Rosendale, 1997, (Berlin: Springer).
• Reinicke, P. and Meyer-ter-Vehn, J. 1991, Phys. Fluids A, 3, 1807
• Ricker, P. M. 2008, arXiv: 0710.4397, ApJS, 176, 293
• Rider, W. J. & Kothe, D. B. 1998, JCP, 141, 112-152
• Ross, R., Nurmi, D., Cheng, A. & Zingale, M. 2001, Proceedings of SC2001.
• Salmon, J. K. & Warren, M. S. 1994, JCP, 111, 136
• Schulz-Rinne, C. W, Collins, J. P., and Glaz, H. M. 1993, SIAM J. Sci. Comput. 14, 1394.
• Sedov, L. I. 1959, Similarity and Dimensional Methods in Mechanics (New York: Academic)
• Shu, C.-W. 1998, in Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, ed. A. Quarteroni, Lecture Notes in Mathematics, 1697, (Berlin: Springer)
• Shu, C.-W. & Osher, S. 1989, JCP, 83, 32
• Skinner, M. A., & Ostriker, E. C. ApJS, 188, 290
• Spitzer, L. 1962, Physics of Fully Ionized Gases. (New York: Wiley)
• Sportisse, B. 2000, JCP, 161, 140
• Springel, V. 2005, MNRAS, 364, 1105
• Sod, G. 1978, JCP, 27, 1
• Strang, G. 1968, SIAM J. Numer. Anal., 5, 506
• Timmes, F. X. 1992, ApJ, 390, L107
• Timmes, F. X. 1999, ApJS, 124, 241
• Timmes, F. X. 2000, ApJ, 528, 913
• Timmes, F. X. & Arnett, D. 2000, ApJS, 125, 294
• Timmes, F. X. & Brown, E. 2002 (in preparation)
• Timmes, F. X. & Swesty, F. D. 2000, ApJS, 126, 501
• Timmes, F. X. & Zingale, M. & Olson, K. & Fryxell, B. & Ricker, P. & Calder, A. C. & Dursi, L. J. & Tufo, H. & MacNeice, P. & Truran, J. W. & Rosner, R. 2000, ApJ543, 938
• Toro, E. F. 1999, Riemann Solvers and Numerical Methods for Fluid Dynamics, 2nd Ed. (New York: Springer)
• Tóth, G. 2000, JCP, 161, 605
• Townsley, D. M. & Calder, A. C. & Asida, S. M. & Seitenzahl, I. R. & Peng, F. & Vladimirova, N. & Lamb, D. Q. & Truran, J. W. 2007, ApJ, 668, 1118
• Trottenberg, U., Oosterlee, C., & Schüller, A. 2001, Multigrid (San Diego: Academic Press)
• Tzeferacos, P., Fatenejad, M., Flocke, N., Gregori, G., Lamb, D. Q., Lee, D., Meinecke, J., Scopatz, A., & Weide, K. 2012 HEDP, 8, 322, doi:10.1016/j.hedp.2012.08.001
• Uhlenbeck, G. E. & Ornstein, L. S. 1930, Phys. Rev. 36, 823
• van der Vorst, H. 1992, “Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems”, SIAM J. Sci. and Stat. Comput., 13:2, 631-644
• van Leer, B. 1979, JCP, 32, 101
• Vanella, M., Rabenold, P. & Balaras, E. 2010, J. Comput. Phys., 229:18, 6427-6449
• von Neumann, J. 1942, ORSD Rep. No. 549
• Velikovich, A. L., Giuliani, J. L., Zalesak, S. T., Thornhill, J. W., & Gardiner, T. A. 2012, Phys. Plasmas, 19, 012707
• Vladimirova, N. & Weirs, G. & Ryzhik, L. 2006, Combustion Theory and Modelling, 10, 727
• Wallace, R. K., Woosley, S. E., & Weaver, T. A. 1982, ApJ, 258, 696
• Warren, M. S. & Salmon, J. K. 1993, in Proc. Supercomputing 1993 (Washington, DC: IEEE Computer Soc.)
• Weaver, T. A., Zimmerman, G. B., & Woosley, S. E. 1978, ApJ, 225, 1021
• Williams, F. A. 1988, Combustion Theory (Menlo Park: Benjamin-Cummings)
• Williamson, J. H. 1980, JCP, 35, 48
• Winske, D. and Leroy, M. M., Diffuse ions produced by electromagnetic ion beam instabilities, Journal of Geophysical Research, 89, 2673-2688, 1984.
• Winske, D. and Quest, K. B., Electromagnetic Ion Beam Instabilities: Comparison of one- and two-dimensional simulations, Journal of Geophysical Research, 91, 8789-8797, 1986.
• Woodward, P. & Colella, P. 1984, JCP, 54, 115
• Xin, J. 2000, SIAM Rev., 42, 161
• Yakovlev, D. G., & Urpin, V. A. (YU) 1980 24, 303
• Yang. J. & Balaras, E. 2006, J. Comput. Phys., 215:1, 12-40
• Yee, H. C., Vinokur, M., and Djomehri, M. J. 2000, JCP, 162, 33
• Yee, K. S., IEEE Trans. Antenna Propagation, 1966, AP-14, 302
• Youngs, D. L., 1984, AWRE/44/92/35
• Zachary, A., Malagoli, A., Colella, P. 1994, SIAM, 15, 263
• Zalesak, S. T. 1987, in Advances in Computer Methods for Partial Differential Equations VI, eds. Vichnevetsky, R. and Stepleman, R. S. (IMACS), 15
• Zel'dovich, Ya. B. 1970, A&A, 5, 84
• Zel'dovich, Ya. B. and Raizer, Yu. P. 2002, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, Dover
• Zhang, W., Howell, L., Almgren, A., Burrows, A., & Bell, J. 2011, ApJS, 196, 20
• Zingale, M., Dursi, L. J., ZuHone, J., Calder, A. C., Fryxell, B., Plewa, T., Truran, J. W., Caceres, A., Olson, K., Ricker, P. M., Riley, K., Rosner, R., Siegel, A., Timmes, F. X., and Vladimirova, N. 2002, ApJS, 143, 539