Abstract
We carry out the adaptive mesh refinement (AMR) implementation of our solar–interplanetary space-time conservation element and solution element (CESE) magnetohydrodynamic model (SIP–CESE MHD model) using a six-component grid system (Feng, Zhou, and Wu, Astrophys. J. 655, 1110, 2007; Feng et al., Astrophys. J. 723, 300, 2010). By transforming the governing MHD equations from the physical space (x,y,z) to the computational space (ξ,η,ζ) while retaining the form of conservation (Jiang et al., Solar Phys. 267, 463, 2010), the SIP–AMR–CESE MHD model is implemented in the reference coordinates with the aid of the parallel AMR package PARAMESH available at http://sourceforge.net/projects/paramesh/ . Meanwhile, the volumetric heating source terms derived from the topology of the magnetic-field expansion factor and the minimum angular separation (at the photosphere) between an open-field foot point and its nearest coronal-hole boundary are also included. We show the preliminary results of applying the SIP–AMR–CESE MHD model for simulating the solar-wind background of different solar-activity phases by comparison with SOHO observations and other spacecraft data from OMNI. Our numerical results show overall good agreements in the solar corona and in interplanetary space with these multiple-spacecraft observations.
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Abramenko, V., Yurchyshyn, V., Linker, J., Mikić, Z., Luhmann, J., Lee, C.O.: 2010, Low-latitude coronal holes at the minimum of the 23rd solar cycle. Astrophys. J. 712, 813.
Arge, C.N., Pizzo, V.J.: 2000, Improvement in the prediction of solar wind conditions using near-real time solar magnetic field updates. J. Geophys. Res. 105, 10465.
Arge, C.N., Odstrcil, D., Pizzo, V.J., Mayer, L.R.: 2003, Improved method for specifying solar wind speed near the Sun. In: Velli, M., Bruno, R., Malara, F., Bucci, B. (eds.) Solar Wind Ten, AIP Conf. Ser. 679, 190.
Aschwanden, M.J., Burlaga, L.F., Kaiser, M.L., Ng, C.K., Reames, D.V., Reiner, M.J., Gombosi, T.I., Lugaz, N., Manchester, W., Roussev, I.I., Zurbuchen, T.H., Farrugia, C.J., Galvin, A.B., Lee, M.A., Linker, J.A., Mikić, Z., Riley, P., Alexander, D., Sandman, A.W., Cook, J.W., Howard, R.A., Odstrčil, D., Pizzo, V.J., Kóta, J., Liewer, P.C., Luhmann, J.G., Inhester, B., Schwenn, R.W., Solanki, S.K., Vasyliunas, V.M., Wiegelmann, T., Blush, L., Bochsler, P., Cairns, I.H., Robinson, P.A., Bothmer, V., Kecskemety, K., Llebaria, A., Maksimovic, M., Scholer, M., Wimmer-Schweingruber, R.F.: 2008, Theoretical modeling for the STEREO mission. Space Sci. Rev. 136, 565.
Baumann, I., Schmitt, D., Schüssler, M.: 2006, A necessary extension of the surface flux transport model. Astron. Astrophys. 446, 307.
Bilenko, I.A.: 2002, Coronal holes and the solar polar field reversal. Astron. Astrophys. 396, 657.
Bridges, T.J.: 2008, Conservation laws in curvilinear coordinates: A short proof of Vinokur’s theorem using differential forms. Appl. Math. Comput. 202, 882.
Cameron, R.H., Jiang, J., Schmitt, D., Schüssler, M.: 2010, Surface flux transport modeling for solar cycles 15-21: Effects of cycle-dependent tilt angles of sunspot groups. Astrophys. J. 719, 264.
Charbonneau, P.: 2005, Dynamo models of the solar cycle. Living Rev. Solar Phys. 2, 2. http://solarphysics.livingreviews.org/Articles/Irsp-2010-3/ .
Cohen, O., Sokolov, I.V., Roussev, I.I., Gombosi, T.I.: 2008, Validation of a synoptic solar wind model. J. Geophys. Res. 113, A03104.
Colella, P., Graves, D.T., Keen, N.D., Ligocki, T.J., Martin, D.F., McCorquodale, P.W., Modiano, D., Schwartz, P.O., Sternberg, T.D., Van Straalen, B.: 2007, Chombo software package for AMR applications design document. Technical report, Applied Numerical Algorithms Group, NERSC Division, Lawrence Berkeley National Laboratory Berkeley.
Cranmer, S.R.: 2010, An efficient approximation of the coronal heating rate for use in global Sun-heliosphere simulations. Astrophys. J. 710, 676.
Cranmer, S.R., Matthaeus, W.H., Breech, B.A., Kasper, J.C.: 2009, Empirical constraints on proton and electron heating in the fast solar wind. Astrophys. J. 702, 1604.
De Zeeuw, D.L.: 1993, A quadtree-based adaptively refined Cartesian-grid algorithm for solution of the Euler equations. PhD thesis, Ann Arbor, MI, USA. UMI Order No. GAX94-09674.
Dryer, M.: 2007, Space weather simulation in 3D MHD from the Sun to the Earth and beyond to 100 AU: A modeler’s perspective of the present state of the art. Asian J. Phys. 16, 97.
Feng, X., Zhou, Y., Wu, S.T.: 2007, A novel numerical implementation for solar wind modeling by the modified conservation element/solution element method. Astrophys. J. 655, 1110.
Feng, X.S., Xiang, C.Q., Zhong, D.K.: 2011, The state-of-art of three-dimensional numerical study for corona-interplanetary process of solar storms. Sci. Sin.-Terr. 41, 1 (in Chinese).
Feng, X., Yang, L., Xiang, C., Wu, S.T., Zhou, Y., Zhong, D.: 2010, Three-dimensional solar wind modeling from the Sun to Earth by a SIP–CESE MHD model with a six-component grid. Astrophys. J. 723, 300.
Feng, X., Zhang, S., Xiang, C., Yang, L., Jiang, C., Wu, S.T.: 2011, A hybrid solar wind model of the CESE+HLL method with a Yin-Yang overset grid and an AMR grid. Astrophys. J. 734, 50.
Fisk, L.A., Schwadron, N.A., Zurbuchen, T.H.: 1999, Acceleration of the fast solar wind by the emergence of new magnetic flux. J. Geophys. Res. 104, 19765.
Fryxell, B., Olson, K., Ricker, P., Timmes, F.X., Zingale, M., Lamb, D.Q., MacNeice, P., Rosner, R., Truran, J.W., Tufo, H.: 2000, FLASH: An adaptive mesh hydrodynamics code for modeling astrophysical thermonuclear flashes. Astrophys. J. Suppl. Ser. 131, 273.
Garaizar, X., Hornung, R., Kohn, S.: 1999, Structured adaptive mesh refinement applications infracture. Technical report, Lawrence Livermore National Laboratory.
Gombosi, T.I., De Zeeuw, D.L., Powell, K.G., Ridley, A.J., Sokolov, I.V., Stout, Q.F., Tóth, G.: 2003, Adaptive mesh refinement for global magnetohydrodynamic simulation. In: Büchner, J., Dum, C., Scholer, M. (eds.) Space Plasma Simulation, Lecture Notes in Physics 615, Springer, Berlin, 247.
Harvey, K.L., Recely, F.: 2002, Polar coronal holes during cycles 22 and 23. Solar Phys. 211, 31.
Hayashi, K.: 2005, Magnetohydrodynamic simulations of the solar corona and solar wind using a boundary treatment to limit solar wind mass flux. Astrophys. J. Suppl. Ser. 161, 480.
Hayashi, K., Zhao, X.P., Liu, Y.: 2008, MHD simulations of the global solar corona around the Halloween event in 2003 using the synchronic frame format of the solar photospheric magnetic field. J. Geophys. Res. 113, 7104.
Hoeksema, J.T.: 2009, Evolution of the large-scale magnetic field over three solar cycles. In: Kosovichev, A.G., Andrei, A.H., Roelot, J.P. (eds.) IAU Symposium 264, Cambridge University Press, Cambridge, 222.
Hoeksema, J.T., Wilcox, J.M., Scherrer, P.H.: 1983, The structure of the heliospheric current sheet: 1978–1982. J. Geophys. Res. 88, 9910.
Jiang, C., Feng, X., Zhang, J., Zhong, D.: 2010, AMR simulations of magnetohydrodynamic problems by the CESE method in curvilinear coordinates. Solar Phys. 267, 463.
Linde, T.: 2002, MHD simulations with the FLASH code. APS Meeting Abstracts, F3005.
Lionello, R., Linker, J.A., Mikić, Z.: 2009, Multispectral emission of the Sun during the first whole Sun month: Magnetohydrodynamic simulations. Astrophys. J. 690, 902.
Lugaz, N., Downs, C., Shibata, K., Roussev, I.I., Asai, A., Gombosi, T.I.: 2011, Numerical investigation of a coronal mass ejection from an Anemone active region: Reconnection and deflection of the 2005 August 22 eruption. Astrophys. J. 738, 127.
Luhmann, J.G., Lee, C.O., Li, Y., Arge, C.N., Galvin, A.B., Simunac, K., Russell, C.T., Howard, R.A., Petrie, G.: 2009, Solar wind sources in the late declining phase of cycle 23: Effects of the weak solar polar field on high speed streams. Solar Phys. 256, 285.
MacNeice, P., Olson, K.M., Mobarry, C., de Fainchtein, R., Packer, C.: 2000, Paramesh: A parallel adaptive mesh refinement community toolkit. Comput. Phys. Commun. 126, 330.
Marder, B.: 1987, A method for incorporating Gauss’ law into electromagnetic PIC codes. J. Comput. Phys. 68, 48.
McComas, D.J., Elliott, H.A., Gosling, J.T., Reisenfeld, D.B., Skoug, R.M., Goldstein, B.E., Neugebauer, M., Balogh, A.: 2002, Ulysses’ second fast-latitude scan: Complexity near solar maximum and the reformation of polar coronal holes. Geophys. Res. Lett. 29, 1290.
McComas, D.J., Elliott, H.A., Schwadron, N.A., Gosling, J.T., Skoug, R.M., Goldstein, B.E.: 2003, The three-dimensional solar wind around solar maximum. Geophys. Res. Lett. 30, 1517.
McComas, D.J., Elliott, H.A., Gosling, J.T., Skoug, R.M.: 2006, Ulysses observations of very different heliospheric structure during the declining phase of solar activity cycle 23. Geophys. Res. Lett. 33, 9102.
Mignone, A., Bodo, G., Massaglia, S., Matsakos, T., Tesileanu, O., Zanni, C., Ferrari, A.: 2007, PLUTO: A numerical code for computational astrophysics. Astrophys. J. Suppl. Ser. 170, 228.
Mikić, Z., Linker, J.A., Schnack, D.D., Lionello, R., Tarditi, A.: 1999, Magnetohydrodynamic modeling of the global solar corona. Phys. Plasmas 6, 2217.
Nakamizo, A., Tanaka, T., Kubo, Y., Kamei, S., Shimazu, H., Shinagawa, H.: 2009, Development of the 3-D MHD model of the solar corona–solar wind combining system. J. Geophys. Res. 114, 7109.
Odstrcil, D., Pizzo, V.J.: 1999, Distortion of the interplanetary magnetic field by three-dimensional propagation of coronal mass ejections in a structured solar wind. J. Geophys. Res. 104, 28225.
Olson, K.: 2006, Paramesh: A parallel adaptive grid tool. In: James, M., Gunther, B., Nobuyuki, S., Akin, E., Anil, D. (eds.) Parallel Computational Fluid Dynamics 2005: Theory and Applications: Proceedings of the Parallel CFD Conference, Elsevier, Amsterdam, 341.
Owens, M.J., Crooker, N.U.: 2006, Coronal mass ejections and magnetic flux buildup in the heliosphere. J. Geophys. Res. 111, A10104.
Owens, M.J., Spence, H.E., McGregor, S., Hughes, W.J., Quinn, J.M., Arge, C.N., Riley, P., Linker, J., Odstrcil, D.: 2008, Metrics for solar wind prediction models: Comparison of empirical, hybrid, and physics-based schemes with 8 years of l1 observations. Space Weather 6, S08001.
Parashar, M.: 2007, Grace grid adaptive computational engine. Technical report, Rutgers University.
Pätzold, M., Tsurutani, B.T., Bird, M.K.: 1997, An estimate of large-scale solar wind density and velocity profiles in a coronal hole and the coronal streamer belt. J. Geophys. Res. 102, 24151.
Porfir’eva, G.A., Yakunina, G.V., Delone, A.B., Oreshina, A.V., Oreshina, I.V.: 2009, Coronal streamers on the Sun and their physical properties. J. Phys. Stud. 13, 2901.
Powell, K.G., Roe, P.L., Linde, T.J., Gombosi, T.I., de Zeeuw, D.L.: 1999, A solution-adaptive upwind scheme for ideal magnetohydrodynamics. J. Comput. Phys. 154, 284.
Rendleman, C.A., Beckner, V.E., Lijewski, M., Crutchfield, W., Bell, J.B.: 2000, Parallelization of structured, hierarchical adaptive mesh refinement algorithms. Comput. Vis. Sci. 3, 147.
Riley, P.: 2007, An alternative interpretation of the relationship between the inferred open solar flux and the interplanetary magnetic field. Astrophys. J. Lett. 667, L97.
Riley, P., Linker, J.A., Mikić, Z., Lionello, R., Ledvina, S.A., Luhmann, J.G.: 2006, A comparison between global solar magnetohydrodynamic and potential field source surface model results. Astrophys. J. 653, 1510.
Riley, P., Lionello, R., Linker, J.A., Mikic, Z., Luhmann, J., Wijaya, J.: 2011, Global MHD modeling of the solar corona and inner heliosphere for the whole heliosphere interval. Solar Phys. 274, 361.
Roussev, I.I., Gombosi, T.I., Sokolov, I.V., Velli, M., Manchester, W. IV, De Zeeuw, D.L., Liewer, P., Tóth, G., Luhmann, J.: 2003, A three-dimensional model of the solar wind incorporating solar magnetogram observations. Astrophys. J. Lett. 595, L57.
Sanderson, T.R., Appourchaux, T., Hoeksema, J.T., Harvey, K.L.: 2003, Observations of the Sun’s magnetic field during the recent solar maximum. J. Geophys. Res. 108, 1035.
Smith, E.J.: 2011, Solar cycle evolution of the heliospheric magnetic field: The Ulysses legacy. J. Atmos. Solar-Terr. Phys. 73, 277.
Smith, E.J., Marsden, R.G., Balogh, A., Gloeckler, G., Geiss, J., McComas, D.J., McKibben, R.B., MacDowall, R.J., Lanzerotti, L.J., Krupp, N., Krueger, H., Landgraf, M.: 2003, The Sun and heliosphere at solar maximum. Science 302, 1165.
Stone, J.M., Gardiner, T.A., Teuben, P., Hawley, J.F., Simon, J.B.: 2008, Athena: A new code for astrophysical MHD. Astrophys. J. Suppl. Ser. 178, 137.
Taktakishvili, A., Pulkkinen, A., MacNeice, P., Kuznetsova, M., Hesse, M., Odstrcil, D.: 2011, Modeling of coronal mass ejections that caused particularly large geomagnetic storms using ENLIL heliosphere cone model. Space Weather 90, 6002.
Tanaka, T.: 1994, Finite volume tvd scheme on an unstructured grid system for three-dimensional mhd simulation of inhomogeneous systems including strong background potential fields. J. Comput. Phys. 111, 381.
Tokumaru, M., Kojima, M., Fujiki, K., Hayashi, K.: 2009, Non-dipolar solar wind structure observed in the cycle 23/24 minimum. Geophys. Res. Lett. 36, 9101.
Tóth, G., Sokolov, I.V., Gombosi, T.I., Chesney, D.R., Clauer, C.R., De Zeeuw, D.L., Hansen, K.C., Kane, K.J., Manchester, W.B., Oehmke, R.C., 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.: 2005, Space weather modeling framework: A new tool for the space science community. J. Geophys. Res. 110, 12226.
Tóth, G., van der Holst, B., Sokolov, I.V., De Zeeuw, D.L., Gombosi, T.I., Fang, F., Manchester, W.B., Meng, X., Najib, D., Powell, K.G., Stout, Q.F., Glocer, A., Ma, Y.-J., Opher, M.: 2012, Adaptive numerical algorithms in space weather modeling. J. Comput. Phys. 231, 870.
Usmanov, A.V.: 1996, A global 3-D MHD solar wind model with Alfvén waves. In: Winterhalter, D., Gosling, J.T., Habbal, S.R., Kurth, W.S., Neugebauer, M. (eds.) AIP Conf. Ser. 382, 141.
Usmanov, A.V., Goldstein, M.L.: 2006, A three-dimensional MHD solar wind model with pickup protons. J. Geophys. Res. 111, A07101.
van der Holst, B., Keppens, R.: 2007, Hybrid block-AMR in Cartesian and curvilinear coordinates: MHD applications. J. Comput. Phys. 226, 925.
van der Holst, B., Manchester, W.B., Frazin, R.A., Vásquez, A.M., Tóth, G., Gombosi, T.I.: 2010, A data-driven, two-temperature solar wind model with Alfvén waves. Astrophys. J. 725, 1373.
Vinokur, M.: 1974, Conservation equations of gasdynamics in curvilinear coordinate systems. J. Comput. Phys. 14, 105.
Waldmeier, M.: 1981, Cyclic variations of the polar coronal hole. Solar Phys. 70, 251.
Wang, Y.M., Sheeley, N.R. Jr.: 1990, Solar wind speed and coronal flux-tube expansion. Astrophys. J. 355, 726.
Wang, Y.M., Robbrecht, E., Sheeley, N.R. Jr.: 2009, On the weakening of the polar magnetic fields during solar cycle 23. Astrophys. J. 707, 1372.
Wang, Y.M., Sheeley, N.R. Jr., Walters, J.H., Brueckner, G.E., Howard, R.A., Michels, D.J., Lamy, P.L., Schwenn, R., Simnett, G.M.: 1998, Origin of streamer material in the outer corona. Astrophys. J. Lett. 498, L165. doi: 10.1086/311321 .
Wang, A.H., Wu, S.T., Tandberg-Hanssen, E., Hill, F.: 2011, Utilization of multiple measurements for global three-dimensional magnetohydrodynamic simulations. Astrophys. J. 732, 19.
Watermann, J., Wintoft, P., Sanahuja, B., Saiz, E., Poedts, S., Palmroth, M., Milillo, A., Metallinou, F.-A., Jacobs, C., Ganushkina, N.Y., Daglis, I.A., Cid, C., Cerrato, Y., Balasis, G., Aylward, A.D., Aran, A.: 2009, Models of solar wind structures and their interaction with the Earth’s space environment. Space Sci. Rev. 147, 233.
Wei, F., Feng, X., Cai, H., Zhou, Q.: 2003, Global distribution of coronal mass outputs and its relation to solar magnetic field structures. J. Geophys. Res. 108, 1238.
Wu, S.T., Wang, A.H., Liu, Y., Hoeksema, J.T.: 2006, Data-driven magnetohydrodynamic model for active region evolution. Astrophys. J. 652, 800.
Yang, L., Feng, X., Xiang, C., Zhang, S., Wu, S.T.: 2011, Simulation of the unusual solar minimum with 3D SIP–CESE MHD model by comparison with multi-satellite observations. Solar Phys. 271, 91.
Yeates, A.R., Mackay, D.H., van Ballegooijen, A.A., Constable, J.A.: 2010a, A nonpotential model for the Sun’s open magnetic flux. J. Geophys. Res. 115, A09112.
Yeates, A.R., Attrill, G.D.R., Nandy, D., Mackay, D.H., Martens, P.C.H., van Ballegooijen, A.A.: 2010b, Comparison of a global magnetic evolution model with observations of coronal mass ejections. Astrophys. J. 709, 1238.
Ziegler, U.: 2008, The NIRVANA code: Parallel computational MHD with adaptive mesh refinement. Comput. Phys. Commun. 179, 227.
Acknowledgements
The work is jointly supported by the National Natural Science Foundation of China (41031066, 40921063, 40874091, 40890162, 40904050, 40874077, 41074121, and 41074122), 973 program 2012CB825601 and the Specialized Research Fund for State Key Laboratories. S.T. Wu is supported by AFOSR (grant FA9550-07-1-0468), AURA Sub-Award C10569A of NSO’s Cooperative Agreement AST 0132798, and NSF (grant ATM-0754378). The numerical calculation has been completed on our SIGMA Cluster computing system. The PARAMESH software used in this work was developed at the NASA Goddard Space Flight Center and Drexel University under NASA’s HPCC and ESTO/CT projects and under grant NNG04GP79G from the NASA/AISR project. Wilcox Solar Observatory data used in this study were obtained via http://wso.stanford.edu . The Wilcox Solar Observatory is currently supported by NASA. SOHO is a project of international cooperation between ESA and NASA. The OMNI data is obtained from the GSFC/SPDF OMNIWeb interface http://omniweb.gsfc.nasa.gov . Special thanks go to our reviewer for the invaluable comments on the improvement of the article.
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Feng, X., Yang, L., Xiang, C. et al. Validation of the 3D AMR SIP–CESE Solar Wind Model for Four Carrington Rotations. Sol Phys 279, 207–229 (2012). https://doi.org/10.1007/s11207-012-9969-9
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DOI: https://doi.org/10.1007/s11207-012-9969-9