Space Science Reviews

, Volume 107, Issue 1–2, pp 43–53

A Class of TVD Type Combined Numerical Scheme for MHD Equations With a Survey About Numerical Methods in Solar Wind Simulations

  • Xueshang Feng
  • S.T. Wu
  • Fengsi Wei
  • Quanlin Fan
Article

DOI: 10.1023/A:1025547016708

Cite this article as:
Feng, X., Wu, S., Wei, F. et al. Space Science Reviews (2003) 107: 43. doi:10.1023/A:1025547016708

Abstract

It has been believed that three-dimensional, numerical, magnetohydrodynamic (MHD) modelling must play a crucial role in a seamless forecasting system. This system refers to space weather originating on the sun; propagation of disturbances through the solar wind and interplanetary magnetic field (IMF), and thence, transmission into the magnetosphere, ionosphere, and thermosphere. This role comes as no surprise to numerical modelers that participate in the numerical modelling of atmospheric environments as well as the meteorological conditions at Earth. Space scientists have paid great attention to operational numerical space weather prediction models. To this purpose practical progress has been made in the past years. Here first is reviewed the progress of the numerical methods in solar wind modelling. Then, based on our discussion, a new numerical scheme of total variation diminishing (TVD) type for magnetohydrodynamic equations in spherical coordinates is proposed by taking into account convergence, stability and resolution. This new MHD model is established by solving the fluid equations of MHD system with a modified Lax-Friedrichs scheme and the magnetic induction equations with MacCormack II scheme for the purpose of developing a combined scheme of quick convergence as well as of TVD property. To verify the validation of the scheme, the propagation of one-dimensional MHD fast and slow shock problem is discussed with the numerical results conforming to the existing results obtained by the piece-wise parabolic method (PPM). Finally, some conclusions are made.

combined numerical scheme of TVD type numerical methods solar wind simulations 

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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Xueshang Feng
    • 1
  • S.T. Wu
    • 2
  • Fengsi Wei
    • 1
  • Quanlin Fan
    • 1
  1. 1.Laboratory for Space Weather, Center for Space Science and Applied ResearchBeijing
  2. 2.Center for Space Physics and Aeronomic ResearchThe University ofAlabama in HuntsvilleUSA

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