A BOUT++ extension for full annular tokamak edge MHD and turbulence simulations. (English) Zbl 1528.76064
Summary: For tokamak edge plasma simulation, a plasma simulation framework BOUT++ employs a dual coordinate system to simulate moderate-\(n\) and high-\(n\) plasma instability with reasonable computational cost, where \(n\) is the toroidal mode number. This coordinate system however limits the computational domain to the toroidal wedge (full torus divided into \(N\) parts in the toroidal direction) for computational efficiency and the use of flute-ordering approximation in the field solver calculating the flow potential from the vorticity which may not be valid for low-\(n\) modes. Improving numerical treatment of low-\(n\) modes is however indispensable to address simulations of low-\(n\) current-driven edge localized mode (ELM), ELM control by resonant magnetic perturbations (RMPs), edge turbulence with RMPs and so on. In this work, BOUT++ is extended to simulate the interplay between \(n = 0\), low-\(n\) and high-\(n\) plasma components in a full annular tokamak edge domain through hybrid modeling of the flow potential and the vorticity. Low-\(n\) modes of flow potential are calculated in an orthogonal flux surface coordinate and high-\(n\) modes in the dual coordinate system separately in Fourier space. The proposed scheme can capture an interplay between \(n = 1\) global modes and high-\(n\) turbulence during pedestal collapse in a full annular torus domain with a circular cross section.
MSC:
| 76M99 | Basic methods in fluid mechanics |
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 76X05 | Ionized gas flow in electromagnetic fields; plasmic flow |
| 76F99 | Turbulence |
Keywords:
field solver; reduced MHD model; flow potential; vorticity; resonant magnetic perturbation; orthogonal flux surface coordinate; Fourier space; circular torus domainReferences:
| [1] | Loarte, A.; Lipschultz, B.; Kukushkin, A. S.; Matthews, G. F.; Stangeby, P. C.; Asakura, N.; Counsell, G. F.; Federici, G.; Kallenbach, A.; Krieger, K.; Mahdavi, A.; Philipps, V.; Reiter, D.; Roth, J.; Strachan, J.; Whyte, D.; Doerner, R.; Eich, T.; Fundamenski, W.; Herrmann, A.; Fenstermacher, M.; Ghendrih, P.; Groth, M.; Kirschner, A.; Konoshima, S.; LaBombard, B.; Lang, P.; Leonard, A. W.; Monier-Garbet, P.; Neu, R.; Pacher, H.; Pegourie, B.; Pitts, R. A.; Takamura, S.; Terry, J.; Tsitrone, E., Nucl. Fusion, 47, 6, S203-S263 (2007) |
| [2] | Wenninger, R.; Kembleton, R.; Bachmann, C.; Biel, W.; Bolzonella, T.; Ciattaglia, S.; Cismondi, F.; Coleman, M.; Donné, A. J.H.; Eich, T.; Fable, E.; Federici, G.; Franke, T.; Lux, H.; Maviglia, F.; Meszaros, B.; Pütterich, T.; Saarelma, S.; Snickers, A.; Villone, F.; Vincenzi, P.; Wolff, D.; Zohm, H., Nucl. Fusion, 57, 1, Article 016011 pp. (2016) |
| [3] | Asakura, N.; Hoshino, K.; Homma, Y.; Sakamoto, Y., Nucl. Mater. Energy, 26, Article 100864 pp. (2021) |
| [4] | Wagner, F.; Becker, G.; Behringer, K.; Campbell, D.; Eberhagen, A.; Engelhardt, W.; Fussmann, G.; Gehre, O.; Gernhardt, J.; Gierke, G.v.; Haas, G.; Huang, M.; Karger, F.; Keilhacker, M.; Klüber, O.; Kornherr, M.; Lackner, K.; Lisitano, G.; Lister, G. G.; Mayer, H. M.; Meisel, D.; Müller, E. R.; Murmann, H.; Niedermeyer, H.; Poschenrieder, W.; Rapp, H.; Röhr, H.; Schneider, F.; Siller, G.; Speth, E.; Stäbler, A.; Steuer, K. H.; Venus, G.; Vollmer, O.; Yü, Z., Phys. Rev. Lett., 49, 19, 1408-1412 (1982) |
| [5] | Zohm, H., Plasma Phys. Control. Fusion, 38, 8, 1213-1223 (1996) |
| [6] | Kukushkin, A.; Pacher, H.; Kotov, V.; Pacher, G.; Reiter, D., Fusion Eng. Des., 86, 12, 2865-2873 (2011) |
| [7] | Gunn, J.; Carpentier-Chouchana, S.; Escourbiac, F.; Hirai, T.; Panayotis, S.; Pitts, R.; Corre, Y.; Dejarnac, R.; Firdaouss, M.; Kočan, M.; Komm, M.; Kukushkin, A.; Languille, P.; Missirlian, M.; Zhao, W.; Zhong, G., Nucl. Fusion, 57, 4, Article 046025 pp. (2017) |
| [8] | Huysmans, G. T.A.; Czarny, O., Nucl. Fusion, 47, 7, 659-666 (2007) |
| [9] | Czarny, O.; Huysmans, G., J. Comput. Phys., 227, 16, 7423-7445 (2008) · Zbl 1141.76035 |
| [10] | Hoelzl, M.; Huijsmans, G.; Pamela, S.; Bécoulet, M.; Nardon, E.; Artola, F.; Nkonga, B.; Atanasiu, C.; Bandaru, V.; Bhole, A.; Bonfiglio, D.; Cathey, A.; Czarny, O.; Dvornova, A.; Fehér, T.; Fil, A.; Franck, E.; Futatani, S.; Gruca, M.; Guillard, H.; Haverkort, J.; Holod, I.; Hu, D.; Kim, S.; Korving, S.; Kos, L.; Krebs, I.; Kripner, L.; Latu, G.; Liu, F.; Merkel, P.; Meshcheriakov, D.; Mitterauer, V.; Mochalskyy, S.; Morales, J.; Nies, R.; Nikulsin, N.; Orain, F.; Pratt, J.; Ramasamy, R.; Ramet, P.; Reux, C.; Särkimäki, K.; Schwarz, N.; Verma, P. S.; Smith, S.; Sommariva, C.; Strumberger, E.; van Vugt, D.; Verbeek, M.; Westerhof, E.; Wieschollek, F.; Zielinski, J., Nucl. Fusion, 61, 6, Article 065001 pp. (2021) |
| [11] | Sovinec, C. R.; Glasser, A. H.; Gianakon, T. A.; Barnes, D. C.; Nebel, R. A.; Kruger, S. E.; Schnack, D. D.; Plimpton, S. J.; Tarditi, A.; Chu, M. S., J. Comput. Phys., 195, 1, 355-386 (2004) · Zbl 1087.76070 |
| [12] | Ferraro, N. M.; Jardin, S. C.; Snyder, P. B., Phys. Plasmas, 17, 10, Article 102508 pp. (2010) |
| [13] | Wingen, A.; Ferraro, N. M.; Shafer, M. W.; Unterberg, E. A.; Canik, J. M.; Evans, T. E.; Hillis, D. L.; Hirshman, S. P.; Seal, S. K.; Snyder, P. B.; Sontag, A. C., Plasma Phys. Control. Fusion, 57, 10, Article 104006 pp. (2015) |
| [14] | Dudson, B. D.; Umansky, M. V.; Xu, X. Q.; Snyder, P. B.; Wilson, H. R., Comput. Phys. Commun., 180, 9, 1467-1480 (2009) · Zbl 07872388 |
| [15] | Xu, X. Q.; Dudson, B.; Snyder, P. B.; Umansky, M. V.; Wilson, H., Phys. Rev. Lett., 105, 17, Article 949 pp. (2010) |
| [16] | Zhu, B.; Seto, H.; Xu, X. qiao; Yagi, M., Comput. Phys. Commun., 267, Article 108079 pp. (2021) · Zbl 1539.76289 |
| [17] | Beer, M. A.; Cowley, S. C.; Hammett, G. W., Phys. Plasmas, 2, 7, 2687-2700 (1995) |
| [18] | D’haeseleer, W. D.; Hitchon, W. N.G.; Callen, J. D.; Shohet, J. L., Flux Coordinates and Magnetic Field Structure (1991), Springer-Verlag · Zbl 0989.76500 |
| [19] | Dimits, A. M., Phys. Rev. E, 48, 5, 4070-4079 (1993) |
| [20] | Scott, B., Phys. Plasmas, 8, 2, 447-458 (2001) |
| [21] | Dudson, B. D.; Leddy, J., Plasma Phys. Control. Fusion, 59, 5, Article 054010 pp. (2017) |
| [22] | Seto, H.; Xu, X. Q.; Dudson, B. D.; Yagi, M., Phys. Plasmas, 26, 5, Article 052507 pp. (2019) |
| [23] | Seto, H.; Xu, X.; Dudson, B. D.; Yagi, M., Contrib. Plasma Phys., 60, 5-6, Article e201900158 pp. (2020) |
| [24] | Burrell, K. H.; Austin, M. E.; Brennan, D. P.; DeBoo, J. C.; Doyle, E. J.; Gohil, P.; Greenfield, C. M.; Groebner, R. J.; Lao, L. L.; Luce, T. C.; Makowski, M. A.; McKee, G. R.; Moyer, R. A.; Osborne, T. H.; Porkolab, M.; Rhodes, T. L.; Rost, J. C.; Schaffer, M. J.; Stallard, B. W.; Strait, E. J.; Wade, M. R.; Wang, G.; Watkins, J. G.; West, W. P.; Zeng, L., Plasma Phys. Control. Fusion, 44, 5A, A253-A263 (2002) |
| [25] | Burrell, K. H.; Osborne, T. H.; Snyder, P. B.; West, W. P.; Fenstermacher, M. E.; Groebner, R. J.; Gohil, P.; Leonard, A. W.; Solomon, W. M., Phys. Rev. Lett., 102, Article 155003 pp. (2009) |
| [26] | Liu, F.; Huijsmans, G.; Loarte, A.; Garofalo, A.; Solomon, W.; Snyder, P.; Hoelzl, M.; Zeng, L., Nucl. Fusion, 55, 11, Article 113002 pp. (2015) |
| [27] | Evans, T. E.; Moyer, R. A.; Thomas, P. R.; Watkins, J. G.; Osborne, T. H.; Boedo, J. A.; Doyle, E. J.; Fenstermacher, M. E.; Finken, K. H.; Groebner, R. J.; Groth, M.; Harris, J. H.; La Haye, R. J.; Lasnier, C. J.; Masuzaki, S.; Ohyabu, N.; Pretty, D. G.; Rhodes, T. L.; Reimerdes, H.; Rudakov, D. L.; Schaffer, M. J.; Wang, G.; Zeng, L., Phys. Rev. Lett., 92, Article 235003 pp. (2004) |
| [28] | Orain, F.; Becoulet, M.; Dif-Pradalier, G.; Huijsmans, G.; Pamela, S.; Nardon, E.; Passeron, C.; Latu, G.; Grandgirard, V.; Fil, A.; Ratnani, A.; Chapman, I.; Kirk, A.; Thornton, A.; Hoelzl, M.; Cahyna, P., Phys. Plasmas, 20, 10, Article 102510 pp. (2013) |
| [29] | Orain, F.; Bécoulet, M.; Huijsmans, G. T.A.; Dif-Pradalier, G.; Hoelzl, M.; Morales, J.; Garbet, X.; Nardon, E.; Pamela, S.; Passeron, C.; Latu, G.; Fil, A.; Cahyna, P., Phys. Rev. Lett., 114, Article 035001 pp. (2015) |
| [30] | BOUT++ public git-hub |
| [31] | Hazeltine, R.; Meiss, J., Phys. Rep., 121, 1, 1-164 (1985) |
| [32] | Snyder, P. B.; Wilson, H. R.; Ferron, J. R.; Lao, L. L.; Leonard, A. W.; Osborne, T. H.; Turnbull, A. D.; Mossessian, D.; Murakami, M.; Xu, X. Q., Phys. Plasmas, 9, 5, 2037-2043 (2002) |
| [33] | Wilson, H. R.; Snyder, P. B.; Huysmans, G. T.A.; Miller, R. L., Phys. Plasmas, 9, 4, 1277-1286 (2002) |
| [34] | Curtiss, C. F.; Hirschfelder, J. O., Proc. Natl. Acad. Sci., 38, 3, 235-243 (1952) · Zbl 0046.13602 |
| [35] | Cohen, S. D.; Hindmarsh, A. C.; Dubois, P. F., Comput. Phys., 10, 2, 138-143 (1996); https://aip.scitation.org/doi/abs/10.1063/1.4822377 |
| [36] | Dudson, B. D.; Xu, X. Q.; Umansky, M. V.; Wilson, H. R.; Snyder, P. B., Plasma Phys. Control. Fusion, 53, 5, Article 054005 pp. (2011) |
| [37] | Balay, S.; Abhyankar, S.; Adams, M. F.; Brown, J.; Brune, P.; Buschelman, K.; Dalcin, L.; Eijkhout, V.; Gropp, W. D.; Kaushik, D.; Knepley, M. G.; May, D. A.; McInnes, L. C.; Rupp, K.; Smith, B. F.; Zampini, S.; Zhang, H.; Zhang, H., PETSc Web page (2017) |
| [38] | Balay, S.; Gropp, W. D.; McInnes, L. C.; Smith, B. F., (Arge, E.; Bruaset, A. M.; Langtangen, H. P., Modern Software Tools in Scientific Computing (1997), Birkhäuser Press), 163-202 |
| [39] | Saad, Y.; Schultz, M. H., SIAM J. Sci. Stat. Comput., 7, 3, 856-869 (1986) · Zbl 0599.65018 |
| [40] | Frankel, S. P., Math. Tables Other Aids Comput., 4, 30, 65-75 (1950) |
| [41] | Young, D., Trans. Am. Math. Soc., 1, 76, 92-111 (1954) · Zbl 0055.35704 |
| [42] | Brandt, A.; McCormick, S.; Ruge, J., (Sparsity and Its Applications (1984)), 257-284 · Zbl 0548.65014 |
| [43] | Falgout, R. D.; Jones, J. E.; Yang, U. M., (Bruaset, A. M.; Tveito, A., Numerical Solution of Partial Differential Equations on Parallel Computers (2006), Springer Berlin Heidelberg: Springer Berlin Heidelberg Berlin, Heidelberg), 267-294 · Zbl 1084.65001 |
| [44] | Miller, R. L.; Vandam, J. W., Nucl. Fusion, 27, 12, 2101-2112 (1987) |
| [45] | Burke, B. J.; Kruger, S. E.; Hegna, C. C.; Zhu, P.; Snyder, P. B.; Sovinec, C. R.; Howell, E. C., Phys. Plasmas, 17, 3, Article 032103 pp. (2010) |
| [46] | Connor, J. W.; Hastie, R. J.; Taylor, J. B., Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci., 365, 1720, 1-17 (1979) |
| [47] | Bernard, L.; Helton, F.; Moore, R., Comput. Phys. Commun., 24, 3, 377-380 (1981) |
| [48] | Chang, Z.; Callen, J. D., Phys. Fluids, B Plasma Phys., 4, 7, 1766-1771 (1992) |
| [49] | Itoh, K.; Itoh, S.-I., Plasma Phys. Control. Fusion, 38, 1, 1-49 (1996) |
| [50] | JFRS-1 in IFERC project webpage |
| [51] | JFRS-1 in top500.org |
| [52] | Xi, P. W.; Xu, X. Q.; Diamond, P. H., Phys. Rev. Lett., 112, 8, Article 085001 pp. (2014) |
| [53] | Xi, P. W.; Xu, X. Q.; Diamond, P. H., Phys. Plasmas, 21, 5, Article 056110 pp. (2014) |
| [54] | Furth, H. P.; Killeen, J.; Rosenbluth, M. N., Phys. Fluids, 6, 4, 459-484 (1963) |
| [55] | Furth, H. P.; Rutherford, P. H.; Selberg, H., Phys. Fluids, 16, 7, 1054-1063 (1973) |
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