Moving mesh methods with locally varying time steps

  • Authors:

  • Zhijun Tan;Zhengru Zhang;Yunqing Huang;Tao Tang

  • Affiliations:

  • Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China;Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China;Department of Mathematics and Institute for Computational and Applied Mathematics, Xiangtan University, Xiangtan, Hunan 411105, China;Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China and Institute of Computational Mathematics, The Chinese Academy of Sciences, Beijing 100080, China

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2004

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Abstract

The time steps associated with moving mesh methods are proportional to the smallest mesh size in space and as a result they are very small at each time level. For some practical problems, the physical phenomena develop dynamically singular or nearly singular solutions in fairly localized regions, and therefore the smallest time step at each time level occurs only in these localized regions. In this work, we will develop a local time stepping algorithm for the moving mesh methods. The principal idea will be demonstrated by investigating the nonlinear hyperbolic conservation laws. Numerical experiments are carried out to demonstrate the efficiency and robustness of the proposed methods.