并行自适应技术在背景太阳风及快速磁场重联数值模拟中的应用研究
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摘要
基于磁流体力学(MHD)方程组的数值模拟是研究空间等离子体问题的一种强有力手段,可以弥补空间观测的缺乏和理论分析的局限,极大加深人们对于各种复杂物理过程的认识。计算网格对于MHD数值模拟至关重要,特别是对于空间尺度变化复杂的物理问题,先进网格技术的引进可以很大程度上提高计算效能。本文把自适应网格技术和混合网格技术引入MHD数值模拟,建立了用于日地空间天气模拟的三维(3D)耦合太阳风模式和用于日冕快速磁场重联的二维半(2.5D)自适应磁场重联模式,分别重点研究了2069卡林顿周的稳态太阳风和日冕条件下快速的磁场重联,这两个具有不同时间和空间尺度的物理问题。
首先使用自适应软件包PARAMESH ,把基于MHD方程组分裂,二阶精度Godunov型有限体积算法和CT算法,并行自适应化,实现了二维和三维的理想MHD并行自适应CT模式。多个典型的二维、三维理想MHD问题的模拟结果表明,该模式具有较高的精度、很强的稳定性,能把磁场散度控制在非常低的水平(10~(-11)～10~(-12)数量级),同时可以有效地自动捕捉到流场中的物理突变结构,比如激波、强间断面等。
接下来把理想的MHD模拟算法推广到带电阻的MHD (即RMHD )算法,建立了2.5D自适应RMHD磁场重联模式。基于该模式研究了高磁雷诺数条件下,太阳日冕爆发性磁场重联的剧烈演化过程、快速磁能转换以及对于电子的有效加速机制。结果显示: (1)长而薄的电流片由于撕裂膜不稳定性被撕裂成许多片段,产生的磁岛不断长大、发生合并不稳定性而相互融合,最好形成了几个很大的磁岛,同时有更小尺度磁岛持续不断地产生并与大磁岛结合在一起。(2)通过包围在磁场重联出流区附近的慢激波对,磁能被有效转换为等离子体动能和热能,这为太阳耀斑爆发过程中的磁能快速释放提供了一个可能的途径。(3)利用模拟产生的时变电场和磁场,进一步使用测试粒子方法研究了电子的加速过程。发现电子在大约0.3秒之内可以被加速到高达120 MeV,磁场重联产生的磁岛的约束作用是维持电子加速状态的最关键因素。(4)利用并行自适应网格技术,该模型可以自动分辨出很多精细结构,比如,近奇异性的磁场重联扩散区和两个互相融合的磁岛之间形成的非常微小的磁岛等。同时与均匀计算网格相比,它能够节约大量计算资源,这对于进一步研究日冕中的三维磁场重联问题是尤其需要的。
最后,基于混合网格系统和算法,把上面实现的三维并行自适应网格与阴阳嵌套网格结合,完成了耦合的三维太阳风MHD模型。我们采用双网格系统,近太阳(near-Sun: 1.0 RS - 7.0 RS)和远太阳(o--Sun: 6.0 RS - 250 RS)计算区域分别用阴阳嵌套网格系统和自适应笛卡尔网格系统覆盖,通过区域连接模块(DCM)执行这两套网格系统之间的变量插值与交换,来把这两部分连接在一起。这样的计算网格有很大的优势:(1)近太阳的阴阳嵌套网格系统可以避免球坐标系下常见的极区奇点问题和网格汇聚问题,它的贴体特性极大简化了太阳表面计算边界的处理,又能获得较高精度的数值解。(2)远太阳区域的自适应网格系统可以很容易实现高性能并行自适应功能,自动加密和放粗网格,捕捉到等离子体的特征结构,比如,行星际电流片和共转流等。利用这个耦合太阳风模式,计算了2069卡林顿周的背景太阳风,并且把模拟结果与多观测数据( MLSO/MK4, SOHO LASCO/C2, SOHO/EIT, Ulysses和OMNI ),做了比较。结果表明,该模式成功捕捉到了2007太阳活动低年观测到的日冕附近许多奇特的特征,比如,朝赤道极大扩展的极区冕洞,独立的赤道冕洞,φ= 200-和φ= 330-之间扭曲的磁场中性线(MNL)等。耦合的三维MHD太阳风模型也产生了大尺度的共转相互作用区(CIR)结构,得到的太阳风参数与Ulysses飞船观测和L1点附近多飞船观测的OMNI数据都基本一致。
MHD simulations, which can make up the lack of observations and the limitsof analysis and can also significantly get a deeper understanding of many kindsdi-cult physical processes, have been very powerful tools to investigate the spaceplasma physics. Computational grid is critical to MHD simulations, especially forthe problems that have large and complicated space variations, so the introduceof advanced grid technique can enormously speed up the computational e-ciency.In this paper, by introducing adaptive mesh refinement (AMR) and hybrid gridtechnique into MHD simulations, we have developed a three dimensional (3D)hybrid solar wind model for the Sun-to-Earth space weather simulations andanother two and half dimensional (2.5D) AMR magnetic reconnection modelfor fast magnetic reconnections in solar coronal, by which we have studied twoimportant process that have very di-erent space and time scales, the steadysolar wind of Carrington rotation (CR) 2069 and the spontaneous fast magneticreconnection occurring in solar coronal conditions.
First, we realized the 2D and 3D ideal MHD models with the help of theAMR package named PARAMESH. We use a splitting based finite volume schemewhich splits the resistive MHD equations into -uid part and magnetic inductionpart. The -uid part is solved with the second order Godunov-type central schemeand the magnetic part is handled with constrained transport (CT) approach.The results of several typical 2D and 3D ideal MHD problems show that themodels have higher-precision, are very robust, can control·B to be about10-11～10-12 and can automatically capture the abruptly changed structures,e.g., shocks, strong layers and so on.
Then we developed the ideal MHD simulation to resistive MHD simula-tion and establish a 2.5D AMR RMHD magnetic reconnection model, by whichwe investigated the tempestuous evolution, the fast magnetic energy conversionand the e-ective electron acceleration process in the spontaneous fast magneticreconnection with high Lundquist number. We found that: (1) the long-thin current sheet was broken up into many small pieces because of tearing instabil-ity, the islands grown more and more big and merged with each other, finallyseveral very big islands were formed with even smaller islands being constantlyproduced and merged with them. (2) Through the shocks around the magneticreconnection -ow regions, magnetic energy were e-ectively converted into the ki-netic and thermal energy of plasma by motor e-ect, which might be responsiblefor explosive release of magnetic energy in solar -are phenomena. (3) Based onthe time-dependent electric and magnetic fields generated by the resistive MHDsimulation, we further adopted the test particle method to study the accelerationprocess of electrons. The results showed that the electron can be accelerated upto 120 MeV within about 0.3 s, during which the trapping e-ect of the magneticconfiguration was very important to maintain the electron acceleration status.(4) Moreover, taking advantage of AMR technique, the model can automaticallyresolve many fine structures, e.g., near-singular di-usion regions and very smallislands formed between two merging islands, and at the same time can signifi-cantly save computational resources, which is especially favorable for our furtherthree-dimensional (3D) magnetic reconnection studies of solar -ares.
Finally, a hybrid three-dimensional (3D) MHD model for the solar windstudy is established with combined grid systems and solvers. The computa-tional domain from the Sun to Earth space is decomposed into the near-Sun(1.0 RS - 7.0 RS) and o--Sun (6.0 RS - 250 RS) domains, which are respec-tively constructed with Yin-Yang overset grid system and Cartesian adaptivemesh refinement (AMR) grid system and coupled together with a domain con-nection interface between the near-Sun and o--Sun domains. This kind of gridsystems have great advantages: (1) The Yin-Yang overset grid can avoid thewell-known singularity and polar grid convergence problems and its body-fittingproperty helps achieve high-quality resolution near the solar surface very eas-ily. (2) The block structured AMR Cartesian grid can automatically capturethe far-field plasma -ow features, such as the heliospheric current sheets (HCS)and corotating structrures and so on. Numerical study of solar wind structurefor Carrington rotation (CR) 2069 shows that the newly developed hybrid MHDsolar wind model successfully produces many realistic features of the background solar wind, in both the solar corona and interplanetary space, by the compar-isons with multiple solar and interplanetary observations ( MLSO/MK4, SOHOLASCO/C2, SOHO/EIT, Ulysses and OMNI ). The comparisons show that themodel captures a lot of peculiarities in the corona in the 2007 solar minimum, e.g.,the observed large equatorial extensions of the southern PCH and the presence ofthe isolated equatorial holes and the warp structure of the magnetic neutral line(MNL) betweenφ= 200- andφ= 330-. The solar wind parameters from thehybrid 3D MHD model also produces the corotating interaction regions (CIRs)and the solar wind parameters are roughly consistent with Ulysses observationsand with the temporal variations from OMNI data combining the measurementsby multiple spacecraft near L1 point.
首先使用自适应软件包PARAMESH ,把基于MHD方程组分裂,二阶精度Godunov型有限体积算法和CT算法,并行自适应化,实现了二维和三维的理想MHD并行自适应CT模式。多个典型的二维、三维理想MHD问题的模拟结果表明,该模式具有较高的精度、很强的稳定性,能把磁场散度控制在非常低的水平(10~(-11)～10~(-12)数量级),同时可以有效地自动捕捉到流场中的物理突变结构,比如激波、强间断面等。
接下来把理想的MHD模拟算法推广到带电阻的MHD (即RMHD )算法,建立了2.5D自适应RMHD磁场重联模式。基于该模式研究了高磁雷诺数条件下,太阳日冕爆发性磁场重联的剧烈演化过程、快速磁能转换以及对于电子的有效加速机制。结果显示: (1)长而薄的电流片由于撕裂膜不稳定性被撕裂成许多片段,产生的磁岛不断长大、发生合并不稳定性而相互融合,最好形成了几个很大的磁岛,同时有更小尺度磁岛持续不断地产生并与大磁岛结合在一起。(2)通过包围在磁场重联出流区附近的慢激波对,磁能被有效转换为等离子体动能和热能,这为太阳耀斑爆发过程中的磁能快速释放提供了一个可能的途径。(3)利用模拟产生的时变电场和磁场,进一步使用测试粒子方法研究了电子的加速过程。发现电子在大约0.3秒之内可以被加速到高达120 MeV,磁场重联产生的磁岛的约束作用是维持电子加速状态的最关键因素。(4)利用并行自适应网格技术,该模型可以自动分辨出很多精细结构,比如,近奇异性的磁场重联扩散区和两个互相融合的磁岛之间形成的非常微小的磁岛等。同时与均匀计算网格相比,它能够节约大量计算资源,这对于进一步研究日冕中的三维磁场重联问题是尤其需要的。
最后,基于混合网格系统和算法,把上面实现的三维并行自适应网格与阴阳嵌套网格结合,完成了耦合的三维太阳风MHD模型。我们采用双网格系统,近太阳(near-Sun: 1.0 RS - 7.0 RS)和远太阳(o--Sun: 6.0 RS - 250 RS)计算区域分别用阴阳嵌套网格系统和自适应笛卡尔网格系统覆盖,通过区域连接模块(DCM)执行这两套网格系统之间的变量插值与交换,来把这两部分连接在一起。这样的计算网格有很大的优势:(1)近太阳的阴阳嵌套网格系统可以避免球坐标系下常见的极区奇点问题和网格汇聚问题,它的贴体特性极大简化了太阳表面计算边界的处理,又能获得较高精度的数值解。(2)远太阳区域的自适应网格系统可以很容易实现高性能并行自适应功能,自动加密和放粗网格,捕捉到等离子体的特征结构,比如,行星际电流片和共转流等。利用这个耦合太阳风模式,计算了2069卡林顿周的背景太阳风,并且把模拟结果与多观测数据( MLSO/MK4, SOHO LASCO/C2, SOHO/EIT, Ulysses和OMNI ),做了比较。结果表明,该模式成功捕捉到了2007太阳活动低年观测到的日冕附近许多奇特的特征,比如,朝赤道极大扩展的极区冕洞,独立的赤道冕洞,φ= 200-和φ= 330-之间扭曲的磁场中性线(MNL)等。耦合的三维MHD太阳风模型也产生了大尺度的共转相互作用区(CIR)结构,得到的太阳风参数与Ulysses飞船观测和L1点附近多飞船观测的OMNI数据都基本一致。
MHD simulations, which can make up the lack of observations and the limitsof analysis and can also significantly get a deeper understanding of many kindsdi-cult physical processes, have been very powerful tools to investigate the spaceplasma physics. Computational grid is critical to MHD simulations, especially forthe problems that have large and complicated space variations, so the introduceof advanced grid technique can enormously speed up the computational e-ciency.In this paper, by introducing adaptive mesh refinement (AMR) and hybrid gridtechnique into MHD simulations, we have developed a three dimensional (3D)hybrid solar wind model for the Sun-to-Earth space weather simulations andanother two and half dimensional (2.5D) AMR magnetic reconnection modelfor fast magnetic reconnections in solar coronal, by which we have studied twoimportant process that have very di-erent space and time scales, the steadysolar wind of Carrington rotation (CR) 2069 and the spontaneous fast magneticreconnection occurring in solar coronal conditions.
First, we realized the 2D and 3D ideal MHD models with the help of theAMR package named PARAMESH. We use a splitting based finite volume schemewhich splits the resistive MHD equations into -uid part and magnetic inductionpart. The -uid part is solved with the second order Godunov-type central schemeand the magnetic part is handled with constrained transport (CT) approach.The results of several typical 2D and 3D ideal MHD problems show that themodels have higher-precision, are very robust, can control·B to be about10-11～10-12 and can automatically capture the abruptly changed structures,e.g., shocks, strong layers and so on.
Then we developed the ideal MHD simulation to resistive MHD simula-tion and establish a 2.5D AMR RMHD magnetic reconnection model, by whichwe investigated the tempestuous evolution, the fast magnetic energy conversionand the e-ective electron acceleration process in the spontaneous fast magneticreconnection with high Lundquist number. We found that: (1) the long-thin current sheet was broken up into many small pieces because of tearing instabil-ity, the islands grown more and more big and merged with each other, finallyseveral very big islands were formed with even smaller islands being constantlyproduced and merged with them. (2) Through the shocks around the magneticreconnection -ow regions, magnetic energy were e-ectively converted into the ki-netic and thermal energy of plasma by motor e-ect, which might be responsiblefor explosive release of magnetic energy in solar -are phenomena. (3) Based onthe time-dependent electric and magnetic fields generated by the resistive MHDsimulation, we further adopted the test particle method to study the accelerationprocess of electrons. The results showed that the electron can be accelerated upto 120 MeV within about 0.3 s, during which the trapping e-ect of the magneticconfiguration was very important to maintain the electron acceleration status.(4) Moreover, taking advantage of AMR technique, the model can automaticallyresolve many fine structures, e.g., near-singular di-usion regions and very smallislands formed between two merging islands, and at the same time can signifi-cantly save computational resources, which is especially favorable for our furtherthree-dimensional (3D) magnetic reconnection studies of solar -ares.
Finally, a hybrid three-dimensional (3D) MHD model for the solar windstudy is established with combined grid systems and solvers. The computa-tional domain from the Sun to Earth space is decomposed into the near-Sun(1.0 RS - 7.0 RS) and o--Sun (6.0 RS - 250 RS) domains, which are respec-tively constructed with Yin-Yang overset grid system and Cartesian adaptivemesh refinement (AMR) grid system and coupled together with a domain con-nection interface between the near-Sun and o--Sun domains. This kind of gridsystems have great advantages: (1) The Yin-Yang overset grid can avoid thewell-known singularity and polar grid convergence problems and its body-fittingproperty helps achieve high-quality resolution near the solar surface very eas-ily. (2) The block structured AMR Cartesian grid can automatically capturethe far-field plasma -ow features, such as the heliospheric current sheets (HCS)and corotating structrures and so on. Numerical study of solar wind structurefor Carrington rotation (CR) 2069 shows that the newly developed hybrid MHDsolar wind model successfully produces many realistic features of the background solar wind, in both the solar corona and interplanetary space, by the compar-isons with multiple solar and interplanetary observations ( MLSO/MK4, SOHOLASCO/C2, SOHO/EIT, Ulysses and OMNI ). The comparisons show that themodel captures a lot of peculiarities in the corona in the 2007 solar minimum, e.g.,the observed large equatorial extensions of the southern PCH and the presence ofthe isolated equatorial holes and the warp structure of the magnetic neutral line(MNL) betweenφ= 200- andφ= 330-. The solar wind parameters from thehybrid 3D MHD model also produces the corotating interaction regions (CIRs)and the solar wind parameters are roughly consistent with Ulysses observationsand with the temporal variations from OMNI data combining the measurementsby multiple spacecraft near L1 point.
引文
傅竹风,胡友秋.空间等离子体数值模拟.安徽科学技术出版社, 1995.
呼延奇.日冕大尺度结构演化及快速磁场重联的数值研究. PhD thesis,中国科学院研究生院(空间科学与应用研究中心), 2008.
林元章.太阳物理导论.科学出版社, 2000.
刘振兴等.太阳物理学.哈尔滨工业大学版社, 2005.
涂传诒.日地空间物理学.科学出版社, 1988.
王水,魏奉思.中国空间天气研究进展.地球物理学进展, 22, August 2007.
王水,李罗权.磁场重联.安徽教育出版社, 1998.
阎超.计算流体力学方法及应用.北京航空航天大学出版社, 2006.
章振大.日冕物理.科学出版社, 2000.
Charles N. Arge, Dusan Odstrcil, Victor J. Pizzo, and Leslie R. Mayer. Im-proved method for specifying solar wind speed near the sun. AIP ConferenceProceedings, 679(1):190–193, 2003. doi: 10.1063/1.1618574.
M. J. Aschwanden. Particle acceleration and kinematics in solar (?)ares-A Syn-thesis of Recent Observations and Theoretical Concepts (Invited Review). SpaceScience Reviews, 101:1–227, January 2002. doi: 10.1023/A:1019712124366.
Daniel Baker. Introduction to space weather. In Klaus Scherer, Horst Fichtner,Bernd Heber, and Urs Mall, editors, Space Weather, volume 656 of LectureNotes in Physics, pages 993–1020. Springer Berlin / Heidelberg, 2005. doi:10.1007/978-3-540-31534-6 1.
D. S. Balsara and D. Spicer. Maintaining Pressure Positivity in Magnetohy-drodynamic Simulations. J. Comput. Phys., 148:133–148, January 1999a. doi:10.1006/jcph.1998.6108.
D. S. Balsara and D. S. Spicer. A Staggered Mesh Algorithm Using High OrderGodunov Fluxes to Ensure Solenoidal Magnetic Fields in MagnetohydrodynamicSimulations. J. Comput. Phys., 149:270–292, March 1999b. doi: 10.1006/jcph.1998.6153.
Dinshaw S. Balsara, Tobias Rumpf, Michael Dumbser, and Claus-Dieter Munz.E(?)cient, high accuracy ader-weno schemes for hydrodynamics and divergence-free magnetohydrodynamics. J. Comput. Phys., 228(7):2480–2516, 2009. ISSN0021-9991. doi: DOI:10.1016/j.jcp.2008.12.003.
M. B′arta, M. Karlicky′, and R. zemlicka. Plasmoid dynamics in (?)are reconnectionand the frequency drift of the drifting pulsating structure. Solar Physics, 253:173–189, 2008. ISSN 0038-0938. 10.1007/s11207-008-9217-5.
M. B′arta, J. Bu¨chner, and M. Karlicky′. Multi-scale MHD approach to thecurrent sheet filamentation in solar coronal reconnection. Advances in SpaceResearch, 45:10–17, January 2010a. doi: 10.1016/j.asr.2009.07.025.
M. B′arta, J. Bu¨chner, M. Karlicky′, and P. Kotrc. Spontaneous current-layerfragmentation and cascading reconnection in solar (?)ares: II. Relation to obser-vations. ArXiv e-prints, November 2010b.
M. B′arta, J. Bu¨chner, M. Karlicky′, and J. Sk′ala. Spontaneous current-layerfragmentation and cascading reconnection in solar (?)ares: I. Model and analysis.ArXiv e-prints, November 2010c.
M. J. Berger and P. Colella. Local adaptive mesh refinement for shock hydro-dynamics. J. Comput. Phys., 82:64–84, May 1989.
Marsha J Berger and Joseph Oliger. Adaptive mesh refinement for hyperbolicpartial di(?)erential equations. J. Comput. Phys., 53(3):484–512, 1984. ISSN0021-9991. doi: 10.1016/0021-9991(84)90073-1.
J. Birn and E. R. Priest. Reconnection of Magnetic Fields. CambridgeUniversity Press, New York, 2006. ISBN 9780521854207. doi: 10.1017/CBO9780511536151.
J. Birn, J. F. Drake, M. A. Shay, B. N. Rogers, R. E. Denton, M. Hesse, M.Kuznetsova, Z. W. Ma, A. Bhattacharjee, A. Otto, and P. L. Pritchett. GeospaceEnvironmental Modeling (GEM) magnetic reconnection challenge. J. Geophys.Res., 106:3715–3720, March 2001. doi: 10.1029/1999JA900449.
D. Biskamp. Magnetic reconnection via current sheets. Physics of Fluids, 29:1520–1531, May 1986. doi: 10.1063/1.865670.
J. U. Brackbill and D. C. Barnes. The e(?)ect of nonzero product of magnetic gra-dient and B on the numerical solution of the magnetohydrodynamic equations.J. Comput. Phys., 35:426–430, May 1980. doi: 10.1016/0021-9991(80)90079-0.
K. D. Brislawn, D. L. Brown, G. S. Chesshire, and J. S. Saltzman. Adaptively-refined overlapping grids for the numerical solution of systems of hyperbolicconservation laws. In J. C. South Jr., J. L. Thomas, & J. Vanrosendale, editor,ICASE/LaRC Workshop on Adaptive Grid Methods, pages 95–110, October1995.
David Brown, William Henshaw, and Daniel Quinlan. Overture: An object-oriented framework for solving partial di(?)erential equations. In Yutaka Ishikawa,Rodney Oldehoeft, John Reynders, and Marydell Tholburn, editors, ScientificComputing in Object-Oriented Parallel Environments, volume 1343 of LectureNotes in Computer Science, pages 177–184. Springer Berlin / Heidelberg.Jinsheng Cai, Her Mann Tsai, and Feng Liu. A parallel viscous (?)ow solver onmulti-block overset grids. Computers and Fluids, 35(10):1290–1301, 2006. ISSN0045-7930. doi: 10.1016/j.comp(?)uid.2005.02.006.
P. Cassak and M. Shay. Magnetic reconnection for coronal conditions: Recon-nection rates, secondary islands and onset. Space Science Reviews, pages 1–20,2011. ISSN 0038-6308. 10.1007/s11214-011-9755-2.
P. A. Cassak, M. A. Shay, and J. F. Drake. Scaling of Sweet-Parker reconnectionwith secondary islands. Physics of Plasmas, 16(12):120702–120712, December2009. doi: 10.1063/1.3274462.
S. Chang. The Method of Space-Time Conservation Element and Solution Ele-ment: A New Approach for Solving the Navier-Stokes and Euler Equations. J.Comput. Phys., 119:295–324, July 1995. doi: 10.1006/jcph.1995.1137.
S.-C. Chang, X.-Y. Wang, and C.-Y. Chow. The Space-Time ConservationElement and Solution Element Method: A New High-Resolution and GenuinelyMultidimensional Paradigm for Solving Conservation Laws. J. Comput. Phys.,156:89–136, November 1999. doi: 10.1006/jcph.1999.6354.
S. Chapman and H. Zirin. Notes on the Solar Corona and the Terrestrial Iono-sphere. Smithsonian Contributions to Astrophysics, 2:1–14, 1957.
G. Chesshire and W. D. Henshaw. Composite overlapping meshes for the so-lution of partial di(?)erential equations. J. Comput. Phys., 90:1–64, September1990.
IT Chiu and RL. Meakin. On automating domain connectivity for overset grids.1995. 33rd Aero. Sci. Mtg. Reno, NV, 1995, (paper AIAA-95-054).
P. Colella et al. Chombo, software package for amr applications. Technicalreport, Lawrence Berkely National Laboratory, 2007.
Phillip Colella, Daniel T. Graves, Benjamin J. Keen, and David Modiano. Acartesian grid embedded boundary method for hyperbolic conservation laws. J.Comput. Phys., 211:347–366, January 2006. ISSN 0021-9991. doi: 10.1016/j.jcp.2005.05.026.
A. J. Cunningham, A. Frank, P. Varni`ere, S. Mitran, and T. W. Jones. Simu-lating Magnetohydrodynamical Flow with Constrained Transport and AdaptiveMesh Refinement: Algorithms and Tests of the AstroBEAR Code. Astrophys.J. Suppl., 182:519–542, June 2009. doi: 10.1088/0067-0049/182/2/519.
W. Dai. A Simple Finite Di(?)erence Scheme for Multidimensional Magneto-hydrodynamical Equations. J. Comput. Phys., 142:331–369, May 1998. doi:10.1006/jcph.1998.5944.
W. Dai and P. R. Woodward. An approximate Riemann solver for idealmagnetohydrodynamics. J. Comput. Phys., 111:354–372, April 1994. doi:10.1006/jcph.1994.1069.
W. Daughton, V. Roytershteyn, B. J. Albright, H. Karimabadi, L. Yin, andKevin J. Bowers. Transition from collisional to kinetic regimes in large-scalereconnection layers. Phys. Rev. Lett., 103(6):065004, Aug 2009. doi: 10.1103/PhysRevLett.103.065004.
A. Dedner, F. Kemm, D. Kr¨oner, C.-D. Munz, T. Schnitzer, and M. Wesenberg.Hyperbolic Divergence Cleaning for the MHD Equations. J. Comput. Phys.,175:645–673, January 2002. doi: 10.1006/jcph.2001.6961.
P. J. Dellar. A Note on Magnetic Monopoles and the One-Dimensional MHDRiemann Problem. J. Comput. Phys., 172:392–398, September 2001. doi: 10.1006/jcph.2001.6815.
D. Dezeeuw and K. G. Powell. An Adaptively Refined Cartesian Mesh Solverfor the Euler Equations. J. Comput. Phys., 104:56–68, January 1993.
M Dryer. Space weather simulation in 3d mhd from the sun to the earth andbeyond to 100 au: A modeler’s perspective of the present state of the art.Asian J Phys, 16:97–121, 2007.
A. Dubey, L. B. Reid, and R. Fisher. Introduction to FLASH 3.0, with applica-tion to supersonic turbulence. Physica Scripta Volume T, 132(1):014046–014056,December 2008. doi: 10.1088/0031-8949/2008/T132/014046.
Terry Forbes E R Priest. Magnetic reconnection : MHD theory and applications.New York : Cambridge University Press, 2000.
C. R. Evans and J. F. Hawley. Simulation of magnetohydrodynamic (?)ows: Aconstrained transport method. Astrophys. J., 332:659–677, September 1988.doi: 10.1086/166684.
X. Feng, Y. Hu, and F. Wei. Modeling the Resistive MHD by the Cese Method.Solar Phys., 235:235–257, May 2006a. doi: 10.1007/s11207-006-0040-6.
X. Feng, Y. Zhou, and Y. Q. Hu. A 3rd order WENO GLM-MHD scheme formagnetic reconnection. Chin. J. Space science, 655:1–7, 2006b.
X. Feng, Y. Zhou, and S. T. Wu. A Novel Numerical Implementation for So-lar Wind Modeling by the Modified Conservation Element/Soluti on ElementMethod. Astrophys. J., 655:1110–1126, February 2007.
X. S. Feng, L. P. Yang, C. Q. Xiang, S. T. Wu, Y. F. Zhou, and D. K. Zhong.Three-dimensional solar wind modelling from the Sun to Earth by a SIP-CESEMHD model with a six-component grid. Astrophys. J., 723:300–319, 2010.
X S Feng, C Q Xiang, and D K Zhong. The state-of-art of three-dimensionalnumerical study for corona-interplanetary process of solar storms (in chinese).Sci Sin-Terrae, 41:1–28, 2011.
C. Foullon, E. Verwichte, V. M. Nakariakov, and L. Fletcher. X-ray quasi-periodic pulsations in solar (?)ares as magnetohydrodynamic oscillations. Astron.Astrophys., 440:L59–L62, September 2005. doi: 10.1051/0004-6361:200500169.
P. C. Fragile, P. Anninos, K. Gustafson, and S. D. Murray. Magnetohydrody-namic Simulations of Shock Interactions with Radiative Clouds. Astrophys. J.,619:327–339, January 2005. doi: 10.1086/426313.
F. G. Fuchs, S. Mishra, and N. H. Risebro. Splitting based finite volume schemesfor ideal mhd equations. J. Comput. Phys., 228:641–660, February 2009. ISSN0021-9991.
S. E. Gibson, J. U. Kozyra, G. de Toma, B. A. Emery, T. Onsager, and B. J.Thompson. If the Sun is so quiet, why is the Earth ringing(?) A comparisonof two solar minimum intervals. J. Geophys. Res., 114:9105–9111, September2009. doi: 10.1029/2009JA014342.
Tamas Gombosi, Darren De Zeeuw, Kenneth Powell, Aaron Ridley, IgorSokolov, Quentin Stout, and G′abor T′oth. Adaptive mesh refinement forglobal magnetohydrodynamic simulation. In J¨org Bu¨chner, Manfred Scholer,and Christian Dum, editors, Space Plasma Simulation, volume 615 of Lec-ture Notes in Physics, pages 247–274. Springer Berlin Heidelberg, 2003. doi:10.1007/3-540-36530-3 12.
M. Gordovskyy, P. K. Browning, and G. E. Vekstein. Particle Acceleration inFragmenting Periodic Reconnecting Current Sheets in Solar Flares. Astrophys.J., 720:1603–1611, September 2010. doi: 10.1088/0004-637X/720/2/1603.J. T. Gosling. Corotating and Transient Solar Wind Flows in Three Dimensions.Ann. Rev. Astron. and Astrophys., 34:35–74, 1996. doi: 10.1146/annurev.astro.34.1.35.
J. T. Gosling, J. R. Asbridge, S. J. Bame, W. C. Feldman, G. Borrini, and R.T. Hansen. Coronal streamers in the solar wind at 1 AU. 86:5438–5448, July1981. doi: 10.1029/JA086iA07p05438.
C. P. T. Groth, D. L. De Zeeuw, T. I. Gombosi, and K. G. Powell. Globalthree-dimensional MHD simulation of a space weather event: CME formation,interplanetary propagation, and interaction with the magnetosphere. J. Geo-phys. Res., 105:25053–25078, November 2000.
Brian T.N. Gunney, Andrew M. Wissink, and David A. Hysom. Parallel cluster-ing algorithms for structured amr. J. Parallel. Distr. Com., 66(11):1419–1430,2006. ISSN 0743-7315. doi: 10.1016/j.jpdc.2006.03.011.
Amiram Harten, Peter D. Lax, and Bram van Leer. On upstream di(?)erencingand godunov-type schemes for hyperbolic conservation laws. SIAM Review, 25(1):35–61, 1983.
W. D. Henshaw. Solving Partial Di(?)erential Equations on Overlapping Grids. InN. V. Pogorelov, E. Audit, P. Colella, & G. P. Zank, editor, Astronomical Societyof the Pacific Conference Series, volume 406, pages 231–236, April 2009.
W. D. Henshaw and D. W. Schwendeman. Parallel computation of three-dimensional (?)ows using overlapping grids with adaptive mesh refinement. J.Comput. Phys., 227:7469–7502, August 2008.
J. T. Hoeksema, J. M. Wilcox, and P. H. Scherrer. The structure of the helio-spheric current sheet-1978-1982. J. Geophys. Res., 88:9910–9918, December1983. doi: 10.1029/JA088iA12p09910.
Richard Hornung, Andrew Wissink, and Scott Kohn. Managing complex dataand geometry in parallel structured amr applications. Engineering with Com-puters, 22:181–195, 2006. ISSN 0177-0667.
Y. Q. Hu, X. S. Feng, S. T. Wu, and W. B. Song. Three-dimensional MHDmodeling of the global corona throughout solar cycle 23. Journal of Geo-physical Research (Space Physics), 113:3106–3114, March 2008. doi: 10.1029/2007JA012750.
Y.-M. Huang and A. Bhattacharjee. Scaling laws of resistive magnetohydrody-namic reconnection in the high-Lundquist-number, plasmoid-unstable regime.Physics of Plasmas, 17(6):062104–062111, June 2010. doi: 10.1063/1.3420208.
D. M. Ingram, D. M. Causon, and C. G. Mingham. Developments in cartesiancut cell methods. Math. Comput. Simul., 61:561–572, January 2003. ISSN0378-4754.
Hiroaki Isobe and Kazunari Shibata. Reconnection in solar (?)ares: Outstandingquestions. Journal of Astrophysics and Astronomy, 30:79–85, 2009. ISSN 0250-6335. 10.1007/s12036-009-0007-8.
Chaowei Jiang, Xueshang Feng, Jian Zhang, and Dingkun Zhong. Amr sim-ulations of magnetohydrodynamic problems by the cese method in curvi-linear coordinates. Sol. Phys., 267:463–491, 2010. ISSN 0038-0938. doi:10.1007/s11207-010-9649-6.
J. R. Jokipii and B. Thomas. E(?)ects of drift on the transport of cosmic rays.IV-Modulation by a wavy interplanetary current sheet. Astrophys. J., 243:1115–1122, February 1981. doi: 10.1086/158675.
A. Kageyama and T. Sato.“Yin-Yang grid”: An overset grid in spherical ge-ometry. Geochem. Geophys. Geosyst., 5:9005–9019, September 2004.
M. Karlicky′and M. B′arta. Successive merging of plasmoids and fragmentationin (?)are current sheet and their X-ray and radio signatures. ArXiv e-prints,January 2011.
M. Karlicky′, M. B′arta, H. M′esz′arosov′a, and P. Zlobec. Time scales of the slowlydrifting pulsating structure observed during the April 12, 2001 (?)are. Astron.Astrophys., 432:705–712, March 2005. doi: 10.1051/0004-6361:20041551.
M. Karlicky′, M. B′arta, and J. Ryb′ak. Radio spectra generated during coales-cence processes of plasmoids in a (?)are current sheet. Astron. Astrophys., 514:A28, May 2010. doi: 10.1051/0004-6361/200913547.
J. T. Karpen, S. K. Antiochos, and C. R. Devore. The Role of Magnetic Recon-nection in Chromospheric Eruptions. Astrophys. J., 450:422–434, September1995. doi: 10.1086/176152.
J. Kleimann, A. Kopp, H. Fichtner, and R. Grauer. A novel code for numerical3-d mhd studies of cme expansion. Ann. Geophys., 27(3):989–1004, 2009.
Jens Kleimann, Andreas Kopp, Horst Fichtner, Rainer Grauer, and Kai Ger-maschewski. Three-dimensional mhd high-resolution computations with cwenoemploying adaptive mesh refinement. Comput. Phys. Commun., 158(1):47–56,2004. ISSN 0010-4655. doi: DOI:10.1016/j.comphy.2003.12.003.
B. Kliem, M. Karlicky′, and A. O. Benz. Solar (?)are radio pulsations as a signatureof dynamic magnetic reconnection. Astronomy and Astrophysics, 360:715–728,August 2000.
R. A. Kopp and G. W. Pneuman. Magnetic reconnection in the corona andthe loop prominence phenomenon. Solar Phys., 50:85–98, October 1976. doi:10.1007/BF00206193.
A. S. Krieger, A. F. Timothy, and E. C. Roelof. A Coronal Hole and Its Identi-fication as the Source of a High Velocity Solar Wind Stream. 29:505–525, April1973. doi: 10.1007/BF00150828.
S. Krucker, S. M. White, and R. P. Lin. Solar Flare Hard X-Ray Emissionfrom the High Corona. Astrophys. J. Lett., 669:L49–L52, November 2007. doi:10.1086/523759.
S. Krucker, H. S. Hudson, L. Glesener, S. M. White, S. Masuda, J.-P. Wuelser,and R. P. Lin. Measurements of the Coronal Acceleration Region of a SolarFlare. Astrophys. J., 714:1108–1119, May 2010. doi: 10.1088/0004-637X/714/2/1108.
Alexander Kurganov, Sebastian Noelle, and Guergana Petrova. Semidiscretecentral-upwind schemes for hyperbolic conservation laws and hamilton–jacobiequations. SIAM J. Sci. Comput., 23(3):707–740, 2001.
D. Lee and A. E. Deane. An unsplit staggered mesh scheme for multidimensionalmagnetohydrodynamics. J. Comput. Phys., 228:952–975, March 2009. doi:10.1016/j.jcp.2008.08.026.
S. Li. High order central scheme on overlapping cells for magneto-hydrodynamic(?)ows with and without constrained transport method. J. Comput. Phys., 227:7368–7393, July 2008. doi: 10.1016/j.jcp.2008.04.022.
Shengtai Li and Hui Li. A novel approach of divergence-free reconstruction foradaptive mesh refinement. J. Comput. Phys., 199:1–15, September 2004. ISSN0021-9991. doi: 10.1016/j.jcp.2004.01.027.
T. Linde. MHD simulations with the FLASH code. APS Meeting Abstracts,page F3005, March 2002.
T. J. Linde. A Three-Dimensional Adaptive Multi(?)uid MHD Model of the He-liosphere. PhD thesis, The University of Michigan, 1998.
Yuri E. Litvinenko. Particle acceleration in reconnecting current sheets in impul-sive electron-rich solar (?)ares. Solar Physics, 194:327–343, 2000. ISSN 0038-0938.10.1023/A:1005298816626.
Yuri E. Litvinenko. Electron acceleration in solar (?)ares. Advances in SpaceResearch, 32(12):2385–2391, 2003. ISSN 0273-1177. doi: DOI:10.1016/j.asr.2003.10.014.
R. Liu, J. Lee, T. Wang, G. Stenborg, C. Liu, and H. Wang. A ReconnectingCurrent Sheet Imaged in a Solar Flare. Astrophys. J. Lett., 723:L28–L33,November 2010. doi: 10.1088/2041-8205/723/1/L28.
P. Londrillo and L. del Zanna. On the divergence-free condition in Godunov-typeschemes for ideal magnetohydrodynamics: the upwind constrained transportmethod. J. Comput. Phys., 195:17–48, March 2004. doi: 10.1016/j.jcp.2003.09.016.
N. F. Loureiro, S. C. Cowley, W. D. Dorland, M. G. Haines, and A. A. Schekochi-hin. X-Point Collapse and Saturation in the Nonlinear Tearing Mode Recon-nection. Physical Review Letters, 95(23):235003–235007, December 2005. doi:10.1103/PhysRevLett.95.235003.
N. F. Loureiro, A. A. Schekochihin, and S. C. Cowley. Instability of currentsheets and formation of plasmoid chains. Physics of Plasmas, 14(10):100703–100707, October 2007. doi: 10.1063/1.2783986.
P. MacNeice, K. M. Olson, C. Mobarry, R. de Fainchtein, and C. Packer.PARAMESH: A parallel adaptive mesh refinement community toolkit. Comput.Phys. Commun., 126:330–354, April 2000.
W.B. Manchester, A.J. Ridley, T.I. Gombosi, and D.L. DeZeeuw. Modeling thesun-to-earth propagation of a very fast cme. Adv. Space. Res., 38(2):253–262,2006. ISSN 0273-1177. doi: 10.1016/j.asr.2005.09.044.
Markus J Aschwanden. Physics of the solar corona : an introduction. Berlin ;New York : Springer, 2004.
S. Masuda, T. Kosugi, H. Hara, S. Tsuneta, and Y. Ogawara. A loop-top hardX-ray source in a compact solar (?)are as evidence for magnetic reconnection.Nature, 371:495–497, October 1994. doi: 10.1038/371495a0.
N. M. Maurits, H. van der Ven, and A. E. P. Veldman. Explicit multi-timestepping methods for convection-dominated (?)ow problems. Computer Methodsin Applied Mechanics and Engineering, 157(1-2):133–150, 1998. ISSN 0045-7825.doi: DOI:10.1016/S0045-7825(98)80002-9.
D. J. McComas, B. L. Barraclough, H. O. Funsten, J. T. Gosling, E. Santiago-Mun(?)oz, R. M. Skoug, B. E. Goldstein, M. Neugebauer, P. Riley, and A. Balogh.Solar wind observations over Ulysses’first full polar orbit. J. Geophys. Res.,105:10419–10434, May 2000. doi: 10.1029/1999JA000383.
D. J. McComas, H. A. Elliott, N. A. Schwadron, J. T. Gosling, R. M. Skoug,and B. E. Goldstein. The three-dimensional solar wind around solar maximum.Geophys. Res. Lett., 30(10):1517, May 2003. doi: 10.1029/2003GL017136.
R.L. Meakin. Adaptive spatial partitioning and refinement for overset structuredgrids. Comput. Meth. Appl. Mech. Eng., 189(4):1077–1117, 2000.
Andrea Mignone and Petros Tzeferacos. A second-order unsplit godunov schemefor cell-centered mhd: The ctu-glm scheme. J. Comput. Phys., 229(6):2117–2138, 2010. ISSN 0021-9991. doi: 10.1016/j.jcp.2009.11.026.
Takahiro Miyoshi and Kanya Kusano. A multi-state hll approximate rie-mann solver for ideal magnetohydrodynamics. J. Comput. Phys., 208:315–344,September 2005. ISSN 0021-9991.
A. Nakamizo, T. Tanaka, Y. Kubo, S. Kamei, H. Shimazu, and H. Shinagawa.Development of the 3-D MHD model of the solar corona-solar wind combin-ing system. J. Geophys. Res., 114:7109–7124, July 2009. doi: 10.1029/2008JA013844.
V. M. Nakariakov, A. R. Inglis, I. V. Zimovets, C. Foullon, E. Verwichte, R.Sych, and I. N. Myagkova. Oscillatory processes in solar (?)ares. Plasma Physicsand Controlled Fusion, 52(12):124009–124016, December 2010. doi: 10.1088/0741-3335/52/12/124009.
Michael Norman. The impact of amr in numerical astrophysics and cosmology.In Timothy J. Barth, Michael Griebel, David E. Keyes, Risto M. Nieminen,Dirk Roose, Tamar Schlick, Tomasz Plewa, Timur Linde, and V. Gregory Weirs,editors, Adaptive Mesh Refinement-Theory and Applications, volume 41, pages413–430. Springer Berlin Heidelberg, 2005. ISBN 978-3-540-27039-3. doi: 10.1007/3-540-27039-6-31.
M. Oka, M. Fujimoto, I. Shinohara, and T. D. Phan.”Island surfing”mech-anism of electron acceleration during magnetic reconnection. Journal of Geo-physical Research (Space Physics), 115:A08223, August 2010a. doi: 10.1029/2010JA015392.
M. Oka, T.-D. Phan, S. Krucker, M. Fujimoto, and I. Shinohara. Electron Accel-eration by Multi-Island Coalescence. Astrophys. J., 714:915–926, May 2010b.doi: 10.1088/0004-637X/714/1/915.
Kevin Olson. Paramesh: A parallel adaptive grid tool. In Parallel Computa-tional Fluid Dynamics, pages 341–348. Elsevier, 2006.
Kevin Olson and Peter MacNeice. An over of the paramesh amr software andsome of its applications. In Adaptive Mesh Refinement-Theory and Applications,Proceedings of the Chicago Workshop on Adaptive Mesh Refinement Methods,Berlin, 2005. Springer.
S. A. Orszag and C.-M. Tang. Small-scale structure of two-dimensional magne-tohydrodynamic turbulence. Journal of Fluid Mechanics, 90:129–143, January1979. doi: 10.1017/S002211207900210X.
M. J. Owens, H. E. Spence, S. McGregor, W. J. Hughes, J. M. Quinn, C. N. Arge,P. Riley, J. Linker, and D. Odstrcil. Metrics for solar wind prediction models:
Comparison of empirical, hybrid, and physics-based schemes with 8 years of l1observations. Space Weather, 6:S08001, 2008.
E. N. Parker. Dynamics of the Interplanetary Gas and Magnetic Fields. As-trophys. J., 128:664–677, November 1958. doi: 10.1086/146579.
Ue-Li Pen, Phil Arras, and ShingKwong Wong. A free, fast, simple, and e(?)cienttotal variation diminishing magnetohydrodynamic code. ApJS, 149(2):447.H. E. Petschek. Magnetic Field Annihilation. NASA Special Publication, 50:425–439, 1964.
K. G. Powell, P. L. Roe, and J. Quirk. Adaptive-mesh algorithms for com-putational (?)uid dynamics. In Algorithmic trends in computational (?)uid dy-namics; The Institute for Computer Applications in Science and Engineering(ICASE)/LaRC Workshop, NASA Langley Research Center, Hampton, VA, US,pages 303–337, 1993.
K. G. Powell, P. L. Roe, T. J. Linde, T. I. Gombosi, and D. L. de Zeeuw. ASolution-Adaptive Upwind Scheme for Ideal Magnetohydrodynamics. J. Com-put. Phys., 154:284–309, September 1999.
E.R. Priest and T.G. Forbes. The magnetic nature of solar (?)ares. Astronomyand Astrophysics Review, 10:313–377, 2002. ISSN 0935-4956. doi: 10.1007/s001590100013.
R. Samtaney, N. F. Loureiro, D. A. Uzdensky, A. A. Schekochihin, and S. C.Cowley. Formation of plasmoid chains in magnetic reconnection. Phys. Rev.Lett., 103(10):105004, Sep 2009. doi: 10.1103/PhysRevLett.103.105004.
V. Sankaran, J. Sitaraman, A. Wissink, A. Datta, B. Jayaraman, M. Potsdam,D. Mavriplis, Z. Yang, D. O’Brien, H. Saberi, R. Cheng, N. Hariharan, and R.Strawn. Application of the helios computational platform to rotorcraft (?)owfields. AIAA-2010-1230, 2010.
V. Sankaran, A. Wissink, A. Datta, J. Sitaraman, B. Jayaraman, M. Potsdam,A. Katz, S. Kamkar, B. Roget, D. Mavriplis, H. Saberi, W. Chen, W. Johnson,and R. Strawn. Overview of the helios version 2.0 computational platform forrotorcraft simulations. 2011. 49th AIAA Aerospace Sciences Meeting includingthe New Horizons Forum and Aerospace Exposition, Orlando, Florida, Jan 4-7,2011, (paper AIAA-2011-1105).
J. Schumacher and B. Kliem. Coalescence of magnetic islands includinganomalous resistivity. Physics of Plasmas, 4:3533–3543, October 1997. doi:10.1063/1.872250.
N. R. Sheeley, Y.-M. Wang, S. H. Hawley, G. E. Brueckner, K. P. Dere, R. A.Howard, M. J. Koomen, C. M. Korendyke, D. J. Michels, S. E. Paswaters, D.G. Socker, O. C. St. Cyr, D. Wang, P. L. Lamy, A. Llebaria, R. Schwenn, G. M.Simnett, S. Plunkett, and D. A. Biesecker. Measurements of (?)ow speeds in thecorona between 2 and 30 r. ApJ, 484(1):472, 1997.
K. Shibata and S. Tanuma. Plasmoid-induced-reconnection and fractal recon-nection. Earth, Planets, and Space, 53:473–482, June 2001.
K. Shibata, S. Masuda, M. Shimojo, H. Hara, T. Yokoyama, S. Tsuneta, T.Kosugi, and Y. Ogawara. Hot-Plasma Ejections Associated with Compact-LoopSolar Flares. Astrophys. J. Lett., 451:L83–L85, October 1995. doi: 10.1086/309688.
Chi-Wang Shu and Stanley Osher. E(?)cient implementation of essentially non-oscillatory shock-capturing schemes, ii. J. Comput. Phys., 83(1):32–78, 1989.ISSN 0021-9991. doi: DOI:10.1016/0021-9991(89)90222-2.
Jayanarayanan Sitaraman, Matthew Floros, Andrew Wissink, and Mark Pots-dam. Parallel domain connectivity algorithm for unsteady (?)ow computationsusing overlapping and adaptive grids. J. Comput. Phys., 229(12):4703–4723,2010. ISSN 0021-9991. doi: 10.1016/j.jcp.2010.03.008.
E. J. Smith and J. H. Wolfe. Observations of interaction regions and corotatingshocks between one and five AU: Pioneers 10 and 11. Geophys. Res. Lett., 2:137–140, 1976.
E. J. Smith, R. G. Marsden, and D. E. Page. ULYSSES above the Sun’s SouthPole-an Introduction. Science, 268:1005–1007, May 1995. doi: 10.1126/science.7754377.
Joseph L. Steger and John A. Benek. On the use of composite grid schemes incomputational aerodynamics. Comput. Meth. Appl. Mech. Eng., 64(1-3):301–320, 1987. ISSN 0045-7825. doi: 10.1016/0045-7825(87)90045-4.
J. M. Stone and T. Gardiner. A simple unsplit Godunov method for multidi-mensional MHD. New Astronomy, 14:139–148, February 2009. doi: 10.1016/j.newast.2008.06.003.
Roger Strawn. High-performance computing for rotorcraft modeling and simu-lation. Computing in Science and Engineering, 12:27–35, 2010. ISSN 1521-9615.doi: 10.1109/MCSE.2010.110.
K. G. Tanaka, T. Yumura, M. Fujimoto, I. Shinohara, S. V. Badman, and A. Gro-cott. Merging of magnetic islands as an e(?)cient accelerator of electrons. Physicsof Plasmas, 17(10):102902–102907, October 2010. doi: 10.1063/1.3491123.
K. G. Tanaka, M. Fujimoto, S. V. Badman, and I. Shinohara. Dynamic magneticisland coalescence and associated electron acceleration. Physics of Plasmas, 18(2):022903–022913, February 2011. doi: 10.1063/1.3554660.
T. Tanaka. Finite volume tvd scheme on an unstructured grid system for three-dimensional mhd simulation of inhomogeneous systems including strong back-ground potential fields. J. Comput. Phys., 111(2):381–389, 1994. ISSN 0021-9991. doi: 10.1006/jcph.1994.1071.
S. Tanuma and K. Shibata. Internal Shocks in the Magnetic Reconnection Jetin Solar Flares: Multiple Fast Shocks Created by the Secondary Tearing Insta-bility. Astrophys. J. Lett., 628:L77–L80, July 2005. doi: 10.1086/432418.
Eleuterio F Toro. Riemann Solvers and Numerical Methods for Fluid Dynamics.Springer Verlag, 2009.
G. T′oth. The·B = 0 Constraint in Shock-Capturing MagnetohydrodynamicsCodes. J. Comput. Phys., 161:605–652, July 2000. doi: 10.1006/jcph.2000.6519.
G. T′oth, I. V. Sokolov, T. I. Gombosi, D. R. Chesney, C. R. Clauer, D. L. DeZeeuw, K. C. Hansen, K. J. Kane, W. B. Manchester, R. C. Oehmke, K. G.Powell, A. J. Ridley, I. I. Roussev, Q. F. Stout, O. Volberg, R. A. Wolf, S.Sazykin, A. Chan, B. Yu, and J. K′ota. Space Weather Modeling Framework: Anew tool for the space science community. J. Geophys. Res., 110:12226–12246,December 2005.
G. T′oth, D. L. de Zeeuw, T. I. Gombosi, and K. G. Powell. A parallel ex-plicit/implicit time stepping scheme on block-adaptive grids. J. Comput. Phys.,217:722–758, September 2006a.
G. T′oth, D. L. de Zeeuw, T. I. Gombosi, and K. G. Powell. A parallel ex-plicit/implicit time stepping scheme on block-adaptive grids. J. Comput. Phys.,217:722–758, September 2006b. doi: 10.1016/j.jcp.2006.01.029.
R. Touma and P. Arminjon. Central finite volume schemes with constrainedtransport divergence treatment for three-dimensional ideal MHD. J. Comput.Phys., 212:617–636, March 2006. doi: 10.1016/j.jcp.2005.07.013.
S. Tsuneta. Structure and Dynamics of Magnetic Reconnection in a Solar Flare.Astrophys. J., 456:840–849, January 1996. doi: 10.1086/176701.M. Ugai. Basic physical mechanism of fast reconnection evolution in spaceplasmas. Space Science Reviews, 95:601–611, 2001. ISSN 0038-6308. doi: 10.1023/A:1005205222921.
A. V. Usmanov, M. L. Goldstein, B. P. Besser, and J. M. Fritzer. A global MHDsolar wind model with WKB Alfv′en waves: Comparison with Ulysses data. J.Geophys. Res., 105:12675–12696, June 2000. doi: 10.1029/1999JA000233.
D. A. Uzdensky. Petschek-like Reconnection with Current-driven AnomalousResistivity and Its Application to Solar Flares. Astrophys. J., 587:450–457,April 2003. doi: 10.1086/368075.
B. van der Holst and R. Keppens. Hybrid block-amr in cartesian and curvilinearcoordinates: Mhd applications. J. Comput. Phys., 226(1):925–946, 2007. ISSN0021-9991. doi: 10.1016/j.jcp.2007.05.007.
H. van der Ven, B. E. Niemann-Tuitman, and A. E. P. Veldman. An explicitmulti-time-stepping algorithm for aerodynamic (?)ows. J. Comput. Appl. Math.,82(1-2):423–431, 1997. ISSN 0377-0427. doi: 10.1016/S0377-0427(97)00054-X.
Rongsheng Wang, Quanming Lu, Aimin Du, and Shui Wang. In situ obser-vations of a secondary magnetic island in an ion di(?)usion region and asso-ciated energetic electrons. Phys. Rev. Lett., 104(17):175003, Apr 2010. doi:10.1103/PhysRevLett.104.175003.
Y. Wang, F. S. Wei, X. S. Feng, S. H. Zhang, P. B. Zuo, and T. R. Sun. Ener-getic Electrons Associated with Magnetic Reconnection in the Magnetic CloudBoundary Layer. Physical Review Letters, 105(19):195007–195010, November2010. doi: 10.1103/PhysRevLett.105.195007.
Y.-M. Wang, E. Robbrecht, and N. R. Sheeley. On the Weakening of the PolarMagnetic Fields during Solar Cycle 23. Astrophys. J., 707:1372–1386, December2009. doi: 10.1088/0004-637X/707/2/1372.
A. Wissink, S. Kamkar, T. Pulliam, J. Sitaraman, and V Sankaran. Cartesianadaptive mesh refinement for rotorcraft wake resolution. 2010. 40th AIAAFluid Dynamics Conference and Exhibit, Chicago, Illinois, June 28-July 1, 2010,(paper AIAA-2010-4554).
A.M. Wissink and R.L. Meakin. On parallel implementations of dynamic oversetgrid methods. In ACM/IEEE 1997 Conference Supercomputing, pages 15–15,1997.
C. Xiao, X. Wang, Z. Pu, H. Zhao, J. Wang, Z. Ma, S. Fu, M. Kivelson, Z. Liu,Q. Zong, K. Glassmeier, A. Balogh, A. Korth, H. Reme, and C. Escoubet. Insitu evidence for the structure of the magnetic null in a 3D reconnection eventin the Earth’s magnetotail. AGU Fall Meeting Abstracts, December 2006.
H. C. Yee and B. Sj¨ogreen. Development of low dissipative high order filterschemes for multiscale navier-stokes/mhd systems. J. Comput. Phys., 225:910–934, July 2007. ISSN 0021-9991.
H. C. Yee and Bj¨orn Sj¨ogreen. E(?)cient low dissipative high order schemes formultiscale mhd (?)ows, ii: Minimization of·B numerical error. J. Sci. Comput.,29:115–164. ISSN 0885-7474.
T. Yokoyama, K. Akita, T. Morimoto, K. Inoue, and J. Newmark. Clear Evi-dence of Reconnection In(?)ow of a Solar Flare. Astrophys. J. Lett., 546:L69–L72,January 2001. doi: 10.1086/318053.
M. Yoshida and A. Kageyama. Application of the Yin-Yang grid to a ther-mal convection of a Boussinesq (?)uid with infinite Prandtl number in a three-dimensional spherical shell. Geophys. Res. Lett., 31:12609–12613, June 2004.
M. Zhang, S.-T. John Yu, S.-C. Henry Lin, S.-C. Chang, and I. Blankson.Solving the MHD equations by the space time conservation element and so-lution element method. J. Comput. Phys., 214:599–617, May 2006. doi:10.1016/j.jcp.2005.10.006.
U. Ziegler. NIRVANA + : An adaptive mesh refinement code for gas dynamicsand MHD. Comput. Phys. Commun., 109:111–134, April 1998.
U. Ziegler. Adaptive Mesh Refinement in MHD Modeling. Realization, Testsand Application. In E. Falgarone & T. Passot, editor, Turbulence and MagneticFields in Astrophysics, volume 614 of Lecture Notes in Physics, Berlin SpringerVerlag, pages 127–151, 2003.
U. Ziegler. A central-constrained transport scheme for ideal magnetohydrody-namics. J. Comput. Phys., 196:393–416, May 2004. ISSN 0021-9991.
U. Ziegler. A solution-adaptive central-constraint transport scheme for mag-netohydrodynamics. Comput. Phys. Commun., 170(2):153–174, 2005. ISSN0010-4655. doi: 10.1016/j.cpc.2005.04.002.
U. Ziegler. The NIRVANA code: Parallel computational MHD with adaptivemesh refinement. Comput. Phys. Commun., 179:227–244, August 2008. doi:10.1016/j.cpc.2008.02.017.
U. Ziegler. A semi-discrete central scheme for magnetohydrodynamics onorthogonal-curvilinear grids. J. Comput. Phys., 230:1035–1063, January 2011.ISSN 0021-9991.
呼延奇.日冕大尺度结构演化及快速磁场重联的数值研究. PhD thesis,中国科学院研究生院(空间科学与应用研究中心), 2008.
林元章.太阳物理导论.科学出版社, 2000.
刘振兴等.太阳物理学.哈尔滨工业大学版社, 2005.
涂传诒.日地空间物理学.科学出版社, 1988.
王水,魏奉思.中国空间天气研究进展.地球物理学进展, 22, August 2007.
王水,李罗权.磁场重联.安徽教育出版社, 1998.
阎超.计算流体力学方法及应用.北京航空航天大学出版社, 2006.
章振大.日冕物理.科学出版社, 2000.
Charles N. Arge, Dusan Odstrcil, Victor J. Pizzo, and Leslie R. Mayer. Im-proved method for specifying solar wind speed near the sun. AIP ConferenceProceedings, 679(1):190–193, 2003. doi: 10.1063/1.1618574.
M. J. Aschwanden. Particle acceleration and kinematics in solar (?)ares-A Syn-thesis of Recent Observations and Theoretical Concepts (Invited Review). SpaceScience Reviews, 101:1–227, January 2002. doi: 10.1023/A:1019712124366.
Daniel Baker. Introduction to space weather. In Klaus Scherer, Horst Fichtner,Bernd Heber, and Urs Mall, editors, Space Weather, volume 656 of LectureNotes in Physics, pages 993–1020. Springer Berlin / Heidelberg, 2005. doi:10.1007/978-3-540-31534-6 1.
D. S. Balsara and D. Spicer. Maintaining Pressure Positivity in Magnetohy-drodynamic Simulations. J. Comput. Phys., 148:133–148, January 1999a. doi:10.1006/jcph.1998.6108.
D. S. Balsara and D. S. Spicer. A Staggered Mesh Algorithm Using High OrderGodunov Fluxes to Ensure Solenoidal Magnetic Fields in MagnetohydrodynamicSimulations. J. Comput. Phys., 149:270–292, March 1999b. doi: 10.1006/jcph.1998.6153.
Dinshaw S. Balsara, Tobias Rumpf, Michael Dumbser, and Claus-Dieter Munz.E(?)cient, high accuracy ader-weno schemes for hydrodynamics and divergence-free magnetohydrodynamics. J. Comput. Phys., 228(7):2480–2516, 2009. ISSN0021-9991. doi: DOI:10.1016/j.jcp.2008.12.003.
M. B′arta, M. Karlicky′, and R. zemlicka. Plasmoid dynamics in (?)are reconnectionand the frequency drift of the drifting pulsating structure. Solar Physics, 253:173–189, 2008. ISSN 0038-0938. 10.1007/s11207-008-9217-5.
M. B′arta, J. Bu¨chner, and M. Karlicky′. Multi-scale MHD approach to thecurrent sheet filamentation in solar coronal reconnection. Advances in SpaceResearch, 45:10–17, January 2010a. doi: 10.1016/j.asr.2009.07.025.
M. B′arta, J. Bu¨chner, M. Karlicky′, and P. Kotrc. Spontaneous current-layerfragmentation and cascading reconnection in solar (?)ares: II. Relation to obser-vations. ArXiv e-prints, November 2010b.
M. B′arta, J. Bu¨chner, M. Karlicky′, and J. Sk′ala. Spontaneous current-layerfragmentation and cascading reconnection in solar (?)ares: I. Model and analysis.ArXiv e-prints, November 2010c.
M. J. Berger and P. Colella. Local adaptive mesh refinement for shock hydro-dynamics. J. Comput. Phys., 82:64–84, May 1989.
Marsha J Berger and Joseph Oliger. Adaptive mesh refinement for hyperbolicpartial di(?)erential equations. J. Comput. Phys., 53(3):484–512, 1984. ISSN0021-9991. doi: 10.1016/0021-9991(84)90073-1.
J. Birn and E. R. Priest. Reconnection of Magnetic Fields. CambridgeUniversity Press, New York, 2006. ISBN 9780521854207. doi: 10.1017/CBO9780511536151.
J. Birn, J. F. Drake, M. A. Shay, B. N. Rogers, R. E. Denton, M. Hesse, M.Kuznetsova, Z. W. Ma, A. Bhattacharjee, A. Otto, and P. L. Pritchett. GeospaceEnvironmental Modeling (GEM) magnetic reconnection challenge. J. Geophys.Res., 106:3715–3720, March 2001. doi: 10.1029/1999JA900449.
D. Biskamp. Magnetic reconnection via current sheets. Physics of Fluids, 29:1520–1531, May 1986. doi: 10.1063/1.865670.
J. U. Brackbill and D. C. Barnes. The e(?)ect of nonzero product of magnetic gra-dient and B on the numerical solution of the magnetohydrodynamic equations.J. Comput. Phys., 35:426–430, May 1980. doi: 10.1016/0021-9991(80)90079-0.
K. D. Brislawn, D. L. Brown, G. S. Chesshire, and J. S. Saltzman. Adaptively-refined overlapping grids for the numerical solution of systems of hyperbolicconservation laws. In J. C. South Jr., J. L. Thomas, & J. Vanrosendale, editor,ICASE/LaRC Workshop on Adaptive Grid Methods, pages 95–110, October1995.
David Brown, William Henshaw, and Daniel Quinlan. Overture: An object-oriented framework for solving partial di(?)erential equations. In Yutaka Ishikawa,Rodney Oldehoeft, John Reynders, and Marydell Tholburn, editors, ScientificComputing in Object-Oriented Parallel Environments, volume 1343 of LectureNotes in Computer Science, pages 177–184. Springer Berlin / Heidelberg.Jinsheng Cai, Her Mann Tsai, and Feng Liu. A parallel viscous (?)ow solver onmulti-block overset grids. Computers and Fluids, 35(10):1290–1301, 2006. ISSN0045-7930. doi: 10.1016/j.comp(?)uid.2005.02.006.
P. Cassak and M. Shay. Magnetic reconnection for coronal conditions: Recon-nection rates, secondary islands and onset. Space Science Reviews, pages 1–20,2011. ISSN 0038-6308. 10.1007/s11214-011-9755-2.
P. A. Cassak, M. A. Shay, and J. F. Drake. Scaling of Sweet-Parker reconnectionwith secondary islands. Physics of Plasmas, 16(12):120702–120712, December2009. doi: 10.1063/1.3274462.
S. Chang. The Method of Space-Time Conservation Element and Solution Ele-ment: A New Approach for Solving the Navier-Stokes and Euler Equations. J.Comput. Phys., 119:295–324, July 1995. doi: 10.1006/jcph.1995.1137.
S.-C. Chang, X.-Y. Wang, and C.-Y. Chow. The Space-Time ConservationElement and Solution Element Method: A New High-Resolution and GenuinelyMultidimensional Paradigm for Solving Conservation Laws. J. Comput. Phys.,156:89–136, November 1999. doi: 10.1006/jcph.1999.6354.
S. Chapman and H. Zirin. Notes on the Solar Corona and the Terrestrial Iono-sphere. Smithsonian Contributions to Astrophysics, 2:1–14, 1957.
G. Chesshire and W. D. Henshaw. Composite overlapping meshes for the so-lution of partial di(?)erential equations. J. Comput. Phys., 90:1–64, September1990.
IT Chiu and RL. Meakin. On automating domain connectivity for overset grids.1995. 33rd Aero. Sci. Mtg. Reno, NV, 1995, (paper AIAA-95-054).
P. Colella et al. Chombo, software package for amr applications. Technicalreport, Lawrence Berkely National Laboratory, 2007.
Phillip Colella, Daniel T. Graves, Benjamin J. Keen, and David Modiano. Acartesian grid embedded boundary method for hyperbolic conservation laws. J.Comput. Phys., 211:347–366, January 2006. ISSN 0021-9991. doi: 10.1016/j.jcp.2005.05.026.
A. J. Cunningham, A. Frank, P. Varni`ere, S. Mitran, and T. W. Jones. Simu-lating Magnetohydrodynamical Flow with Constrained Transport and AdaptiveMesh Refinement: Algorithms and Tests of the AstroBEAR Code. Astrophys.J. Suppl., 182:519–542, June 2009. doi: 10.1088/0067-0049/182/2/519.
W. Dai. A Simple Finite Di(?)erence Scheme for Multidimensional Magneto-hydrodynamical Equations. J. Comput. Phys., 142:331–369, May 1998. doi:10.1006/jcph.1998.5944.
W. Dai and P. R. Woodward. An approximate Riemann solver for idealmagnetohydrodynamics. J. Comput. Phys., 111:354–372, April 1994. doi:10.1006/jcph.1994.1069.
W. Daughton, V. Roytershteyn, B. J. Albright, H. Karimabadi, L. Yin, andKevin J. Bowers. Transition from collisional to kinetic regimes in large-scalereconnection layers. Phys. Rev. Lett., 103(6):065004, Aug 2009. doi: 10.1103/PhysRevLett.103.065004.
A. Dedner, F. Kemm, D. Kr¨oner, C.-D. Munz, T. Schnitzer, and M. Wesenberg.Hyperbolic Divergence Cleaning for the MHD Equations. J. Comput. Phys.,175:645–673, January 2002. doi: 10.1006/jcph.2001.6961.
P. J. Dellar. A Note on Magnetic Monopoles and the One-Dimensional MHDRiemann Problem. J. Comput. Phys., 172:392–398, September 2001. doi: 10.1006/jcph.2001.6815.
D. Dezeeuw and K. G. Powell. An Adaptively Refined Cartesian Mesh Solverfor the Euler Equations. J. Comput. Phys., 104:56–68, January 1993.
M Dryer. Space weather simulation in 3d mhd from the sun to the earth andbeyond to 100 au: A modeler’s perspective of the present state of the art.Asian J Phys, 16:97–121, 2007.
A. Dubey, L. B. Reid, and R. Fisher. Introduction to FLASH 3.0, with applica-tion to supersonic turbulence. Physica Scripta Volume T, 132(1):014046–014056,December 2008. doi: 10.1088/0031-8949/2008/T132/014046.
Terry Forbes E R Priest. Magnetic reconnection : MHD theory and applications.New York : Cambridge University Press, 2000.
C. R. Evans and J. F. Hawley. Simulation of magnetohydrodynamic (?)ows: Aconstrained transport method. Astrophys. J., 332:659–677, September 1988.doi: 10.1086/166684.
X. Feng, Y. Hu, and F. Wei. Modeling the Resistive MHD by the Cese Method.Solar Phys., 235:235–257, May 2006a. doi: 10.1007/s11207-006-0040-6.
X. Feng, Y. Zhou, and Y. Q. Hu. A 3rd order WENO GLM-MHD scheme formagnetic reconnection. Chin. J. Space science, 655:1–7, 2006b.
X. Feng, Y. Zhou, and S. T. Wu. A Novel Numerical Implementation for So-lar Wind Modeling by the Modified Conservation Element/Soluti on ElementMethod. Astrophys. J., 655:1110–1126, February 2007.
X. S. Feng, L. P. Yang, C. Q. Xiang, S. T. Wu, Y. F. Zhou, and D. K. Zhong.Three-dimensional solar wind modelling from the Sun to Earth by a SIP-CESEMHD model with a six-component grid. Astrophys. J., 723:300–319, 2010.
X S Feng, C Q Xiang, and D K Zhong. The state-of-art of three-dimensionalnumerical study for corona-interplanetary process of solar storms (in chinese).Sci Sin-Terrae, 41:1–28, 2011.
C. Foullon, E. Verwichte, V. M. Nakariakov, and L. Fletcher. X-ray quasi-periodic pulsations in solar (?)ares as magnetohydrodynamic oscillations. Astron.Astrophys., 440:L59–L62, September 2005. doi: 10.1051/0004-6361:200500169.
P. C. Fragile, P. Anninos, K. Gustafson, and S. D. Murray. Magnetohydrody-namic Simulations of Shock Interactions with Radiative Clouds. Astrophys. J.,619:327–339, January 2005. doi: 10.1086/426313.
F. G. Fuchs, S. Mishra, and N. H. Risebro. Splitting based finite volume schemesfor ideal mhd equations. J. Comput. Phys., 228:641–660, February 2009. ISSN0021-9991.
S. E. Gibson, J. U. Kozyra, G. de Toma, B. A. Emery, T. Onsager, and B. J.Thompson. If the Sun is so quiet, why is the Earth ringing(?) A comparisonof two solar minimum intervals. J. Geophys. Res., 114:9105–9111, September2009. doi: 10.1029/2009JA014342.
Tamas Gombosi, Darren De Zeeuw, Kenneth Powell, Aaron Ridley, IgorSokolov, Quentin Stout, and G′abor T′oth. Adaptive mesh refinement forglobal magnetohydrodynamic simulation. In J¨org Bu¨chner, Manfred Scholer,and Christian Dum, editors, Space Plasma Simulation, volume 615 of Lec-ture Notes in Physics, pages 247–274. Springer Berlin Heidelberg, 2003. doi:10.1007/3-540-36530-3 12.
M. Gordovskyy, P. K. Browning, and G. E. Vekstein. Particle Acceleration inFragmenting Periodic Reconnecting Current Sheets in Solar Flares. Astrophys.J., 720:1603–1611, September 2010. doi: 10.1088/0004-637X/720/2/1603.J. T. Gosling. Corotating and Transient Solar Wind Flows in Three Dimensions.Ann. Rev. Astron. and Astrophys., 34:35–74, 1996. doi: 10.1146/annurev.astro.34.1.35.
J. T. Gosling, J. R. Asbridge, S. J. Bame, W. C. Feldman, G. Borrini, and R.T. Hansen. Coronal streamers in the solar wind at 1 AU. 86:5438–5448, July1981. doi: 10.1029/JA086iA07p05438.
C. P. T. Groth, D. L. De Zeeuw, T. I. Gombosi, and K. G. Powell. Globalthree-dimensional MHD simulation of a space weather event: CME formation,interplanetary propagation, and interaction with the magnetosphere. J. Geo-phys. Res., 105:25053–25078, November 2000.
Brian T.N. Gunney, Andrew M. Wissink, and David A. Hysom. Parallel cluster-ing algorithms for structured amr. J. Parallel. Distr. Com., 66(11):1419–1430,2006. ISSN 0743-7315. doi: 10.1016/j.jpdc.2006.03.011.
Amiram Harten, Peter D. Lax, and Bram van Leer. On upstream di(?)erencingand godunov-type schemes for hyperbolic conservation laws. SIAM Review, 25(1):35–61, 1983.
W. D. Henshaw. Solving Partial Di(?)erential Equations on Overlapping Grids. InN. V. Pogorelov, E. Audit, P. Colella, & G. P. Zank, editor, Astronomical Societyof the Pacific Conference Series, volume 406, pages 231–236, April 2009.
W. D. Henshaw and D. W. Schwendeman. Parallel computation of three-dimensional (?)ows using overlapping grids with adaptive mesh refinement. J.Comput. Phys., 227:7469–7502, August 2008.
J. T. Hoeksema, J. M. Wilcox, and P. H. Scherrer. The structure of the helio-spheric current sheet-1978-1982. J. Geophys. Res., 88:9910–9918, December1983. doi: 10.1029/JA088iA12p09910.
Richard Hornung, Andrew Wissink, and Scott Kohn. Managing complex dataand geometry in parallel structured amr applications. Engineering with Com-puters, 22:181–195, 2006. ISSN 0177-0667.
Y. Q. Hu, X. S. Feng, S. T. Wu, and W. B. Song. Three-dimensional MHDmodeling of the global corona throughout solar cycle 23. Journal of Geo-physical Research (Space Physics), 113:3106–3114, March 2008. doi: 10.1029/2007JA012750.
Y.-M. Huang and A. Bhattacharjee. Scaling laws of resistive magnetohydrody-namic reconnection in the high-Lundquist-number, plasmoid-unstable regime.Physics of Plasmas, 17(6):062104–062111, June 2010. doi: 10.1063/1.3420208.
D. M. Ingram, D. M. Causon, and C. G. Mingham. Developments in cartesiancut cell methods. Math. Comput. Simul., 61:561–572, January 2003. ISSN0378-4754.
Hiroaki Isobe and Kazunari Shibata. Reconnection in solar (?)ares: Outstandingquestions. Journal of Astrophysics and Astronomy, 30:79–85, 2009. ISSN 0250-6335. 10.1007/s12036-009-0007-8.
Chaowei Jiang, Xueshang Feng, Jian Zhang, and Dingkun Zhong. Amr sim-ulations of magnetohydrodynamic problems by the cese method in curvi-linear coordinates. Sol. Phys., 267:463–491, 2010. ISSN 0038-0938. doi:10.1007/s11207-010-9649-6.
J. R. Jokipii and B. Thomas. E(?)ects of drift on the transport of cosmic rays.IV-Modulation by a wavy interplanetary current sheet. Astrophys. J., 243:1115–1122, February 1981. doi: 10.1086/158675.
A. Kageyama and T. Sato.“Yin-Yang grid”: An overset grid in spherical ge-ometry. Geochem. Geophys. Geosyst., 5:9005–9019, September 2004.
M. Karlicky′and M. B′arta. Successive merging of plasmoids and fragmentationin (?)are current sheet and their X-ray and radio signatures. ArXiv e-prints,January 2011.
M. Karlicky′, M. B′arta, H. M′esz′arosov′a, and P. Zlobec. Time scales of the slowlydrifting pulsating structure observed during the April 12, 2001 (?)are. Astron.Astrophys., 432:705–712, March 2005. doi: 10.1051/0004-6361:20041551.
M. Karlicky′, M. B′arta, and J. Ryb′ak. Radio spectra generated during coales-cence processes of plasmoids in a (?)are current sheet. Astron. Astrophys., 514:A28, May 2010. doi: 10.1051/0004-6361/200913547.
J. T. Karpen, S. K. Antiochos, and C. R. Devore. The Role of Magnetic Recon-nection in Chromospheric Eruptions. Astrophys. J., 450:422–434, September1995. doi: 10.1086/176152.
J. Kleimann, A. Kopp, H. Fichtner, and R. Grauer. A novel code for numerical3-d mhd studies of cme expansion. Ann. Geophys., 27(3):989–1004, 2009.
Jens Kleimann, Andreas Kopp, Horst Fichtner, Rainer Grauer, and Kai Ger-maschewski. Three-dimensional mhd high-resolution computations with cwenoemploying adaptive mesh refinement. Comput. Phys. Commun., 158(1):47–56,2004. ISSN 0010-4655. doi: DOI:10.1016/j.comphy.2003.12.003.
B. Kliem, M. Karlicky′, and A. O. Benz. Solar (?)are radio pulsations as a signatureof dynamic magnetic reconnection. Astronomy and Astrophysics, 360:715–728,August 2000.
R. A. Kopp and G. W. Pneuman. Magnetic reconnection in the corona andthe loop prominence phenomenon. Solar Phys., 50:85–98, October 1976. doi:10.1007/BF00206193.
A. S. Krieger, A. F. Timothy, and E. C. Roelof. A Coronal Hole and Its Identi-fication as the Source of a High Velocity Solar Wind Stream. 29:505–525, April1973. doi: 10.1007/BF00150828.
S. Krucker, S. M. White, and R. P. Lin. Solar Flare Hard X-Ray Emissionfrom the High Corona. Astrophys. J. Lett., 669:L49–L52, November 2007. doi:10.1086/523759.
S. Krucker, H. S. Hudson, L. Glesener, S. M. White, S. Masuda, J.-P. Wuelser,and R. P. Lin. Measurements of the Coronal Acceleration Region of a SolarFlare. Astrophys. J., 714:1108–1119, May 2010. doi: 10.1088/0004-637X/714/2/1108.
Alexander Kurganov, Sebastian Noelle, and Guergana Petrova. Semidiscretecentral-upwind schemes for hyperbolic conservation laws and hamilton–jacobiequations. SIAM J. Sci. Comput., 23(3):707–740, 2001.
D. Lee and A. E. Deane. An unsplit staggered mesh scheme for multidimensionalmagnetohydrodynamics. J. Comput. Phys., 228:952–975, March 2009. doi:10.1016/j.jcp.2008.08.026.
S. Li. High order central scheme on overlapping cells for magneto-hydrodynamic(?)ows with and without constrained transport method. J. Comput. Phys., 227:7368–7393, July 2008. doi: 10.1016/j.jcp.2008.04.022.
Shengtai Li and Hui Li. A novel approach of divergence-free reconstruction foradaptive mesh refinement. J. Comput. Phys., 199:1–15, September 2004. ISSN0021-9991. doi: 10.1016/j.jcp.2004.01.027.
T. Linde. MHD simulations with the FLASH code. APS Meeting Abstracts,page F3005, March 2002.
T. J. Linde. A Three-Dimensional Adaptive Multi(?)uid MHD Model of the He-liosphere. PhD thesis, The University of Michigan, 1998.
Yuri E. Litvinenko. Particle acceleration in reconnecting current sheets in impul-sive electron-rich solar (?)ares. Solar Physics, 194:327–343, 2000. ISSN 0038-0938.10.1023/A:1005298816626.
Yuri E. Litvinenko. Electron acceleration in solar (?)ares. Advances in SpaceResearch, 32(12):2385–2391, 2003. ISSN 0273-1177. doi: DOI:10.1016/j.asr.2003.10.014.
R. Liu, J. Lee, T. Wang, G. Stenborg, C. Liu, and H. Wang. A ReconnectingCurrent Sheet Imaged in a Solar Flare. Astrophys. J. Lett., 723:L28–L33,November 2010. doi: 10.1088/2041-8205/723/1/L28.
P. Londrillo and L. del Zanna. On the divergence-free condition in Godunov-typeschemes for ideal magnetohydrodynamics: the upwind constrained transportmethod. J. Comput. Phys., 195:17–48, March 2004. doi: 10.1016/j.jcp.2003.09.016.
N. F. Loureiro, S. C. Cowley, W. D. Dorland, M. G. Haines, and A. A. Schekochi-hin. X-Point Collapse and Saturation in the Nonlinear Tearing Mode Recon-nection. Physical Review Letters, 95(23):235003–235007, December 2005. doi:10.1103/PhysRevLett.95.235003.
N. F. Loureiro, A. A. Schekochihin, and S. C. Cowley. Instability of currentsheets and formation of plasmoid chains. Physics of Plasmas, 14(10):100703–100707, October 2007. doi: 10.1063/1.2783986.
P. MacNeice, K. M. Olson, C. Mobarry, R. de Fainchtein, and C. Packer.PARAMESH: A parallel adaptive mesh refinement community toolkit. Comput.Phys. Commun., 126:330–354, April 2000.
W.B. Manchester, A.J. Ridley, T.I. Gombosi, and D.L. DeZeeuw. Modeling thesun-to-earth propagation of a very fast cme. Adv. Space. Res., 38(2):253–262,2006. ISSN 0273-1177. doi: 10.1016/j.asr.2005.09.044.
Markus J Aschwanden. Physics of the solar corona : an introduction. Berlin ;New York : Springer, 2004.
S. Masuda, T. Kosugi, H. Hara, S. Tsuneta, and Y. Ogawara. A loop-top hardX-ray source in a compact solar (?)are as evidence for magnetic reconnection.Nature, 371:495–497, October 1994. doi: 10.1038/371495a0.
N. M. Maurits, H. van der Ven, and A. E. P. Veldman. Explicit multi-timestepping methods for convection-dominated (?)ow problems. Computer Methodsin Applied Mechanics and Engineering, 157(1-2):133–150, 1998. ISSN 0045-7825.doi: DOI:10.1016/S0045-7825(98)80002-9.
D. J. McComas, B. L. Barraclough, H. O. Funsten, J. T. Gosling, E. Santiago-Mun(?)oz, R. M. Skoug, B. E. Goldstein, M. Neugebauer, P. Riley, and A. Balogh.Solar wind observations over Ulysses’first full polar orbit. J. Geophys. Res.,105:10419–10434, May 2000. doi: 10.1029/1999JA000383.
D. J. McComas, H. A. Elliott, N. A. Schwadron, J. T. Gosling, R. M. Skoug,and B. E. Goldstein. The three-dimensional solar wind around solar maximum.Geophys. Res. Lett., 30(10):1517, May 2003. doi: 10.1029/2003GL017136.
R.L. Meakin. Adaptive spatial partitioning and refinement for overset structuredgrids. Comput. Meth. Appl. Mech. Eng., 189(4):1077–1117, 2000.
Andrea Mignone and Petros Tzeferacos. A second-order unsplit godunov schemefor cell-centered mhd: The ctu-glm scheme. J. Comput. Phys., 229(6):2117–2138, 2010. ISSN 0021-9991. doi: 10.1016/j.jcp.2009.11.026.
Takahiro Miyoshi and Kanya Kusano. A multi-state hll approximate rie-mann solver for ideal magnetohydrodynamics. J. Comput. Phys., 208:315–344,September 2005. ISSN 0021-9991.
A. Nakamizo, T. Tanaka, Y. Kubo, S. Kamei, H. Shimazu, and H. Shinagawa.Development of the 3-D MHD model of the solar corona-solar wind combin-ing system. J. Geophys. Res., 114:7109–7124, July 2009. doi: 10.1029/2008JA013844.
V. M. Nakariakov, A. R. Inglis, I. V. Zimovets, C. Foullon, E. Verwichte, R.Sych, and I. N. Myagkova. Oscillatory processes in solar (?)ares. Plasma Physicsand Controlled Fusion, 52(12):124009–124016, December 2010. doi: 10.1088/0741-3335/52/12/124009.
Michael Norman. The impact of amr in numerical astrophysics and cosmology.In Timothy J. Barth, Michael Griebel, David E. Keyes, Risto M. Nieminen,Dirk Roose, Tamar Schlick, Tomasz Plewa, Timur Linde, and V. Gregory Weirs,editors, Adaptive Mesh Refinement-Theory and Applications, volume 41, pages413–430. Springer Berlin Heidelberg, 2005. ISBN 978-3-540-27039-3. doi: 10.1007/3-540-27039-6-31.
M. Oka, M. Fujimoto, I. Shinohara, and T. D. Phan.”Island surfing”mech-anism of electron acceleration during magnetic reconnection. Journal of Geo-physical Research (Space Physics), 115:A08223, August 2010a. doi: 10.1029/2010JA015392.
M. Oka, T.-D. Phan, S. Krucker, M. Fujimoto, and I. Shinohara. Electron Accel-eration by Multi-Island Coalescence. Astrophys. J., 714:915–926, May 2010b.doi: 10.1088/0004-637X/714/1/915.
Kevin Olson. Paramesh: A parallel adaptive grid tool. In Parallel Computa-tional Fluid Dynamics, pages 341–348. Elsevier, 2006.
Kevin Olson and Peter MacNeice. An over of the paramesh amr software andsome of its applications. In Adaptive Mesh Refinement-Theory and Applications,Proceedings of the Chicago Workshop on Adaptive Mesh Refinement Methods,Berlin, 2005. Springer.
S. A. Orszag and C.-M. Tang. Small-scale structure of two-dimensional magne-tohydrodynamic turbulence. Journal of Fluid Mechanics, 90:129–143, January1979. doi: 10.1017/S002211207900210X.
M. J. Owens, H. E. Spence, S. McGregor, W. J. Hughes, J. M. Quinn, C. N. Arge,P. Riley, J. Linker, and D. Odstrcil. Metrics for solar wind prediction models:
Comparison of empirical, hybrid, and physics-based schemes with 8 years of l1observations. Space Weather, 6:S08001, 2008.
E. N. Parker. Dynamics of the Interplanetary Gas and Magnetic Fields. As-trophys. J., 128:664–677, November 1958. doi: 10.1086/146579.
Ue-Li Pen, Phil Arras, and ShingKwong Wong. A free, fast, simple, and e(?)cienttotal variation diminishing magnetohydrodynamic code. ApJS, 149(2):447.H. E. Petschek. Magnetic Field Annihilation. NASA Special Publication, 50:425–439, 1964.
K. G. Powell, P. L. Roe, and J. Quirk. Adaptive-mesh algorithms for com-putational (?)uid dynamics. In Algorithmic trends in computational (?)uid dy-namics; The Institute for Computer Applications in Science and Engineering(ICASE)/LaRC Workshop, NASA Langley Research Center, Hampton, VA, US,pages 303–337, 1993.
K. G. Powell, P. L. Roe, T. J. Linde, T. I. Gombosi, and D. L. de Zeeuw. ASolution-Adaptive Upwind Scheme for Ideal Magnetohydrodynamics. J. Com-put. Phys., 154:284–309, September 1999.
E.R. Priest and T.G. Forbes. The magnetic nature of solar (?)ares. Astronomyand Astrophysics Review, 10:313–377, 2002. ISSN 0935-4956. doi: 10.1007/s001590100013.
R. Samtaney, N. F. Loureiro, D. A. Uzdensky, A. A. Schekochihin, and S. C.Cowley. Formation of plasmoid chains in magnetic reconnection. Phys. Rev.Lett., 103(10):105004, Sep 2009. doi: 10.1103/PhysRevLett.103.105004.
V. Sankaran, J. Sitaraman, A. Wissink, A. Datta, B. Jayaraman, M. Potsdam,D. Mavriplis, Z. Yang, D. O’Brien, H. Saberi, R. Cheng, N. Hariharan, and R.Strawn. Application of the helios computational platform to rotorcraft (?)owfields. AIAA-2010-1230, 2010.
V. Sankaran, A. Wissink, A. Datta, J. Sitaraman, B. Jayaraman, M. Potsdam,A. Katz, S. Kamkar, B. Roget, D. Mavriplis, H. Saberi, W. Chen, W. Johnson,and R. Strawn. Overview of the helios version 2.0 computational platform forrotorcraft simulations. 2011. 49th AIAA Aerospace Sciences Meeting includingthe New Horizons Forum and Aerospace Exposition, Orlando, Florida, Jan 4-7,2011, (paper AIAA-2011-1105).
J. Schumacher and B. Kliem. Coalescence of magnetic islands includinganomalous resistivity. Physics of Plasmas, 4:3533–3543, October 1997. doi:10.1063/1.872250.
N. R. Sheeley, Y.-M. Wang, S. H. Hawley, G. E. Brueckner, K. P. Dere, R. A.Howard, M. J. Koomen, C. M. Korendyke, D. J. Michels, S. E. Paswaters, D.G. Socker, O. C. St. Cyr, D. Wang, P. L. Lamy, A. Llebaria, R. Schwenn, G. M.Simnett, S. Plunkett, and D. A. Biesecker. Measurements of (?)ow speeds in thecorona between 2 and 30 r. ApJ, 484(1):472, 1997.
K. Shibata and S. Tanuma. Plasmoid-induced-reconnection and fractal recon-nection. Earth, Planets, and Space, 53:473–482, June 2001.
K. Shibata, S. Masuda, M. Shimojo, H. Hara, T. Yokoyama, S. Tsuneta, T.Kosugi, and Y. Ogawara. Hot-Plasma Ejections Associated with Compact-LoopSolar Flares. Astrophys. J. Lett., 451:L83–L85, October 1995. doi: 10.1086/309688.
Chi-Wang Shu and Stanley Osher. E(?)cient implementation of essentially non-oscillatory shock-capturing schemes, ii. J. Comput. Phys., 83(1):32–78, 1989.ISSN 0021-9991. doi: DOI:10.1016/0021-9991(89)90222-2.
Jayanarayanan Sitaraman, Matthew Floros, Andrew Wissink, and Mark Pots-dam. Parallel domain connectivity algorithm for unsteady (?)ow computationsusing overlapping and adaptive grids. J. Comput. Phys., 229(12):4703–4723,2010. ISSN 0021-9991. doi: 10.1016/j.jcp.2010.03.008.
E. J. Smith and J. H. Wolfe. Observations of interaction regions and corotatingshocks between one and five AU: Pioneers 10 and 11. Geophys. Res. Lett., 2:137–140, 1976.
E. J. Smith, R. G. Marsden, and D. E. Page. ULYSSES above the Sun’s SouthPole-an Introduction. Science, 268:1005–1007, May 1995. doi: 10.1126/science.7754377.
Joseph L. Steger and John A. Benek. On the use of composite grid schemes incomputational aerodynamics. Comput. Meth. Appl. Mech. Eng., 64(1-3):301–320, 1987. ISSN 0045-7825. doi: 10.1016/0045-7825(87)90045-4.
J. M. Stone and T. Gardiner. A simple unsplit Godunov method for multidi-mensional MHD. New Astronomy, 14:139–148, February 2009. doi: 10.1016/j.newast.2008.06.003.
Roger Strawn. High-performance computing for rotorcraft modeling and simu-lation. Computing in Science and Engineering, 12:27–35, 2010. ISSN 1521-9615.doi: 10.1109/MCSE.2010.110.
K. G. Tanaka, T. Yumura, M. Fujimoto, I. Shinohara, S. V. Badman, and A. Gro-cott. Merging of magnetic islands as an e(?)cient accelerator of electrons. Physicsof Plasmas, 17(10):102902–102907, October 2010. doi: 10.1063/1.3491123.
K. G. Tanaka, M. Fujimoto, S. V. Badman, and I. Shinohara. Dynamic magneticisland coalescence and associated electron acceleration. Physics of Plasmas, 18(2):022903–022913, February 2011. doi: 10.1063/1.3554660.
T. Tanaka. Finite volume tvd scheme on an unstructured grid system for three-dimensional mhd simulation of inhomogeneous systems including strong back-ground potential fields. J. Comput. Phys., 111(2):381–389, 1994. ISSN 0021-9991. doi: 10.1006/jcph.1994.1071.
S. Tanuma and K. Shibata. Internal Shocks in the Magnetic Reconnection Jetin Solar Flares: Multiple Fast Shocks Created by the Secondary Tearing Insta-bility. Astrophys. J. Lett., 628:L77–L80, July 2005. doi: 10.1086/432418.
Eleuterio F Toro. Riemann Solvers and Numerical Methods for Fluid Dynamics.Springer Verlag, 2009.
G. T′oth. The·B = 0 Constraint in Shock-Capturing MagnetohydrodynamicsCodes. J. Comput. Phys., 161:605–652, July 2000. doi: 10.1006/jcph.2000.6519.
G. T′oth, I. V. Sokolov, T. I. Gombosi, D. R. Chesney, C. R. Clauer, D. L. DeZeeuw, K. C. Hansen, K. J. Kane, W. B. Manchester, R. C. Oehmke, K. G.Powell, A. J. Ridley, I. I. Roussev, Q. F. Stout, O. Volberg, R. A. Wolf, S.Sazykin, A. Chan, B. Yu, and J. K′ota. Space Weather Modeling Framework: Anew tool for the space science community. J. Geophys. Res., 110:12226–12246,December 2005.
G. T′oth, D. L. de Zeeuw, T. I. Gombosi, and K. G. Powell. A parallel ex-plicit/implicit time stepping scheme on block-adaptive grids. J. Comput. Phys.,217:722–758, September 2006a.
G. T′oth, D. L. de Zeeuw, T. I. Gombosi, and K. G. Powell. A parallel ex-plicit/implicit time stepping scheme on block-adaptive grids. J. Comput. Phys.,217:722–758, September 2006b. doi: 10.1016/j.jcp.2006.01.029.
R. Touma and P. Arminjon. Central finite volume schemes with constrainedtransport divergence treatment for three-dimensional ideal MHD. J. Comput.Phys., 212:617–636, March 2006. doi: 10.1016/j.jcp.2005.07.013.
S. Tsuneta. Structure and Dynamics of Magnetic Reconnection in a Solar Flare.Astrophys. J., 456:840–849, January 1996. doi: 10.1086/176701.M. Ugai. Basic physical mechanism of fast reconnection evolution in spaceplasmas. Space Science Reviews, 95:601–611, 2001. ISSN 0038-6308. doi: 10.1023/A:1005205222921.
A. V. Usmanov, M. L. Goldstein, B. P. Besser, and J. M. Fritzer. A global MHDsolar wind model with WKB Alfv′en waves: Comparison with Ulysses data. J.Geophys. Res., 105:12675–12696, June 2000. doi: 10.1029/1999JA000233.
D. A. Uzdensky. Petschek-like Reconnection with Current-driven AnomalousResistivity and Its Application to Solar Flares. Astrophys. J., 587:450–457,April 2003. doi: 10.1086/368075.
B. van der Holst and R. Keppens. Hybrid block-amr in cartesian and curvilinearcoordinates: Mhd applications. J. Comput. Phys., 226(1):925–946, 2007. ISSN0021-9991. doi: 10.1016/j.jcp.2007.05.007.
H. van der Ven, B. E. Niemann-Tuitman, and A. E. P. Veldman. An explicitmulti-time-stepping algorithm for aerodynamic (?)ows. J. Comput. Appl. Math.,82(1-2):423–431, 1997. ISSN 0377-0427. doi: 10.1016/S0377-0427(97)00054-X.
Rongsheng Wang, Quanming Lu, Aimin Du, and Shui Wang. In situ obser-vations of a secondary magnetic island in an ion di(?)usion region and asso-ciated energetic electrons. Phys. Rev. Lett., 104(17):175003, Apr 2010. doi:10.1103/PhysRevLett.104.175003.
Y. Wang, F. S. Wei, X. S. Feng, S. H. Zhang, P. B. Zuo, and T. R. Sun. Ener-getic Electrons Associated with Magnetic Reconnection in the Magnetic CloudBoundary Layer. Physical Review Letters, 105(19):195007–195010, November2010. doi: 10.1103/PhysRevLett.105.195007.
Y.-M. Wang, E. Robbrecht, and N. R. Sheeley. On the Weakening of the PolarMagnetic Fields during Solar Cycle 23. Astrophys. J., 707:1372–1386, December2009. doi: 10.1088/0004-637X/707/2/1372.
A. Wissink, S. Kamkar, T. Pulliam, J. Sitaraman, and V Sankaran. Cartesianadaptive mesh refinement for rotorcraft wake resolution. 2010. 40th AIAAFluid Dynamics Conference and Exhibit, Chicago, Illinois, June 28-July 1, 2010,(paper AIAA-2010-4554).
A.M. Wissink and R.L. Meakin. On parallel implementations of dynamic oversetgrid methods. In ACM/IEEE 1997 Conference Supercomputing, pages 15–15,1997.
C. Xiao, X. Wang, Z. Pu, H. Zhao, J. Wang, Z. Ma, S. Fu, M. Kivelson, Z. Liu,Q. Zong, K. Glassmeier, A. Balogh, A. Korth, H. Reme, and C. Escoubet. Insitu evidence for the structure of the magnetic null in a 3D reconnection eventin the Earth’s magnetotail. AGU Fall Meeting Abstracts, December 2006.
H. C. Yee and B. Sj¨ogreen. Development of low dissipative high order filterschemes for multiscale navier-stokes/mhd systems. J. Comput. Phys., 225:910–934, July 2007. ISSN 0021-9991.
H. C. Yee and Bj¨orn Sj¨ogreen. E(?)cient low dissipative high order schemes formultiscale mhd (?)ows, ii: Minimization of·B numerical error. J. Sci. Comput.,29:115–164. ISSN 0885-7474.
T. Yokoyama, K. Akita, T. Morimoto, K. Inoue, and J. Newmark. Clear Evi-dence of Reconnection In(?)ow of a Solar Flare. Astrophys. J. Lett., 546:L69–L72,January 2001. doi: 10.1086/318053.
M. Yoshida and A. Kageyama. Application of the Yin-Yang grid to a ther-mal convection of a Boussinesq (?)uid with infinite Prandtl number in a three-dimensional spherical shell. Geophys. Res. Lett., 31:12609–12613, June 2004.
M. Zhang, S.-T. John Yu, S.-C. Henry Lin, S.-C. Chang, and I. Blankson.Solving the MHD equations by the space time conservation element and so-lution element method. J. Comput. Phys., 214:599–617, May 2006. doi:10.1016/j.jcp.2005.10.006.
U. Ziegler. NIRVANA + : An adaptive mesh refinement code for gas dynamicsand MHD. Comput. Phys. Commun., 109:111–134, April 1998.
U. Ziegler. Adaptive Mesh Refinement in MHD Modeling. Realization, Testsand Application. In E. Falgarone & T. Passot, editor, Turbulence and MagneticFields in Astrophysics, volume 614 of Lecture Notes in Physics, Berlin SpringerVerlag, pages 127–151, 2003.
U. Ziegler. A central-constrained transport scheme for ideal magnetohydrody-namics. J. Comput. Phys., 196:393–416, May 2004. ISSN 0021-9991.
U. Ziegler. A solution-adaptive central-constraint transport scheme for mag-netohydrodynamics. Comput. Phys. Commun., 170(2):153–174, 2005. ISSN0010-4655. doi: 10.1016/j.cpc.2005.04.002.
U. Ziegler. The NIRVANA code: Parallel computational MHD with adaptivemesh refinement. Comput. Phys. Commun., 179:227–244, August 2008. doi:10.1016/j.cpc.2008.02.017.
U. Ziegler. A semi-discrete central scheme for magnetohydrodynamics onorthogonal-curvilinear grids. J. Comput. Phys., 230:1035–1063, January 2011.ISSN 0021-9991.