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• 日球层物理和太阳系探测 • Previous Articles     Next Articles

Application of ADER Scheme in MHD Simulation

ZHANG Yanyan1,2, FENG Xueshang1, JIANG Chaowei1,2, ZHOU Yufen1   

  1. 1. State Key Laboratory of Space Weather, Center for Space Science and Applied Research, Chinese Academy of Sciences, Beijing 100190;
    2. Graduate University of Chinese Academy of Sciences, Beijing 100049
  • Received:2011-01-20 Revised:2011-08-10 Online:2012-03-15 Published:2012-03-15

Abstract: The Arbitrary accuracy Derivatives Riemann problem method (ADER) scheme is a new high order numerical scheme based on the concept of finite volume integration, and it is very easy to be extended up to any order of space and time accuracy by using a Taylor time expansion at the cell interface position. So far the approach has been applied successfully to flow mechanics problems. Our objective here is to carry out the extension of multidimensional ADER schemes to multidimensional MHD systems of conservation laws by calculating several MHD problems in one and two dimensions: (ⅰ) Brio-Wu shock tube problem, (ⅱ) Dai-Woodward shock tube problem, (ⅲ) Orszag-Tang MHD vortex problem. The numerical results prove that the ADER scheme possesses the ability to solve MHD problem, remains high order accuracy both in space and time, keeps precise in capturing the shock. Meanwhile, the compared tests show that the ADER scheme can restrain the oscillation and obtain the high order non-oscillatory result.

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