Citation: | ZHANG Jingke, LI Huichao. Two Upstream Splitting Schemes for Generalized Lagrange Multiplier Magnetohydrodynamics[J]. Chinese Journal of Space Science, 2017, 37(1): 8-18. doi: 10.11728/cjss2017.01.008 |
[1] |
ANNETTE P, DOUGLAS B, DUSAN O, et al. Wang-Sheeley-Arge-Enlil cone model transitions to opera-tions[J]. Space Weather, 2011, 9(3):420-424
|
[2] |
RILEY P, LIONELLO R, LINKER J A, et al. Global MHD modeling of the solar corona and inner heliosphere for the whole heliosphere interval[J]. Solar Phys., 2011, 274 (1/2):361-377
|
[3] |
YANG Liping, FENG Xueshang, XIANG Changqing, et al. Time-dependent MHD modeling of the global solar corona for year 2007:driven by daily-updated magnetic field synoptic data[J]. J. Geophys. Res., 2012, 117(A8):101-110
|
[4] |
FENG X A, ZHOU Y F, WU S T. A novel numerical implementation for solar wind modeling by the modified conservation element/solution element method[J]. Astrophys. J., 2007, 655(2):1110-1126
|
[5] |
FORBES T G, LINKER J A, CHEN J, et al. CME theory and models[J]. Space Sci. Rev., 2006, 123(1/2/3):251-302
|
[6] |
LYON J G, FEDDER J A, MOBARRY C M. The Lyon-Fedder-Mobarry (LFM) global MHD magnetosphe-ric simu-lation code[J]. J. Atmos. Solar-Terr. Phys., 2004, 66(15/16):1333-1350
|
[7] |
FENG Xueshang, XIANG Changqing, ZHONG Dingkun. Numerical study of interplanetary solar storms[J]. Sci. Sin. Terr., 2013, 43(6):912-933(冯学尚, 向长青, 钟鼎坤. 行星际太阳风暴的数值模拟研究[J]. 中国科学:地球科学, 2013, 43(6):912-933)
|
[8] |
HAN S H, LEE J I, KIM K H. Accurate and robust pressure weight advection upstream splitting method for magnetohydrodynamics equations[J]. AIAA J., 2009, 47(4):970-981
|
[9] |
BRIO M, WU C C. An upwind differencing scheme for the equations of ideal magnetohydrodynamics[J]. J. Comput. Phys., 1988, 75(2):400-422
|
[10] |
JANHUNEN P. A positive conservative method for magnetohydrodynamics Based HLL and Roe methods[J]. J. Comput. Phys., 2000, 160(2):649-661
|
[11] |
STEGER J L, WARMING R F. Flux vector splitting of the inviscid gas dynamic equation with application to finite-difference methods[J]. J. Comput. Phys., 1981, 40(2):263-293
|
[12] |
LIN S J, CHAO W C, SUD Y C, et al. A class of the Van Leer-type transport schemes and its application to the moisture transport in a general circulation model[J]. Monthly Weather Rev., 1994, 122(7):1575-1593
|
[13] |
LIOU M S, STEFFEN C J. A new flux splitting scheme[J]. J. Comput. Phys., 1993, 107(1):23-39
|
[14] |
MACCORMACK R W. Numerical computation in magnetofluid dynamics[C]//Computational fluid dynamics for the 21st century. Berlin:Splinger, 2001:369-384
|
[15] |
PAN Yong, WANG Jiangfeng, WU Yizhao. A new Jacobian matrix splitting method for MHD equations upwind scheme[J]. Acta Aerodyn. Sin., 2008, 26(2):249-256(潘勇, 王江峰, 伍贻兆. 一种新的用于MHD方程逆风格式的Jacobian矩阵分裂方法[J]. 空气动力学学报, 2008, 26(2):249-256)
|
[16] |
TÓTH G. The ▽·B=0 constraint in shock-capturing ma-gnetohydrodynamics codes[J]. J. Comput. Phys., 2000, 161(2):605-652
|
[17] |
BRACKBILL J U, BARNES D C. The effect of nonzero a·B on the numerical solution of the magnetohydrodynamic equations[J]. J. Comput. Phys., 1980, 35(3):426-430
|
[18] |
EVANS C R, HAWLEY J F. Simulation of magnetohydrodynamic flows-A constrained transport method[J]. Astrophys. J., 1988, 332(2):659-677
|
[19] |
POWELL K G, ROE P L, LINDE T J, et al. A solution-adaptive upwind scheme for ideal magnetohydrodyna-mics[J]. J. Comput. Phys., 1999, 154(2):284-309
|
[20] |
DEDNER A, KEMM F, KRONER D, et al. Hyperbolic divergence cleaning for the MHD equations[J]. J. Comput. Phys., 2002, 175(2):645-673
|
[21] |
MIGNONE A, TZEFERACOS P. A second-order unsplit Godunov scheme for cell-centered MHD:the CTU-GLM scheme[J]. J. Comput. Phys., 2010, 229(6):2117-2138
|
[22] |
JIANG Chaowei, FENG Xueshang, ZHANG Jian. AMR Simulations of magnetohydrodynamic problems by the CESE method in curvilinear coordinates[J]. Solar Phys., 2010, 267(2):463-491
|
[23] |
ZHANG Deliang. A Course in Computational Fluid Dynamics[M]. Beijing:Higher Education Press, 2011(张德良. 计算流体力学导论[M]. 北京:高等教育出版社, 2011)
|
[24] |
DONTCHEV A L, HAGER W W, VELIOV V M. Second-order Runge-Kutta approximations in control constrained optical control[J]. SIAM J. Numer. Anal., 2000, 38(1):202-226
|
[25] |
ZHANG M, YU S J, LIN S, et al. Solving the MHD equations by the space-time Conserving Element and Solution Element method[J]. J. Comput. Phys., 2006, 214(2):599-617
|
[26] |
FENG Xueshang, ZHOU Yufen, HU Yanqi. A 3rd order WENO GLM-MHD scheme for magnetic reconnection[J]. Chin. J. Space Sci., 2006, 26(1):1-7
|
[27] |
ZACHARY A L, MALAGOLI A, COLELLA P. A higher-order Godunov method for multidimensional ideal magnetohydrodynamics[J]. SIAM J. Sci. Comput., 1994, 15(2):263-284
|
[28] |
TANG Huazhong, XU Kun. A high-order gas-kinetic method for multidimensional ideal magnetohydrodyna-mics[J]. J. Comput. Phys., 2000, 165(1):69-88
|