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一种求解双曲守恒律方程的中心型WENO格式

李辰1,2, 郭启龙1,2, 孙东1,2, 刘朋欣1,2   

  1. 1 中国空气动力研究与发展中心, 空气动力学国家重点实验室, 绵阳 621000;
    2 中国空气动力研究与发展中心, 计算空气动力研究所, 绵阳 621000
  • 收稿日期:2019-10-15 出版日期:2020-09-15 发布日期:2020-09-15
  • 通讯作者: 李辰,Email:lichen@skla.cardc.cn.
  • 基金资助:

    国家数值风洞工程,中国空气动力研究与发展中心前沿技术研究基金(PJD20180204)和国家自然科学基金(11802324)资助.

李辰, 郭启龙, 孙东, 刘朋欣. 一种求解双曲守恒律方程的中心型WENO格式[J]. 数值计算与计算机应用, 2020, 41(3): 246-258.

Li Chen, Guo Qilong, Sun Dong, Liu Pengxin. A CENTRAL WENO SCHEME FOR HYPERBOLIC CONSERVATION LAWS[J]. Journal of Numerical Methods and Computer Applications, 2020, 41(3): 246-258.

A CENTRAL WENO SCHEME FOR HYPERBOLIC CONSERVATION LAWS

Li Chen1,2, Guo Qilong1,2, Sun Dong1,2, Liu Pengxin1,2   

  1. 1 State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, China;
    2 Computational Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China
  • Received:2019-10-15 Online:2020-09-15 Published:2020-09-15
本文发展了一种中心型加权本质无振荡(WENO)格式.该格式通过在原始三阶WENO-JS格式的下风方向增加一个两点候选模板,并将文献[11]中的非线性自适应机制推广到r=2情况,格式记为WENO4-CU.经过近似色散关系分析可以看到,WENO4-CU格式的频谱特性较原始三阶WENO-JS格式具有明显的改进.通过六个典型算例的数值测试表明,WENO4-CU格式在对流动结构的分辨上较原始WENO3-JS、WENO3-M和WENO3-Z格式具有明显提高.
A central weighted essentially non-oscillatory (WENO) scheme is presented in this paper. A two-point candidate sub-stencil is added downwind based on the third-order WENO-JS scheme, and the nonlinear adaption mechanism of reference[11] is extended to the version of r=2. The scheme is named as WENO4-CU, the spectral properties of which are improved compared with the original third-order WENO-JS through approximate dispersion relation analysis. Numerical tests of six benchmarks demonstrate that the WENO4-CU scheme has better performance in contrast with WENO3-JS, WENO3-M and WENO3-Z schemes on resolving flow structures.

MR(2010)主题分类: 

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