广义拉格朗日乘子MHD方程组的两类逆风分裂格式

张珂; 李会超

doi:10.11728/cjss2017.01.008

广义拉格朗日乘子MHD方程组的两类逆风分裂格式

doi: 10.11728/cjss2017.01.008

张珂,
李会超^,

中国科学院国家空间科学中心空间天气学国家重点实验室北京 100190;中国科学院大学北京 100049

基金项目:

国家自然科学基金项目资助（41231068，41204127）

详细信息

通讯作者:
李会超,E-mail:hcli@spaceweather.ac.cn

中图分类号: P353
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- 被引次数: 0
出版历程
- 收稿日期: 2015-05-18
- 修回日期: 2016-09-11
- 刊出日期: 2017-01-15

Two Upstream Splitting Schemes for Generalized Lagrange Multiplier Magnetohydrodynamics

ZHANG Jingke,
LI Huichao^,

State Key Laboratory of Space Weather, National Space Science Center, Chinese Academy of Sciences, Beijing 100190;University of Chinese Academy of Sciences, Beijing 100049

摘要

摘要: 开发高性能的磁流体力学数值模拟方法是提高空间天气数值预报研究的一个重要方面.有限体积法的逆风分裂格式具有良好的间断捕获能力，Steger-Warming和AUSM（Advection Upstream Splitting Method）是逆风分裂格式FVS（Flux Vector Splitting）方法中具有代表性的两种格式.采用这两种格式求解具有伽利略不变性的扩展型广义拉格朗日乘子磁流体力学（EGLM-MHD）方程组，对Orszag-Tang涡流问题和三维爆炸波问题进行数值模拟，结果表明两种格式均能得到稳定精确的数值结果.与Steger-Warming格式相比，AUSM格式产生的磁场散度误差更小，计算速度更快.
- 磁流体力学数值模拟 /
- Steger-Warming格式 /
- AUSM格式
Abstract: To develop a high performance MHD numerical simulation method is an important factor in research of numerical prediction of space weather. The upwind flux splitting scheme based on finite volume method has good ability to capture discontinuities. Steger-Warming and AUSM (Advection Upstream Splitting Method) schemes are two outstanding upwind flux splitting scheme, which are classified as FVS (Flux Vector Splitting) method. In this paper, these two schemes are applied to solve the Extended Generalized Lagrange Multiplier Magnetohydrodynamics (EGLM-MHD) equation with Galilean invariance. Results obtained from Orszag-Tang vortex and three-dimensional blastwave problem indicate that those two schemes are both robust and accurate. Particularly, AUSM scheme is superior to Steger-Warming scheme in divergence error control and computational speed.
- MHD numerical simulation /
- Steger-Warming scheme /
- AUSM scheme

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参考文献(28)

[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