CHINESE JOURNAL OF COMPUTATIONAL PHYSICS ›› 2018, Vol. 35 ›› Issue (5): 525-534.DOI: 10.19596/j.cnki.1001-246x.7811

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Weighted Essentially Non-oscillatory Schemes on Unstructured Quadrilateral Meshes

ZHAO Fengxiang1,2, PAN Liang2, WANG Shuanghu2   

  1. 1. The Graduate School of China Academy of Engineering Physics, Beijing 100088, China;
    2. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
  • Received:2017-12-11 Revised:2017-12-25 Online:2018-09-25 Published:2018-09-25

Abstract: A third-order weighted essentially non-oscillatory (WENO) scheme is developed for hyperbolic conservation laws on unstructured quadrilateral meshes. As starting point of WENO reconstruction, a general stencil is proposed for any local topology on quadrilateral meshes. With selected stencil, a unified linear scheme was constructed. However, very large weights and non-negative may appear, which leads the scheme unstable even for smooth flows. An optimization approach is given to deal with very large linear weights on unstructured meshes. Splitting technique is considered to deal with negative weights obtained by optimization approach. Non-linear weight with a new smooth indicator is proposed as well. With optimization approach for very large weights and splitting technique for negative weights, the current scheme becomes more robust. Numerical tests are presented to validate accuracy. Expected convergence rate of accuracy is obtained. And absolute value of error is not affected by mesh quality. Numerical results for flow with strong discontinuities are presented to validate robustness of the WENO scheme.

Key words: WENO reconstruction, unstructured quadrilateral meshes, hyperbolic conservation laws, finite volume method

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