Adaptive numerical algorithms in space weather modeling

Journal of Computational Physics

Volumn 231, Issue 3, 2012, Pages 870-903

  Tóth, Gábor ^a   van der Holst, Bart ^a   Sokolov, Igor V ^a   De Zeeuw, Darren L ^a   Gombosi, Tamas I ^a   Fang, Fang ^a   Manchester, Ward B ^a   Meng, Xing ^a   Najib, Dalal ^a   Powell, Kenneth G ^a   Stout, Quentin F ^a   Glocer, Alex ^b   Ma, Ying Juan ^c   Opher, Merav ^d  

^a UNIVERSITY OF MICHIGAN   (United States)

^b NASA GODDARD SPACE FLIGHT CENTER   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

^d USA   (United States)

Author keywords

65D99 Numerical approximation; 77A05 Magnetohydrodynamics

Indexed keywords

ADAPTIVE ALGORITHMS; MACHINE COMPONENTS; MAGNETOHYDRODYNAMICS; MESSAGE PASSING; WEATHER FORECASTING;

65D99 NUMERICAL APPROXIMATION; 77A05 MAGNETOHYDRODYNAMIC; ADAPTIVE TREE; NUMERICAL ALGORITHMS; NUMERICAL APPROXIMATIONS; PHYSICS-BASED; SPACE WEATHER; TIME-INTEGRATION SCHEME; UP-WIND SCHEME; WEATHER MODELING;

HEAT CONDUCTION;

EID: 82455175271     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2011.02.006     Document Type: Article

References (92)

1. Goodrich C.C., Sussman A.L., Lyon J.G., Shay M.A., Cassak P.A. The CISM code coupling strategy. J. Atmos. Sol.-Terr. Phys. 2004, 66:1469.
2. J.Y. Lee, A. Sussman, Efficient communication between parallel programs with intercomm, Tech. Rep. 2004-04, UMIACS (2004).
3. Brown D.L., Henshaw W.D., Quinlan D.J. Overture: an object-oriented framework for solving partial differential equations on overlapping grids. SIAM Conference on Object Oriented Methods for Scientific Computing 1999, 177-184. SIAM, Philadelphia, PA.
4. SWMF, Space weather modeling framework at http://csem.engin.umich.edu/swmf.
5. Tóth G., Sokolov I.V., Gombosi T.I., Chesney D.R., Clauer C., Zeeuw D.L.D., Hansen K.C., Kane K.J., Manchester W.B., Powell K.G., Ridley A.J., Roussev I.I., Stout Q.F., Volberg O., Wolf R.A., Sazykin S., Chan A., Yu B., Kóta J. Space weather modeling framework: a new tool for the space science community. J. Geophys. Res. 2005, 110:A12226. 10.1029/2005JA011126.
6. Tóth G. Flexible, efficient and robust algorithm for parallel execution and coupling of components in a framework. Comput. Phys. Commun. 2006, 174:793. 10.1016/j.cpc.2005.12.017.
7. Hill C., DeLuca C., Balaji V., Suarez M., da Silva A., Team The ESMF Joint Specification The architecture of the Earth System Modeling Framework. Comput. Sci. Eng. 2004, 6(1):18-28. 10.1109/MCISE.2004.1255817.
8. Powell K., Roe P., Linde T., Gombosi T., De Zeeuw D.L. A solution-adaptive upwind scheme for ideal magnetohydrodynamics. J. Comput. Phys. 1999, 154:284-309.
9. Gombosi T.I., Powell K.G., De Zeeuw D.L., Clauer C.R., Hansen K.C., Manchester W.B., Ridley A.J., Roussev I.I., Sokolov I.V., Stout Q.F., Tóth G. Solution-adaptive magnetohydrodynamics for space plasmas: Sun-to-Earth simulations. Comput. Sci. Eng. 2004, 06(2):14-35.
10. Linker J.A., Mikić Z., Lionello R., Riley P., Amari T., Odstrcil D. Flux cancellation and coronal mass ejections. Phys. Plasmas 2003, 10:1971-1978.
11. Odstrcil D. Modeling 3-d solar wind structures. Adv. Space Res. 2003, 32(4):497-506.
12. Lyon J., Fedder J., Mobarry C. The Lyon-Fedder-Mobarry (LFM) global MHD magnetospheric simulation code. J. Atmos. Sol-Terr. Phys. 2004, 66:1333.
13. Raeder J., Berchem J., Ashour-Abdalla M., Frank L., Paterson W., Ackerson K., Kokubun S., Yamamoto T., Slavin J. Boundary layer formation in the magnetotail: geotail observations and comparisons with a global MHD simulation. Geophys. Res. Lett. 1997, 24:951.
14. P. Janhunen, GUMICS-3: a global ionosphere-magnetosphere coupling simulation with high ionospheric resolution, in: Proceedings of the ESA 1996 Symposium on Environment Modelling for Space-Based Applications, ESA SP-392, 1996, pp. 233-239.
15. van der Holst B., Keppens R., Meliani Z. A multidimensional grid-adaptive relativistic magnetofluid code. J. Comput. Phys. 2008, 179:617.
16. MacNiece P., Olson K.M., Mobarry C., deFainchtein R., Packer C. PARAMESH: a parallel adaptive mesh refinement community toolkit. Comput. Phys. Comm. 2000, 126:330-354.
17. CHOMBO, Chombo library at http://seesar.lbl.gov/anag/chombo.
18. SAMRAI, Structured adaptive mesh refinement application infrastructure at http://https://computation.llnl.gov/casc/samrai.
19. Tóth G., De Zeeuw D.L., Gombosi T.I., Powell K.G. A parallel explicit/implicit time stepping scheme on block-adaptive grids. J. Comput. Phys. 2006, 217:722-758. 10.1016/j.jcp.2006.01.029.
20. Tóth G., Zeeuw D.L.D., Gombosi T.I., Manchester W.B., Ridley A.J., Sokolov I.V., Roussev I.I. Sun to thermosphere simulation of the October 28-30, 2003 storm with the space weather modeling framework. Space Weather J. 2007, 5:S06003. 10.1029/2006SW000272.
21. Manchester W.B., Vourlidas A., Toth G., Lugaz N., Roussev I.I., Sokolov I.V., Gombosi T.I., Zeeuw D.L.D., Opher M. Three-dimensional MHD simulation of the 2003 October 28 coronal mass ejection: comparison with LASCO coronagraph observations. Astrophys. J. 2008, 684:1448-1460.
22. ISWA, Integrated space weather analysis system at http://iswa.ccmc.gsfc.nasa.gov.
23. Pulkkinen A., Hesse M., Habib S., der Zel L.V., Damsky B., Policelli F., Fugate D., Jacobs W., Creamer E. Solar shield: forecasting and mitigating space weather effects on high-voltage power transmission systems. Nat. Hazards 2009, 53:333-345. 10.1007/s11069-009-9432-x.
24. CCMC, Community coordinated modeling center at http://ccmc.gsfc.nasa.gov.
25. Tsyganenko N.A. A magnetospheric magnetic field model with a warped tail current sheet. Planet. Space Sci. 1989, 37:5.
26. Weimer D. A flexible, IMF dependent model of high-latitude electric potential having " space weather" applications. Geophys. Res. Lett. 1996, 23:2549.
27. Weimer D. An improved model of ionospheric electric potentials including substorm perturbations and application to the Geosphace Environment Modeling November 24, 1996, event. J. Geophys. Res. 2001, 106:407.
28. Antiochos S.K., DeVore C.R., Klimchuk J.A. A model for solar coronal mass ejections. Astrophys. J. 1999, 510:485-493.
29. van der Holst B., Manchester W., Sokolov I., Toth G., Gombosi T., Zeeuw D.D., Cohen O. Breakout coronal mass ejection or streamer blowout: the bugle effect. Astrophys. J. 2009, 693:1178-1187.
30. Fang F., Manchester W.B., Abbett W.P., van der Holst B. Simulation of flux emergence from the convection zone to the corona. Astrophys. J. 2010, 714:1649-1657.
31. Manchester W.B., Gombosi T.I., De Zeeuw D.L., Fan Y. Eruption of a buoyantly emerging magnetic flux rope. Astrophys. J. 2004, 610:588.
32. W. Manchester, T. Gombosi, A. Ridley, I. Roussev, D.D. Zeeuw, I. Sokolov, K. Powell, G. Tóth, Modeling a space weather event from the Sun to the Earth: CME generation and interplanetary propagation, J. Geophys. Res. 109, doi:10.1029/2003JA010150.
33. Lugaz N., Manchester W.B., Roussev I.I., Tóth G., Gombosi T.I. Numerical investigation of the homologous coronal mass ejection events from active region 9236. Astrophys. J. 2007, 659:788-800.
34. Downs C., Roussev I.I., van der Holst B., Lugaz N., Sokolov I.V., Gombosi T.I. Toward a realistic thermodynamic magnetohydrodynamic model of the global solar corona. Astrophys. J. 2010, 712:1219-1231. 10.1088/0004-637X/712/2/1219.
35. van der Holst B., Manchester W., Frazin R., Vásquez A., Tóth G., Gombosi T. A date-driven, two-temperature solar wind model with alfvén waves. Astrophys. J. 2010, 725:1373-1383.
36. Lugaz N., Manchester W.B., Gombosi T.I. Numerial simulation of the interaction of two coronal mass ejections from Sun to Earth. Astrophys. J. 2005, 634:651-662.
37. Manchester W.B., Ridley A.J., Gombosi T.I., De Zeeuw D. Modeling the Sun-Earth propagation of a very fast CME. Adv. Space Res. 2006, 38:253-262.
38. Opher M., Liewer P., Gombosi T., Manchester W., De Zeeuw D., Sokolov I., Tóth G. Probing the edge of the solar system: formation of an unstable jet-sheet. Astrophys. J. 2003, L61:561.
39. Opher M., Bibi F.A., Toth G., Richardson J.D., Izmodenov V.V., Gombosi T.I. A strong, highly-tilted interstellar magnetic field near the solar system. Nature 2009, 462:1036. 10.1038/nature08567.
40. Sokolov I.V., Roussev I.I., Gombosi T.I., Lee M.A., Kóta J., Forbes T.G., Manchester W.B., Sakai J.I. A new field line advection model for solar particle acceleration. Astrophys. J. 2004, 616:L171-L174.
41. Kóta J., Jokipii J.R. Transport of CIR accelerated particles. Proc. 26th Int. Cosmic Ray Conf 1999, vol. 6:612. AIP.
42. De Zeeuw D., Sazykin S., Wolf R., Gombosi T., Ridley A., Tóth G. Coupling of a global MHD code and an inner magnetosphere model: initial results. J. Geophys. Res. 2004, 109(A12):A12219. 10.1029/2003JA010366.
43. Tóth G., Ma Y.J., Gombosi T.I. Hall magnetohydrodynamics on block adaptive grids. J. Comput. Phys. 2008, 227:6967-6984. 10.1016/j.jcp.2008.04.010.
44. A. Glocer, G. Tóth, Y.J. Ma, T. Gombosi, J.-C. Zhang, L.M. Kistler, Multi-fluid BATS-R-US: magnetospheric composition and dynamics during geomagnetic storms, initial results, J. Geophys. Res., in press, doi:10.1029/2009JA014418.
45. Wolf R.A., Harel M., Spiro R.W., Voigt G., Reiff P.H., Chen C.K. Computer simulation of inner magnetospheric dynamics for the magnetic storm of July 29, 1977. J. Geophys. Res. 1982, 87:5949-5962.
46. Toffoletto F., Sazykin S., Spiro R., Wolf R. Inner magnetospheric modeling with the Rice Convection Model. Space Sci. Rev. 2003, 107:175-196.
47. Buzulukova N., Fok M.-C., Pulkkinen A., Kuznetsova M., Moore T.E., Glocer A., Brandt P.C., Toth G., Rastatter L. Dynamics of ring current and electric fields in the inner magnetosphere during disturbed periods: CRCM-BATS-R-US coupled model. J. Geophys. Res. 2010, 115:A05210. 10.1029/2009JA014621.
48. Liemohn M.W., Kozyra J.U., Clauer C.R., Ridley A.J. Computational analysis of the near-Earth magnetospheric current system during two-phase decay storms. J. Geophys. Res. 2001, 106:29. 531.
49. Jordanova V.K., Kozyra J.U., Khazanov G.V., Nagy A.F., Rasmussen C.E., Fok M.-C. A bounce-averaged kinetic model of the ring current ion population. Geophys. Res. Lett. 1994, 21:2785.
50. Zaharia S., Jordanova V.K., Thomsen M.F., Reeves G.D. Self-consistent modeling of magnetic fields and plasmas in the inner magnetosphere: application to a geomagnetic storm. J. Geophys. Res. 2006, 111:A11S14. 10.1029/2006JA011619.
51. Fok M.H., Horne R.E., Meredith N.P., Glauert S.A. Radiation belt environment model: application to space weather nowcasting. J. Geophys. Res. 2008, 113:A03S08. 10.1029/2007JA012558.
52. Glocer A., Tóth G., Fok M., Gombosi T. Integration of the radiation belt environment model into the space weather modeling framework. J. Atmos. Sol.-Terr. Phys. 2009, 71:1653-1663. 10.1016/j.jastp.2009.01.003.
53. Glocer A., Tóth G., Gombosi T.I., Welling D. Polar Wind Outflow Model (PWOM): modeling ionospheric outflows and their effect on the magnetosphere, initial results. J. Geophys. Res. 2009, 114:A05216. 10.1029/2009JA014053.
54. Ridley A., Gombosi T., Dezeeuw D. Ionospheric control of the magnetosphere: conductance. Ann. Geophys. 2004, 22:567-584.
55. Ridley A.J., Deng Y., Tóth G. The global ionosphere thermosphere model. J. Atmos. Sol.-Terr. Phys. 2006, 68:839-864. 10.1016/j.jastp.2006.01.008.
56. Hedin A. Extension of the MSIS thermosphere model into the middle and lower atmosphere. J. Geophys. Res. 1991, 96:1159.
57. Bilitza D. International reference ionosphere 2000. Radio Sci. 2001, 36:261.
58. Godunov S.K. Symmetric form of the equations of magnetohydrodynamics (in Russian). Numerical Methods for Mechanics of Continuum Medium 1972, vol. 1:26-34. Siberian Branch of USSR Acad. of Sci., Novosibirsk.
59. Brackbill J., Barnes D. The effect of nonzero ∇·B on the numerical solution of the magnetohydrodynamic equations. J. Comput. Phys. 1980, 35:426-430.
60. Evans C.R., Hawley J.F. Simulation of magnetohydrodynamic flows: a constrained transport method. Astrophys. J. 1988, 332:659-677.
61. Tóth G., Roe P.L. Divergence- and curl-preserving prolongation and restriction formulae. J. Comput. Phys. 2002, 180:736-750.
62. I.V. Sokolov, K.G. Powell, O. Cohen, T.I. Gombosi, Computational magnetohydrodynamics, based on solution of the well-posed riemann problem, in: N.V. Pogorelov, E. Audit, G.P. Zank (Eds.), Numerical Modeling of Space Plasma Flows, Astronomical Society of the Pacific Conference Series, vol. 385, 2008, p. 291.
63. Dedner A., Kemm F., Kröner D., Munz C., Schnitzer T., Wesenberg M. Hyperbolic divergence cleaning for the MHD equations. J. Comput. Phys. 2003, 175:645-673.
64. Tanaka T. Finite volume TVD scheme on an unstructured grid system for three-diemsnional MHD simulations of inhomogeneous systems including strong background potential field. J. Comput. Phys. 1994, 111:381-389.
65. Gombosi T.I., Tóth G., De Zeeuw D.L., Hansen K.C., Kabin K., Powell K.G. Semi-relativistic magnetohydrodynamics and physics-based convergence acceleration. J. Comput. Phys. 2001, 177:176-205.
66. Rogers F. Ionization equilibrium and equation of state in strongly coupled plasmas. Phys. Plasmas 2000, 7:51.
67. J.P. Boris, A physically motivated solution of the Alfvén problem, Tech. Rep. NRL Memorandum Report 2167, Naval Research Laboratory, Washington, D.C., 1970.
68. Ridley A.J., Zeeuw D.L.D., Gombosi T.I., Hansen K.C., Sokolov I.V., Toth G., Welling D.T. Numerical considerations in simulating the global magnetosphere. Ann. Geophys. 2010, 28:1589-1614. 10.5194/angeo-28-1589-2010.
69. van Leer B. Towards the ultimate conservative difference scheme. V.A second-order sequel to Godunov's method. J. Comput. Phys. 1979, 32:101-136.
70. Koren B. A robust upwind discretisation method for advection, diffusion and source terms. Numerical Methods for Advection-Diffusion Problems 1993, 117. Vieweg, Braunschweig. C. Vreugdenhil, B. Koren (Eds.).
71. Jacques S.A. Momentum and energy transport by waves in the solar atmosphere and solar wind. Astrophys. J. 1977, 215:942-951.
72. Sokolov I.V., Roussev I.I., Skender M., Gombosi T.I., Usmanov A. Transport equation for MHD turbulence: application to particle acceleration at interplanetary shocks. Astrophys. J. 2009, 696:261-267. 10.1088/0004-637X/696/1/261.
73. Harten A., Lax P.D., van Leer B. On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Rev. 1983, 25(1):35-61.
74. Einfeldt B., Munz C.D., Roe P.L., Sjögreen B. On Godunov-type methods near low densities. J. Comput. Phys. 1991, 92:273-295.
75. J.P. Holloway, D. Bingham, C. Chou, F. Doss, R.P. Drake, B. Fryxell, M. Grosskopf, B. van der Holst, R. McClarren, A. Mukherjee, V. Nair, K.G. Powell, D. Ryu, I. Sokolov, G. Tóth, Z. Zhang, Predictive modeling of a radiative shock system, Reliab. Eng. Syst. Safe., in press.
76. R.G. McClarren, D. Ryu, R. Drake, M. Grosskopf, D. Bingham, C. Chou, B. Fryxell, B. van der Holst, J.P. Holloway, C.C. Kuranz, B. Mallick, E. Rutter, B. Torralva, A physics, informed emulator for laser-driven radiating shock simulations, Reliab. Eng. Syst. Safe., in press.
77. Harten A. High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 1983, 49:357-393.
78. Sokolov I.V., Powell K.G., Gombosi T.I., Roussev I.I. A TVD principle and conservative TVD schemes for adaptive Cartesian grids. J. Comput. Phys. 2006, 220:1-5. 10.1016/j.jcp.2006.07.021.
79. Rusanov V. Calculation of interaction of non-steady shock waves with obstacles. J. Comput. Math. Phys. 1961, 1:267.
80. Sokolov I., Timofeev E.V., Ichi Sakai J., Takayama K. Artificial wind - a new framework to construct simple and efficient upwind shock-capturing schemes. J. Comput. Phys. 2002, 181:354-393. 10.1006/jcph.2002.7130.
81. Miyoshi T., Kusano K. A multi-state HLL approximate riemann solver for ideal magnetohydrodynamics. J. Comput. Phys. 2005, 208:315-344. 10.1016/j.jcp.2005.02.017.
82. Roe P.L. Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 1981, 43:357-372.
83. Godunov S.K. A difference scheme for numerical computation of discontinuous solutions of hydrodynamic equations. Mat. Sb. 1959, 47(3):271-306. (in Russian).
84. Q.F. Stout, D.L. De Zeeuw, T.I. Gombosi, C.P.T. Groth, H.G. Marshall, K.G. Powell, Adaptive blocks: a high-performance data structure, in: Proc. Supercomputing'97, 1997.
85. Tóth G. The LASY preprocessor and its application to multidimensional simulations. J. Comput. Phys. 1997, 138:981-990.
86. Berger M.J., Colella P. Local adaptive mesh refinement for shock hydrodynamics. J. Comput. Phys. 1989, 82:67-84.
87. van der Ven H., Niemann-Tuitman B., Veldman A. An explicit multi-time-stepping algorithm for aerodynamic flows. J. Comput. Appl. Math. 1997, 82:423.
88. Keppens R., Tóth G., Botchev M.A., van der Ploeg A. Implicit and semi-implicit schemes: algorithms. Int. J. Num. Method Fluids 1999, 30:335-352.
89. Eisenstat S.C. Efficient implementation of a class of preconditioned conjugate gradient methods. SIAM J. Sci. Stat. Comput. 1981, 2:1-4.
90. van der Vorst H. Bi-cgstab: a fast and smoothly converging variant of bi-cg for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 1992, 13:631-644.
91. Saad Y., Schultz M.H. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear equations. SIAM J. Sci. Stat. Comput. 1986, 7(3):856-869.
92. Jablonowski C., Williamson D.L. The pros and cons of diffusion, filters and fixers in atmospheric general circulation models. Lecture Notes in Computational Science and Engineering 2011, vol. 80:389-504. Springer. P.H. Lauritzen, C. Jablonowski, M.A. Taylor, R.D. Nair (Eds.).