Volume 35 Issue 1
Jan.  2015
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Fu Huazheng, Feng Xueshang. Splitting based scheme for three-dimensional MHD with dual time stepping[J]. Chinese 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]. Chinese Journal of Space Science, 2015, 35(1): 9-17. doi: 10.11728/cjss2015.01.009
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Splitting based scheme for three-dimensional MHD with dual time stepping

doi: 10.11728/cjss2015.01.009 cstr: 32142.14.cjss2015.01.009
  • 1.

    State Key Laboratory for Space Weather, Center for Space Science and Applied Research,Chinese Academy of Sciences, Beijing 100190

  • 2.

    University of Chinese Academy of Sciences, Beijing 100049

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
  • Received Date: 2013-12-18
  • Rev Recd Date: 2014-05-29
  • Publish Date: 2015-01-15
    Abstract
  • 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.

     

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