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2020 | OriginalPaper | Buchkapitel

5. 3D SIP-CESE MHD Model on Six-Component Overset Grid System

verfasst von : Xueshang Feng

Erschienen in: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere

Verlag: Springer Singapore

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Abstract

This chapter introduces the implementation of the SIP-CESE MHD model in six component overset grid system with the aim of mitigating the problem of singularity and mesh convergence near the poles. The SIP-CESE MHD model introduced in Chap. 4 is applied to solar wind simulation with this grid system. New numerical features are also added, including: (1) The \(\nabla \cdot \mathbf {B}\) constraint error cleaning procedure via an easy-to-use fast multigrid Poisson solver, (2) The Courant-number-insensitive method that reduces the numerical viscosity without generating any instability, (3) The time-integration by multiple time stepping, (4) The time-dependent boundary condition at the subsonic region by limiting the mass flux escaping through the solar surface. In order to produce fast and slow plasma streams of the solar wind, the volumetric heating and momentum source terms are included by considering the topological effect of the magnetic field expansion factor \(f_s\) and the minimum angular distance \(\theta _b\) (at the photosphere) between an open field foot point and its nearest coronal hole boundary. The simulation result for the 3D steady-state background solar wind during Carrington rotation (CR) 1911 from the Sun to Earth is presented. The good agreements between numerical result and observations, such as the Large Angle and Spectrometric Coronagraph (LASCO) aboard the Solar Heliospheric Observatory satellite (SOHO) in the corona and Wind observations at 1 AU, demonstrated the efficiency, accuracy and the ability to reasonably produce the structured solar wind of the model.

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Vorheriges Kapitel 3D SIP-CESE MHD Model on Triangular Prism Grids

Nächstes Kapitel AMR Implementation of 3D SIP-CESE MHD Model on Six-Component Overset Grid System

Aprovitola A, Denaro FM (2007) A non-diffusive, divergence-free, finite volume-based double projection method on non-staggered grids. Int J Numer Methods Fluids 53(7):1127–1172MathSciNetMATHCrossRef

Arge CN, Pizzo VJ (2000) Improvement in the prediction of solar wind conditions using near-real time solar magnetic field updates. J Geophys Res 105:10,465–10,480. https://doi.org/10.1029/1999JA900262CrossRef

Arge CN, Luhmann JG, Odstrčil D, Schrijver CJ, Li Y (2004) Stream structure and coronal sources of the solar wind during the May 12th, 1997 CME. J Atmos Sol Terr Phys 66(15–16):1295–1309ADSCrossRef

Aschwanden M (2006) Physics of the solar corona: an introduction with problems and solutions, 2nd edn. Springer, Berlin

Aschwanden MJ (2004) Physics of the solar corona. An introduction. Praxis Publishing Ltd, Chichester

Aschwanden MJ, Burlaga LF, Kaiser ML, Ng CK, Reames DV, Reiner MJ, Gombosi TI, Lugaz N, Manchester W, Roussev II, Zurbuchen TH, Farrugia CJ, Galvin AB, Lee MA, Linker JA, Mikić Z, Riley P, Alexander D, Sandman AW, Cook JW, Howard RA, Odstrčil D, Pizzo VJ, Kóta J, Liewer PC, Luhmann JG, Inhester B, Schwenn RW, Solanki SK, Vasyliunas VM, Wiegelmann T, Blush L, Bochsler P, Cairns IH, Robinson PA, Bothmer V, Kecskemety K, Llebaria A, Maksimovic M, Scholer M, Wimmer-Schweingruber RF (2008) Theoretical modeling for the STEREO mission. Space Sci Rev 136:565–604. https://doi.org/10.1007/s11214-006-9027-8ADSCrossRef

Axford WI, McKenzie JF (1992) The origin of high speed solar wind streams. In: Marsch E, Schwenn R (eds) Solar wind seven. COSPAR colloquia series, vol 3. Pergamon Press, Oxford, pp 1–5

Balbás J, Tadmor E, Wu CC (2004) Non-oscillatory central schemes for one- and two-dimensional MHD equations: I. J Comput Phys 201:261–285. https://doi.org/10.1016/j.jcp.2004.05.020ADSMathSciNetMATHCrossRef

Balsara DS (2009) Divergence-free reconstruction of magnetic fields and WENO schemes for magnetohydrodynamics. J Comput Phys 228:5040–5056. https://doi.org/10.1016/j.jcp.2009.03.038ADSMathSciNetMATHCrossRef

10.

Balsara DS, Kim J (2004) A comparison between divergence-cleaning and staggered-mesh formulations for numerical magnetohydrodynamics. Astrophys J 602:1079–1090. https://doi.org/10.1086/381051ADSCrossRef

11.

Balsara DS, Spicer DS (1999) A staggered mesh algorithm using high order Godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamic simulations. J Comput Phys 149:270–292. https://doi.org/10.1006/jcph.1998.6153ADSMathSciNetCrossRefMATH

12.

Balsara DS, Rumpf T, Dumbser M, Munz CD (2009) Efficient, high accuracy ADER-WENO schemes for hydrodynamics and divergence-free magnetohydrodynamics. J Comput Phys 228:2480–2516. https://doi.org/10.1016/j.jcp.2008.12.003ADSMathSciNetCrossRefMATH

13.

Barnes A (1992) Acceleration of the solar wind. Rev Geophys 30:43–55. https://doi.org/10.1029/91RG02816ADSCrossRef

14.

Brackbill JU, Barnes DC (1980) The effect of nonzero \(\nabla \cdot \mathbf{B}\) on the numerical solution of the magnetohydrodynamic equations. J Comput Phys 35(3):426–430

15.

Breen AR, Thomasson P, Jordan CA, Tappin SJ, Fallows RA, Canals A, Moran PJ (2002) Slow and fast solar wind acceleration near solar maximum. Adv Space Res 30:433–436. https://doi.org/10.1016/S0273-1177(02)00339-3ADSCrossRef

16.

Chang S (1995) The method of space-time conservation element and solution element–a new approach for solving the Navier-Stokes and Euler equations. J Comput Phys 119:295–324. https://doi.org/10.1006/jcph.1995.1137ADSMathSciNetCrossRefMATH

17.

Chang SC, Wang XY (2003) Multi-dimensional Courant number insensitive CE/SE Euler solvers for application involving highly non-uniform meshes. AIAA-2003-5280

18.

Chang SC, Wu Y, Yang V, Wang XY (2005) Local time-stepping procedures for the space-time conservation element and solution element method. Int J Comput Fluid Dyn 19:359–380. https://doi.org/10.1080/10618560500092610MathSciNetCrossRefMATH

19.

Chen CG, Xiao F (2008) Shallow water model on cubed-sphere by multi-moment finite volume method. J Comput Phys 227(10):5019–5044ADSMathSciNetMATHCrossRef

20.

Chesshire G, Henshaw WD (1990) Composite overlapping meshes for the solution of partial differential equations. J Comput Phys 90:1–64. https://doi.org/10.1016/0021-9991(90)90196-8ADSMathSciNetCrossRefMATH

21.

Choblet G (2005) Modelling thermal convection with large viscosity gradients in one block of the cubed sphere. J Comput Phys 205:269–291. https://doi.org/10.1016/j.jcp.2004.11.005ADSCrossRefMATH

22.

Cohen O, Sokolov IV, Roussev II, Arge CN, Manchester WB, Gombosi TI, Frazin RA, Park H, Butala MD, Kamalabadi F, Velli M (2007) A semiempirical magnetohydrodynamical model of the solar wind. Astrophys J Lett 654:L163–L166. https://doi.org/10.1086/511154ADSCrossRef

23.

Cohen O, Sokolov IV, Roussev II, Gombosi TI (2008) Validation of a synoptic solar wind model. J Geophys Res 113(A12):A03104. https://doi.org/10.1029/2007JA012797ADSCrossRef

24.

Cranmer SR (2012) Self-consistent models of the solar wind. Space Sci Rev 172:145–156. https://doi.org/10.1007/s11214-010-9674-7ADSCrossRef

25.

Cranmer SR, van Ballegooijen AA, Edgar RJ (2007) Self-consistent coronal heating and solar wind acceleration from anisotropic magnetohydrodynamic turbulence. Astrophys J Suppl Ser 171:520–551. https://doi.org/10.1086/518001ADSCrossRef

26.

Cranmer SR, Matthaeus WH, Breech BA, Kasper JC (2009) Empirical constraints on proton and electron heating in the fast solar wind. Astrophys J 702:1604–1614. https://doi.org/10.1088/0004-637X/702/2/1604ADSCrossRef

27.

Cranmer SR, Gibson SE, Riley P (2017) Origins of the ambient solar wind: implications for space weather. Space Sci Rev 212(3):1345–1384. https://doi.org/10.1007/s11214-017-0416-yADSCrossRef

28.

Crockett RK, Colella P, Fisher RT, Klein RI, McKee CF (2005) An unsplit, cell-centered Godunov method for ideal MHD. J Comput Phys 203:422–448. https://doi.org/10.1016/j.jcp.2004.08.021ADSMathSciNetMATHCrossRef

29.

Cunningham AJ, Frank A, Varnière P, Mitran S, Jones TW (2009) Simulating magnetohydrodynamical flow with constrained transport and adaptive mesh refinement: algorithms and tests of the AstroBEAR code. Astrophys J Suppl Ser 182:519–542. https://doi.org/10.1088/0067-0049/182/2/519ADSCrossRef

30.

Dedner A, Kemm F, Kröner D, Munz CD, Schnitzer T, Wesenberg M (2002) Hyperbolic divergence cleaning for the MHD equations. J Comput Phys 175:645–673. https://doi.org/10.1006/jcph.2001.6961ADSMathSciNetCrossRefMATH

31.

Dewar RL (1970) Interaction between hydromagnetic waves and a time-dependent, inhomogeneous medium. Phys Fluids 13:2710–2720. https://doi.org/10.1063/1.1692854ADSCrossRefMATH

32.

Downs C, Roussev II, van der Holst B, Lugaz N, Sokolov IV, Gombosi TI (2010) Toward a realistic thermodynamic magnetohydrodynamic model of the global solar corona. Astrophys J 712:1219–1231. https://doi.org/10.1088/0004-637X/712/2/1219ADSCrossRef

33.

Endeve E, Leer E, Holzer TE (2003) Two-dimensional magnetohydrodynamic models of the solar corona: mass loss from the streamer belt. Astrophys J 589:1040–1053. https://doi.org/10.1086/374814ADSCrossRef

34.

Evans CR, Hawley JF (1988) Simulation of magnetohydrodynamic flows - a constrained transport method. Astrophys J 332:659–677. https://doi.org/10.1086/166684ADSCrossRef

35.

Evans RM, Opher M, Oran R, van der Holst B, Sokolov IV, Frazin R, Gombosi TI, Vásquez A (2012) Coronal heating by surface Alfvén wave damping: implementation in a global magnetohydrodynamics model of the solar wind. Astrophys J 756:155. https://doi.org/10.1088/0004-637X/756/2/155ADSCrossRef

36.

Feng XS, Xiang CQ, Zhong DK, Fan QL (2005) A comparative study on 3-D solar wind structure observed by Ulysses and MHD simulation. Chin Sci Bull 50:672–678CrossRef

37.

Feng XS, Zhou YF, Hu YQ (2006) A 3rd order WENO GLM-MHD scheme for magnetic reconnection. Chin J Space Sci 26:1–7

38.

Feng XS, Zhou YF, Wu ST (2007) A novel numerical implementation for solar wind modeling by the modified conservation element/solution element method. Astrophys J 655:1110–1126. https://doi.org/10.1086/510121ADSCrossRef

39.

Feng XS, Zhang Y, Yang LP, Wu ST, Dryer M (2009) An operational method for shock arrival time prediction by one-dimensional CESE-HD solar wind model. J Geophys Res 114(A13):A10103ADS

40.

Feng XS, Yang LP, Xiang CQ, Wu ST, Zhou YF, Zhong DK (2010) Three-dimensional solar WIND modeling from the Sun to Earth by a SIP-CESE MHD model with a six-component grid. Astrophys J 723:300–319. https://doi.org/10.1088/0004-637X/723/1/300ADSCrossRef

41.

Feng XS, Jiang CW, Xiang CQ, Zhao XP, Wu ST (2012) A data-driven model for the global coronal evolution. Astrophys J 758(1):62ADSCrossRef

42.

Feng XS, Xiang CQ, Zhong DK, Zhou YF, Yang LP, Ma XP (2014) SIP-CESE MHD model of solar wind with adaptive mesh refinement of hexahedral meshes. Comput Phys Commun 185:1965–1980. https://doi.org/10.1016/j.cpc.2014.03.027ADSMathSciNetCrossRef

43.

Feng XS, Ma XP, Xiang CQ (2015) Data-driven modeling of the solar wind from 1 Rs to 1 AU. J Geophys Res: Space Phys 120(12):10,159–10,174. https://doi.org/10.1002/2015JA021911

44.

Feng XS, Li CX, Xiang CQ, Zhang M, Li HC, Wei FS (2017) Data-driven modeling of the solar corona by a new three-dimensional path-conservative Osher-Solomon MHD model. Astrophys J Suppl Ser 233(1):10. http://stacks.iop.org/0067-0049/233/i=1/a=10ADSCrossRef

45.

Fisk LA (2003) Acceleration of the solar wind as a result of the reconnection of open magnetic flux with coronal loops. J Geophys Res (Space Phys) 108:1157. https://doi.org/10.1029/2002JA009284ADSCrossRef

46.

Fisk LA, Schwadron NA, Zurbuchen TH (1999) Acceleration of the fast solar wind by the emergence of new magnetic flux. J Geophys Res 104:19,765–19,772. https://doi.org/10.1029/1999JA900256CrossRef

47.

Fox NJ, Velli MC, Bale SD, Decker R, Driesman A, Howard RA, Kasper JC, Kinnison J, Kusterer M, Lario D, Lockwood MK, McComas DJ, Raouafi NE, Szabo A (2016) The Solar Probe Plus mission: humanity’s first visit to our Star. Space Sci Rev 204:7–48. https://doi.org/10.1007/s11214-015-0211-6ADSCrossRef

48.

Fragile PC, Anninos P, Gustafson K, Murray SD (2005) Magnetohydrodynamic simulations of shock interactions with radiative clouds. Astrophys J 619:327–339. https://doi.org/10.1086/426313ADSCrossRef

49.

Fry CD, Dryer M, Smith Z, Sun W, Deehr CS, Akasofu SI (2003) Forecasting solar wind structures and shock arrival times using an ensemble of models. J Geophys Res 108:1070. https://doi.org/10.1029/2002JA009474CrossRef

50.

Gombosi TI, van der Holst B, Manchester WB, Sokolov IV (2018) Extended MHD modeling of the steady solar corona and the solar wind. Living Rev Sol Phys 15(1):4. https://doi.org/10.1007/s41116-018-0014-4ADSCrossRef

51.

Gosling JT, Asbridge JR, Bame SJ, Feldman WC, Borrini G, Hansen RT (1981) Coronal streamers in the solar wind at 1 AU. J Geophys Res 86:5438–5448. https://doi.org/10.1029/JA086iA07p05438ADSCrossRef

52.

Groth CPT, De Zeeuw DL, Gombosi TI, Powell KG (2000) Global three-dimensional MHD simulation of a space weather event: CME formation, interplanetary propagation, and interaction with the magnetosphere. J Geophys Res 105:25,053–25,078. https://doi.org/10.1029/2000JA900093CrossRef

53.

Hartle RE, Barnes A (1970) Nonthermal heating in the two-fluid solar wind model. J Geophys Res 75:6915–6931. https://doi.org/10.1029/JA075i034p06915ADSCrossRef

54.

Hartmann D, Meinke M, Schröder W (2008) An adaptive multilevel multigrid formulation for Cartesian hierarchical grid methods. Comput Fluids 37(9):1103–1125MathSciNetMATHCrossRef

55.

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. https://doi.org/10.1086/491791ADSCrossRef

56.

Hayashi K, Benevolenskaya E, Hoeksema T, Liu Y, Zhao XP (2006) Three-dimensional magnetohydrodynamic simulation of a global solar corona using a temperature distribution map obtained from SOHO EIT measurements. Astrophys J Lett 636:L165–L168ADSCrossRef

57.

Henshaw WD, Schwendeman DW (2008) Parallel computation of three-dimensional flows using overlapping grids with adaptive mesh refinement. J Comput Phys 227:7469–7502ADSMathSciNetMATHCrossRef

58.

Hernlund J, Tackley P (2003) Three-dimensional spherical shell convection at infinite Prandtl number using the ‘cubed sphere’ method. Comput Fluid Solid Mech 931–933

59.

Hollweg JV (1986) Transition region, corona, and solar wind in coronal holes. J Geophys Res 91:4111–4125. https://doi.org/10.1029/JA091iA04p04111ADSCrossRef

60.

Hollweg JV (2008) The solar wind: our current understanding and how we got here. J Astrophys Astron 29:217–237. https://doi.org/10.1007/s12036-008-0028-8ADSCrossRef

61.

Holst M, Saied F (1993) Multigrid solution of the Poisson-Boltzmann equation. J Comput Chem 14(1):105–113CrossRef

62.

Hu YQ, Feng XS, Wu ST, Song WB (2008) Three-dimensional MHD modeling of the global corona throughout solar cycle 23. J Geophys Res 113(A12):A03106. https://doi.org/10.1029/2007JA012750ADSCrossRef

63.

Jacques SA (1977) Momentum and energy transport by waves in the solar atmosphere and solar wind. Astrophys J 215:942–951. https://doi.org/10.1086/155430ADSCrossRef

64.

Kageyama A (2005) Dissection of a sphere and “Yin-Yang grid” grids. J Earth Simulator 3:20–28

65.

Kageyama A, Sato T (2004) “Yin-Yang grid”: an overset grid in spherical geometry. Geochem Geophys Geosyst 5:Q09005. https://doi.org/10.1029/2004GC000734CrossRef

66.

Kasper JC, Abiad R, Austin G, Balat-Pichelin M, Bale SD, Belcher JW, Berg P, Bergner H, Berthomier M, Bookbinder J, Brodu E, Caldwell D, Case AW, Chandran BDG, Cheimets P, Cirtain JW, Cranmer SR, Curtis DW, Daigneau P, Dalton G, Dasgupta B, DeTomaso D, Diaz-Aguado M, Djordjevic B, Donaskowski B, Effinger M, Florinski V, Fox N, Freeman M, Gallagher D, Gary SP, Gauron T, Gates R, Goldstein M, Golub L, Gordon DA, Gurnee R, Guth G, Halekas J, Hatch K, Heerikuisen J, Ho G, Hu Q, Johnson G, Jordan SP, Korreck KE, Larson D, Lazarus AJ, Li G, Livi R, Ludlam M, Maksimovic M, McFadden JP, Marchant W, Maruca BA, McComas DJ, Messina L, Mercer T, Park S, Peddie AM, Pogorelov N, Reinhart MJ, Richardson JD, Robinson M, Rosen I, Skoug RM, Slagle A, Steinberg JT, Stevens ML, Szabo A, Taylor ER, Tiu C, Turin P, Velli M, Webb G, Whittlesey P, Wright K, Wu ST, Zank G (2016) Solar wind electrons alphas and protons (SWEAP) investigation: design of the solar wind and coronal plasma instrument suite for Solar Probe Plus. Space Sci Rev 204:131–186. https://doi.org/10.1007/s11214-015-0206-3ADSCrossRef

67.

Kataoka R, Ebisuzaki T, Kusano K, Shiota D, Inoue S, Yamamoto TT, Tokumaru M (2009) Three-dimensional MHD modeling of the solar wind structures associated with 13 December 2006 coronal mass ejection. J Geophys Res 114(A13):A10102. https://doi.org/10.1029/2009JA014167ADSCrossRef

68.

Kleimann J, Kopp A, Fichtner H, Grauer R (2009) A novel code for numerical 3-D MHD studies of CME expansion. Ann Geophys 27(3):989–1004ADSCrossRef

69.

Klimchuk JA (2006) On solving the coronal heating problem. Sol Phys 234:41–77. https://doi.org/10.1007/s11207-006-0055-zADSCrossRef

70.

Lee D, Deane AE (2009) An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics. J Comput Phys 228:952–975. https://doi.org/10.1016/j.jcp.2008.08.026ADSMathSciNetCrossRefMATH

71.

Levine RH, Altschuler MD, Harvey JW (1977) Solar sources of the interplanetary magnetic field and solar wind. J Geophys Res 82:1061–1065. https://doi.org/10.1029/JA082i007p01061ADSCrossRef

72.

Li B, Habbal SR, Li X, Mountford C (2005) Effect of the latitudinal distribution of temperature at the coronal base on the interplanetary magnetic field configuration and the solar wind flow. J Geophys Res 110(A9):A12112. https://doi.org/10.1029/2005JA011332ADSCrossRef

73.

Li ST (2008) High order central scheme on overlapping cells for magneto-hydrodynamic flows with and without constrained transport method. J Comput Phys 227(15):7368–7393ADSMathSciNetMATHCrossRef

74.

Li ST, Li H (2004) A novel approach of divergence-free reconstruction for adaptive mesh refinement. J Comput Phys 199:1–15. https://doi.org/10.1016/j.jcp.2004.01.027ADSCrossRefMATH

75.

Linker JA, Kivelson MG, Walker RJ (1991) A three-dimensional MHD simulation of plasma flow past Io. J Geophys Res 96:21. https://doi.org/10.1029/91JA02132CrossRef

76.

Linker JA, Mikić Z, Biesecker DA, Forsyth RJ, Gibson SE, Lazarus AJ, Lecinski A, Riley P, Szabo A, Thompson BJ (1999) Magnetohydrodynamic modeling of the solar corona during whole Sun month. J Geophys Res 104:9809–9830. https://doi.org/10.1029/1998JA900159ADSCrossRef

77.

Lionello R, Linker JA, Mikić Z (2001) Including the transition region in models of the large-scale solar corona. Astrophys J 546(1):542ADSCrossRef

78.

Londrillo P, Zanna LD (2004) On the divergence-free condition in Godunov-type schemes for ideal magnetohydrodynamics: the upwind constrained transport method. J Comput Phys 195:17–48ADSMathSciNetMATHCrossRef

79.

Luhmann JG, Li Y, Arge CN, Gazis PR, Ulrich R (2002) Solar cycle changes in coronal holes and space weather cycles. J Geophys Res 107:1154. https://doi.org/10.1029/2001JA007550CrossRef

80.

Matsumoto T, Shibata K (2010) Nonlinear propagation of Alfvén waves driven by observed photospheric motions: application to the coronal heating and spicule formation. Astrophys J 710:1857–1867. https://doi.org/10.1088/0004-637X/710/2/1857ADSCrossRef

81.

Matthaeus WH, Zank GP, Oughton S, Mullan DJ, Dmitruk P (1999) Coronal heating by magnetohydrodynamic turbulence driven by reflected low-frequency waves. Astrophys J Lett 523:L93–L96. https://doi.org/10.1086/312259ADSCrossRef

82.

Maurits NM, van der Ven H, Veldman AEP (1998) Explicit multi-time stepping methods for convection-dominated flow problems. Comput Methods Appl Mech Eng 157(1–2):133–150ADSMathSciNetMATHCrossRef

83.

McComas DJ, Bame SJ, Barraclough BL, Feldman WC, Funsten HO, Gosling JT, Riley P, Skoug R, Balogh A, Forsyth R, Goldstein BE, Neugebauer M (1998) Ulysses’ return to the slow solar wind. Geophys Res Lett 25:1–4. https://doi.org/10.1029/97GL03444ADSCrossRef

84.

McGregor SL, Hughes WJ, Arge CN, Owens MJ, Odstrčil D (2011) The distribution of solar wind speeds during solar minimum: calibration for numerical solar wind modeling constraints on the source of the slow solar wind. J Geophys Res (Space Phys) 116:A03101. https://doi.org/10.1029/2010JA015881ADSCrossRef

85.

McKenzie JF, Axford WI, Banaszkiewicz M (1997) The fast solar wind. Geophys Res Lett 24:2877–2880. https://doi.org/10.1029/97GL02097ADSCrossRef

86.

Meng X, van der Holst B, Tóth G, Gombosi TI (2015) Alfvén wave solar model (AWSoM): proton temperature anisotropy and solar wind acceleration. Mon Not R Astron Soc 454(4):3697–3709. https://doi.org/10.1093/mnras/stv2249ADSCrossRef

87.

Mignone A, Tzeferacos P, Bodo G (2010) High-order conservative finite difference GLM-MHD schemes for cell-centered MHD. J Comput Phys 229(17):5896–5920ADSMathSciNetMATHCrossRef

88.

Mikić Z, Linker JA, Schnack DD, Lionello R, Tarditi A (1999) Magnetohydrodynamic modeling of the global solar corona. Phys Plasmas 6:2217–2224. https://doi.org/10.1063/1.873474ADSCrossRef

89.

Mikić Z, Downs C, Linker JA, Caplan RM, Mackay DH, Upton LA, Riley P, Lionello R, Török T, Titov VS, Wijaya J, Druckmüller M, Pasachoff JM, Carlos W (2018) Predicting the corona for the 21 August 2017 total solar eclipse. Nat Astron 2:913–921. https://doi.org/10.1038/s41550-018-0562-5ADSCrossRef

90.

Miller GH, Colella P (2001) A high-order Eulerian Godunov method for elastic-plastic flow in solids. J Comput Phys 167(1):131–176ADSMATHCrossRef

91.

Mohan Rai M (1986) A conservative treatment of zonal boundaries for Euler equation calculations. J Comput Phys 62(2):472–503ADSMathSciNetMATHCrossRef

92.

Müller D, Marsden RG, St Cyr OC, Gilbert HR (2013) Solar orbiter. Exploring the Sun-heliosphere connection. Sol Phys 285:25–70. https://doi.org/10.1007/s11207-012-0085-7ADSCrossRef

93.

Nakagawa Y, Hu YQ, Wu ST (1987) The method of projected characteristics for the evolution of magnetic arches. Astron Astrophys 179:354–370ADSMATH

94.

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(A13):7109. https://doi.org/10.1029/2008JA013844CrossRef

95.

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 (Space Phys) 114:A07109. https://doi.org/10.1029/2008JA013844CrossRef

96.

Neugebauer M (1999) The three-dimensional solar wind at solar activity minimum. Rev Geophys 37:107–126. https://doi.org/10.1029/1998RG900001ADSCrossRef

97.

Odstrčil D, Pizzo VJ (1999) Distortion of the interplanetary magnetic field by three-dimensional propagation of coronal mass ejections in a structured solar wind. J Geophys Res 104(28):225. https://doi.org/10.1029/1999JA900319CrossRef

98.

Odstrčil D, Linker JA, Lionello R, Mikic Z, Riley P, Pizzo VJ, Luhmann JG (2002) Merging of coronal and heliospheric numerical two-dimensional MHD models. J Geophys Res 107:1493. https://doi.org/10.1029/2002JA009334CrossRef

99.

Ofman L, Viñas AF, Moya PS (2011) Hybrid models of solar wind plasma heating. Ann Geophys 29:1071–1079. https://doi.org/10.5194/angeo-29-1071-2011ADSCrossRef

100.

Ogino T, Walker RJ (1984) A magnetohydrodynamic simulation of the bifurcation of tail lobes during intervals with a northward interplanetary magnetic field. Geophys Res Lett 11:1018–1021. https://doi.org/10.1029/GL011i010p01018ADSCrossRef

101.

Owens MJ, Arge CN, Spence HE, Pembroke A (2005) An event-based approach to validating solar wind speed predictions: high-speed enhancements in the Wang-Sheeley-Arge model. J Geophys Res 110(A9):A12105. https://doi.org/10.1029/2005JA011343ADSCrossRef

102.

Owens MJ, Lockwood M, Barnard LA (2017) Coronal mass ejections are not coherent magnetohydrodynamic structures. Sci Rep 7(1):4152. https://doi.org/10.1038/s41598-017-04546-3

103.

Owens MJ, Lockwood M, Riley P (2017) Global solar wind variations over the last four centuries. Sci Rep 7:41548. https://doi.org/10.1038/srep41548

104.

Parker EN (1963) Interplanetary dynamical processes. Interscience Publishers, New YorkMATH

105.

Pätzold M, Tsurutani BT, Bird MK (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(A11):24,151–24,160CrossRef

106.

Pneuman GW, Kopp RA (1971) Gas-magnetic field interactions in the solar corona. Sol Phys 18(2):258–270ADSCrossRef

107.

Porfir’eva GA, Yakunina GV, Delone AB, Oreshina AV, Oreshina IV (2009) Coronal streamers on the Sun and their physical properties. J Phys Stud 13(2):2901–2906

108.

Powell KG, Roe PL, Linde TJ, Gombosi TI, De Zeeuw DL (1999) A solution-adaptive upwind scheme for ideal magnetohydrodynamics. J Comput Phys 154(2):284–309ADSMathSciNetMATHCrossRef

109.

Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in FORTRAN. The art of scientific computing, vol 1, 2nd edn. Cambridge University Press, Cambridge

110.

Rider WJ (1998) Filtering non-solenoidal modes in numerical solutions of incompressible flows. Int J Numer Methods Fluids 28(5):789–814MathSciNetMATHCrossRef

111.

Riley P, Linker JA, Mikić Z (2001) An empirically-driven global MHD model of the solar corona and inner heliosphere. J Geophys Res 106:15,889–15,902. https://doi.org/10.1029/2000JA000121CrossRef

112.

Riley P, Linker JA, Mikić Z, Lionello R, Ledvina SA, Luhmann JG (2006) A comparison between global solar magnetohydrodynamic and potential field source surface model results. Astrophys J 653:1510–1516ADSCrossRef

113.

Ronchi C, Iacono R, Paolucci PS (1996) The cubed sphere: a new method for the solution of partial differential equations in spherical geometry. J Comput Phys 124(1):93–114ADSMathSciNetMATHCrossRef

114.

Roussev II, Gombosi TI, Sokolov IV, Velli M, Manchester IV, DeZeeuw DL, Liewer P, Tóth G, Luhmann J (2003) A three-dimensional model of the solar wind incorporating solar magnetogram observations. Astrophys J Lett 595:L57–L61ADSCrossRef

115.

Schwadron NA, McComas DJ (2003) Solar wind scaling law. Astrophys J 599:1395–1403. https://doi.org/10.1086/379541ADSCrossRef

116.

Sheeley NR, Wang YM, Hawley SH, Brueckner GE, Dere KP, Howard RA, Koomen MJ, Korendyke CM, Michels DJ, Paswaters SE et al (1997) Measurements of flow speeds in the corona between 2 and 30 R. Astrophys J 484:472–478ADSCrossRef

117.

Shen F, Feng X, Wu ST, Xiang C (2007) Three-dimensional MHD simulation of CMEs in three-dimensional background solar wind with the self-consistent structure on the source surface as input: numerical simulation of the January 1997 Sun-Earth connection event. J Geophys Res 112(A11):A06109. https://doi.org/10.1029/2006JA012164ADSCrossRef

118.

Smith ZK, Dryer M, McKenna-Lawlor SMP, Fry CD, Deehr CS, Sun W (2009) Operational validation of HAFv2’s predictions of interplanetary shock arrivals at Earth: declining phase of solar cycle 23. J Geophys Res 114(A13):A05106. https://doi.org/10.1029/2008JA013836ADSCrossRef

119.

Sokolov IV, van der Holst B, Oran R, Downs C, Roussev II, Jin M, Ward B, Manchester I, Evans RM, Gombosi TI (2013) Magnetohydrodynamic waves and coronal heating: unifying empirical and MHD turbulence models. Astrophys J 764(1):23. http://stacks.iop.org/0004-637X/764/i=1/a=23ADSCrossRef

120.

Steger J, Benek J (1987) On the use of composite grid schemes in computational aerodynamics. Comput Methods Appl Mech Eng 64:301–320. https://doi.org/10.1016/0045-7825(87)90045-4ADSMathSciNetCrossRefMATH

121.

Stone JM, Gardiner T (2009) A simple unsplit Godunov method for multidimensional MHD. New Astron 14(2):139–148ADSCrossRef

122.

Suess ST, Wang AH, Wu ST (1996) Volumetric heating in coronal streamers. J Geophys Res 101(A9):19,957–19,966CrossRef

123.

Suess ST, Wang AH, Wu ST, Poletto G, McComas DJ (1999) A two-fluid, MHD coronal model. J Geophys Res 104(A3):4697–4708ADSCrossRef

124.

Suzuki TK, Inutsuka SI (2006) Solar winds driven by nonlinear low-frequency Alfvén waves from the photosphere: parametric study for fast/slow winds and disappearance of solar winds. J. Geophys. Res (Space Phys) 111:A06101. https://doi.org/10.1029/2005JA011502

125.

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(2):381–389ADSMATHCrossRef

126.

Tanaka T (2003) Finite volume TVD schemes for magnetohydrodynamics on unstructured grids. In: Büchner J, Dum C, Scholer M (eds) Space plasma simulation. Lecture notes in physics, vol 615. Springer, Berlin, pp 275–295

127.

Tóth G (2000) The \({\nabla }\cdot \mathbf{B}=0 \) constraint in shock-capturing magnetohydrodynamics codes. J Comput Phys 161:605–652. https://doi.org/10.1006/jcph.2000.6519ADSMathSciNetMATHCrossRef

128.

Tóth G, de Zeeuw DL, Gombosi TI, Powell KG (2006) A parallel explicit/implicit time stepping scheme on block-adaptive grids. J Comput Phys 217:722–758. https://doi.org/10.1016/j.jcp.2006.01.029ADSMathSciNetCrossRefMATH

129.

Usmanov AV (1993) A global numerical 3-D MHD model of the solar wind. Sol Phys 146(2):377–396ADSCrossRef

130.

Usmanov AV (1996) A global 3-D MHD solar wind model with Alfvén waves. In: Winterhalter D, Gosling JT, Habbal SR, Kurth WS, Neugebauer M (eds) American institute of physics conference series, vol 382, pp 141–144. https://doi.org/10.1063/1.51468

131.

Usmanov AV, Dryer M (1995) A global 3-D simulation of interplanetary dynamics in June 1991. Sol Phys 159(2):347–370ADSCrossRef

132.

Usmanov AV, Goldstein ML (2003) A tilted-dipole MHD model of the solar corona and solar wind. J Geophys Res 108(A9):1354CrossRef

133.

Usmanov AV, Goldstein ML, Besser BP, Fritzer JM (2000) A global MHD solar wind model with WKB Alfvén waves: comparison with Ulysses data. J Geophys Res 105(A6):12,675–12,695CrossRef

134.

van der Holst B, Keppens R (2007) Hybrid block-AMR in Cartesian and curvilinear coordinates: MHD applications. J Comput Phys 226:925–946. https://doi.org/10.1016/j.jcp.2007.05.007ADSCrossRefMATH

135.

van der Holst B, Sokolov IV, Meng X, Jin M, Manchester WB IV, Tóth G, Gombosi TI (2014) Alfvén wave solar model (AWSoM): coronal heating. Astrophys J 782:81ADSCrossRef

136.

Van der Ven H, Niemann-Tuitman BE, Veldman AEP (1997) An explicit multi-time-stepping algorithm for aerodynamic flows. J Comput Appl Math 82(1):423–431MathSciNetMATH

137.

Velli M, Grappin R, Mangeney A (1991) Waves from the Sun. Geophys Astrophys Fluid Dyn 62:101–121. https://doi.org/10.1080/03091929108229128ADSCrossRef

138.

Verdini A, Velli M, Matthaeus WH, Oughton S, Dmitruk P (2010) A turbulence-driven model for heating and acceleration of the fast wind in coronal holes. Astrophys J Lett 708:L116–L120. https://doi.org/10.1088/2041-8205/708/2/L116ADSCrossRef

139.

Vinokur M (1989) An analysis of finite-difference and finite-volume formulations of conservation laws. J Comput Phys 81(1):1–52ADSMathSciNetMATHCrossRef

140.

Wang AH, Wu ST, Suess ST, Poletto G (1998) Global model of the corona with heat and momentum addition. J Geophys Res 103(A2):1913–1922. https://doi.org/10.1029/97JA01770CrossRef

141.

Wang XY, Chang SC (1999) A 2d non-splitting unstructured triangular mesh Euler solver based on the space-time conservation element and solution element method. Comput Fluid Dyn J 8(2):309–325

142.

Wang YM, Sheeley NR Jr (1990) Solar wind speed and coronal flux-tube expansion. Astrophys J 355:726–732. https://doi.org/10.1086/168805ADSCrossRef

143.

Wang YM, Sheeley NR Jr (1991) Why fast solar wind originates from slowly expanding coronal flux tubes. Astrophys J Lett 372:L45–L48. https://doi.org/10.1086/186020ADSCrossRef

144.

Wang YM, Sheeley NR Jr, Walters JH, Brueckner GE, Howard RA, Michels DJ, Lamy PL, Schwenn R, Simnett GM (1998) Origin of streamer material in the outer corona. Astrophys J Lett 498:L165. https://doi.org/10.1086/311321

145.

Wang YM, Ko YK, Grappin R (2009) Slow solar wind from open regions with strong low-coronal heating. Astrophys J 691:760–769. https://doi.org/10.1088/0004-637X/691/1/760ADSCrossRef

146.

Wei FS, Feng XS, Cai HC, Zhou QJ (2003) Global distribution of coronal mass outputs and its relation to solar magnetic field structures. J Geophys Res 108(A6):1238. https://doi.org/10.1029/2002JA009439CrossRef

147.

Wu ST, Wang AH, Guo WP (1996) Numerical boundary conditions for solar magnetic hydrodynamic flows using the method of characteristics. Astrophys Space Sci 243:149–153. https://doi.org/10.1007/BF00644045ADSCrossRefMATH

148.

Wu ST, Guo WP, Michels DJ, Burlaga LF (1999) MHD description of the dynamical relationships between a flux rope, streamer, coronal mass ejection, and magnetic cloud: an analysis of the January 1997 Sun-Earth connection event. J Geophys Res 104:14,789–14,802. https://doi.org/10.1029/1999JA900099CrossRef

149.

Wu ST, Wang AH, Liu Y, Hoeksema JT (2006) Data-driven magnetohydrodynamic model for active region evolution. Astrophys J 652:800–811. https://doi.org/10.1086/507864ADSCrossRef

150.

Yang LP, Feng XS, Xiang CQ, Zhang SH, Wu ST (2011) Simulation of the unusual solar minimum with 3D SIP-CESE MHD model by comparison with multi-satellite observations. Sol Phys 271:91–110. https://doi.org/10.1007/s11207-011-9785-7ADSCrossRef

151.

Yen JC, Duell EG, Martindale W (2006) CAA using 3D CESE method with a simplified Courant number insensitive scheme. AIAA-2006-2417

152.

Yoshida M, Kageyama A (2004) Application of the Yin-Yang grid to a thermal convection of a Boussinesq fluid with infinite Prandtl number in a three-dimensional spherical shell. Geophys Res Lett 31(L12):609

153.

Yu ST, Chang SC (1997) Treatments of stiff source terms in conservation laws by the method of space-time conservation element and solution element. AIAA-97-0435

154.

Zhang ZC, Yu ST (1999) Shock capturing without Riemann solver—a modified space-time CE/SE method for conservation laws. AIAA-99-0904

155.

Zhang ZC, Yu ST, Chang SC, Himansu A, Jorgenson PCE (1999) A modified space-time conservation element and solution element method for Euler and Navier-Stokes equations. AIAA-99-3277

156.

Zhang ZC, Yu ST, Chang SC (2002) A space-time conservation element and solution element method for solving the two- and three-dimensional unsteady Euler equations using quadrilateral and hexahedral meshes. J Comput Phys 175(1):168–199ADSMATHCrossRef

157.

Zhao XP, Hoeksema JT, Liu Y, Scherrer PH (2006) Success rate of predicting the heliospheric magnetic field polarity with Michelson Doppler imager (MDI) synoptic charts. J Geophys Res 111(A10):A10108. https://doi.org/10.1029/2005JA011576ADSCrossRef

158.

Zhou YF, Feng XS (2008) Numerical study of successive CMEs during November 4–5, 1998. Sci China E 51(10):1600–1610MATHCrossRef

159.

Zhou YF, Feng XS, Wu ST (2008) Numerical simulation of the 12 May 1997 CME event. Chin Phys Lett 25(2):790–793ADSCrossRef

160.

Ziegler U (2005) A solution-adaptive central-constraint transport scheme for magnetohydrodynamics. Comput Phys Commun 170:153–174. https://doi.org/10.1016/j.cpc.2005.04.002ADSCrossRefMATH

161.

Zurbuchen TH (2007) A new view of the coupling of the Sun and the heliosphere. Annu Rev Astron Astrophys 45(1):297–338ADSCrossRef

Titel: 3D SIP-CESE MHD Model on Six-Component Overset Grid System
verfasst von: Xueshang Feng
Verlag: Springer Singapore
Buch: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere
Print ISBN: 978-981-13-9080-7

Electronic ISBN: 978-981-13-9081-4

Copyright-Jahr: 2020
DOI: https://doi.org/10.1007/978-981-13-9081-4_5

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