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Hybrid WENO schemes with different indicators on curvilinear grids

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Abstract

In {J. Comput. Phys. 229 (2010) 8105-8129}, we studied hybrid weighted essentially non-oscillatory (WENO) schemes with different indicators for hyperbolic conservation laws on uniform grids for Cartesian domains. In this paper, we extend the schemes to solve two-dimensional systems of hyperbolic conservation laws on curvilinear grids for non-Cartesian domains. Our goal is to obtain similar advantageous properties as those of the hybrid WENO schemes on uniform grids for Cartesian domains. Extensive numerical results strongly support that the hybrid WENO schemes with discontinuity indicators on curvilinear grids can also save considerably on computational cost in contrast to the pure WENO schemes. They also maintain the essentially non-oscillatory property for general solutions with discontinuities and keep the sharp shock transition.

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Authors and Affiliations

  1. School of Mathematical Sciences, Qingdao University, Qingdao, Shandong, 266071, Peoples’s Republic of China

    Gang Li

  2. School of Mathematical Sciences, Xiamen University, Xiamen, Fujian, 361005, Peoples’s Republic of China

    Jianxian Qiu

Authors
  1. Gang Li
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  2. Jianxian Qiu
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Correspondence to Jianxian Qiu.

Additional information

Communicated by: Robert Schaback

The research was partially supported by NSFC grant No. 10931004, 11201254, 91230110, ISTCP of China grant No. 2010DFR00700 and the Project for Scientific Plan of Higher Education in Shandong Providence of China grant No. J12LI08.

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Li, G., Qiu, J. Hybrid WENO schemes with different indicators on curvilinear grids. Adv Comput Math 40, 747–772 (2014). https://doi.org/10.1007/s10444-013-9322-3

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  • DOI: https://doi.org/10.1007/s10444-013-9322-3

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