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Splitting based scheme for three-dimensional MHD with dual time stepping

Fu Huazheng Feng Xueshang

Fu Huazheng, Feng Xueshang. Splitting based scheme for three-dimensional MHD with dual time stepping[J]. 空间科学学报, 2015, 35(1): 9-17. doi: 10.11728/cjss2015.01.009
引用本文: Fu Huazheng, Feng Xueshang. Splitting based scheme for three-dimensional MHD with dual time stepping[J]. 空间科学学报, 2015, 35(1): 9-17. doi: 10.11728/cjss2015.01.009
Fu Huazheng, Feng Xueshang. Splitting based scheme for three-dimensional MHD with dual time stepping[J]. Journal of Space Science, 2015, 35(1): 9-17. doi: 10.11728/cjss2015.01.009
Citation: Fu Huazheng, Feng Xueshang. Splitting based scheme for three-dimensional MHD with dual time stepping[J]. Journal of Space Science, 2015, 35(1): 9-17. doi: 10.11728/cjss2015.01.009

Splitting based scheme for three-dimensional MHD with dual time stepping

doi: 10.11728/cjss2015.01.009
基金项目: Supported by the National Basic Research Program of China (2012CB825601), the National Natural Science Foundation of China (41031066, 41231068, 41274192, 41074121, 41204127), the Knowledge Innovation Program of the Chinese Academy of Sciences (KZZD-EW-01-4), and the Specialized Research Fund for State Key Laboratories
详细信息
  • 中图分类号: P35

Splitting based scheme for three-dimensional MHD with dual time stepping

Funds: Supported by the National Basic Research Program of China (2012CB825601), the National Natural Science Foundation of China (41031066, 41231068, 41274192, 41074121, 41204127), the Knowledge Innovation Program of the Chinese Academy of Sciences (KZZD-EW-01-4), and the Specialized Research Fund for State Key Laboratories
  • 摘要: A new hybrid numerical scheme of combining an E-CUSP (Energy-Convective Upwind and Split Pressure) method for the fluid part and the Constrained Transport (CT) for the magnetic induction part is proposed. In order to avoid the occurrence of negative pressure in the reconstructed profiles and its updated value, a positivity preserving method is provided. Furthermore, the MHD equations are solved at each physical time step by advancing in pseudo time. The use of dual time stepping is beneficial in the computation since the use of dual time stepping allows the physical time step not to be limited by the corresponding values in the smallest cell and to be selected based on the numerical accuracy criterion. This newly established hybrid scheme combined with positivity preserving method and dual time technique has demonstrated the accurateness and robustness through numerical experiments of benchmark problems such as the 2D Orszag-Tang vortex problem and the 3D shock-cloud interaction problem.

     

  • [1] Jameson A. Analysis and design of numerical schemes for gas dynamics, 1: artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence [J]. Intern. J. Comput. Fluid Dyn., 1995, 4(3/4):171-218
    [2] Jameson A. Analysis and design of numerical schemes for gas dynamics, 2: Artificial diffusion and discrete shock structure [J]. Intern. J. Comput. Fluid Dyn., 1995, 5(1/2):1-38
    [3] Fuchs F G, Mishra S, Risebro N H. Splitting based finite volume schemes for ideal MHD equations [J]. J. Comput. Phys., 2009, 228(3):641-660
    [4] Shen Y, Zha G, Huerta M A. E-CUSP scheme for the equations of ideal magnetohydrodynamics with high order WENO Scheme[J]. J. Comput. Phys., 2012, 231(19): 6233-6247
    [5] Balsara D S. Self-adjusting, positivity preserving high order schemes for hydrodynamics and magnetohydrodynamics[J]. J. Comput. Phys., 2012, 231(22):7504-7517
    [6] Ziegler U. A central-constrained transport scheme for ideal magnetohydrodynamics [J]. J. Comput. Phys., 2004, 196(2):393-416
    [7] Ziegler U. A solution-adaptive central-constraint transport scheme for magnetohydrodynamics [J]. Comput. Phys. Commun., 2005, 170(2):153-174
    [8] Uygun M, K1rkköprü K. Computation of time-accurate laminar flows using dual time stepping and local preconditioning with multigrid [J]. Turkish J. Eng. Environ. Sci., 2007, 31(4):211-223
    [9] Zhao Y, Hui Tan H, Zhang B. A high-resolution characteristics-based implicit dual time-stepping VOF method for free surface flow simulation on unstructured grids [J]. J. Comput. Phys., 2002, 183(1):233-273
    [10] Zha G C, Shen Y, Wang B. An improved low diffusion E-CUSP upwind scheme [J]. Comput. Fluid., 2011, 48(1):214-220
    [11] Feng X, Yang L, Xiang C, et al. Three-dimensional solar wind modeling from the Sun to Earth by a SIP-CESE MHD model with a six-component grid [J]. Astrophy. J.,2010, 723(1):300
    [12] Feng X, Zhang S, Xiang C, et al. A hybrid solar wind model of the CESE+ HLL method with a Yin-Yang overset grid and an AMR grid [J]. Astrophys. J., 2011, 734(1):50
    [13] Feng X, Jiang C, Xiang C, et al. A data-driven model for the global coronal evolution [J]. Astrophys. J., 2012, 758(1):62
    [14] Feng X, Xiang C, Zhong D. The state-of-art of three-dimensional numerical study for corona-interplanetary process of solar storms,[J]. Sci. Sin. Terr., 2011, 41:1-28. In Chinese (冯学尚, 向长青, 钟鼎坤. 太阳风暴的日冕行星际过程三维数值研究进展,[J]. 中国科学, 2011, 41:1-28)
    [15] Feng X, Yang L, Xiang C, et al. Validation of the 3D AMR SIP-CESE solar wind model for four Carrington rotations [J]. Solar Phys., 2012, 279(1):207-229
    [16] Keppens R, Meliani Z, Van Marle A J, et al. Parallel, gridadaptive approaches for relativistic hydro and magnetohydrodynamics [J]. J. Comput. Phys., 2012, 231(3):718-744
    [17] Zhao H Y, Li J L. Application analysis on dual-time stepping,[J]. Chin. J. Comput. Phys., 2008, 25(3):5-10. In Chinese (赵慧勇,乐嘉陵.双时间步方法 的应用分析,[J]. 计算物理, 2008, 25(3):5-10)
    [18] Jameson A. Time dependent calculations using multigrid, with applications to unsteady flows past airfoils and wings [R], AIAA 91-1596. Honolulu: AIAA, 1991
    [19] Balbás J, Tadmor E, Wu C C. Non-oscillatory central schemes for one- and two-dimensional MHD equations: I [J]. J. Comput. Phys., 2004, 201(1):261-285
    [20] Xueshang F, Yufen Z, Yanqi H. A 3rd order WENO GLM-MHD scheme for magnetic reconnection [J]. Chin. J. Space Sci., 2006, 26(1): 1-7
    [21] Jiang G S, Wu C. A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics [J]. J. Comput. Phys., 1999, 150(2):561-594
    [22] 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
    [23] Tang H Z, Xu K. A high-order gas-kinetic method for multidimensional ideal magnetohydrodynamics [J]. J. Comput. Phys., 2000, 165(1):69-88
    [24] Zhu Yufen, Feng Xueshang. A new hybrid numerical scheme for two-dimensional ideal MHD equations [J]. Chin. Phys. Lett., 2012, 29(9):094703
    [25] Kifonidis K, Müller E. On multigrid solution of the implicit equations of hydrodynamics Experiments for the compressible Euler equations in general coordinates [J]. Astron. Astrophys., 2012, 544, A47
    [26] Turkel E. Preconditioning techniques in computational fluid dynamics [J]. Ann. Rev. Fluid Mech., 1999, 31(1): 385-416
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出版历程
  • 收稿日期:  2013-12-18
  • 修回日期:  2014-05-29
  • 刊出日期:  2015-01-15

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