采用重组模板的权重优化WENO-Z格式
2024,46(1):187-197
柴得林
中国空气动力研究与发展中心 结冰与防除冰重点实验室, 四川 绵阳 621000，chaidelin@cardc.cn
王强
中国空气动力研究与发展中心 结冰与防除冰重点实验室, 四川 绵阳 621000;
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, 四川 绵阳 621000
易贤
中国空气动力研究与发展中心 结冰与防除冰重点实验室, 四川 绵阳 621000;
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, 四川 绵阳 621000
刘宇
中国空气动力研究与发展中心 结冰与防除冰重点实验室, 四川 绵阳 621000
中国空气动力研究与发展中心 结冰与防除冰重点实验室, 四川 绵阳 621000，chaidelin@cardc.cn
王强
中国空气动力研究与发展中心 结冰与防除冰重点实验室, 四川 绵阳 621000;
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, 四川 绵阳 621000
易贤
中国空气动力研究与发展中心 结冰与防除冰重点实验室, 四川 绵阳 621000;
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, 四川 绵阳 621000
刘宇
中国空气动力研究与发展中心 结冰与防除冰重点实验室, 四川 绵阳 621000
摘要：
针对精确模拟含激波等复杂流动结构的流场对高精度格式的低耗散低色散要求,基于5阶有限差分WENO-Z格式,提出一种模板重组技术。在计算WENO非线性权时,引入一个由3点模板重新组合的4点模板,优化原格式中各模板的权重分配,进而提出了两种改进WENO-Z格式。采用近似色散关系分析方法对改进前后格式色散与耗散特性进行了对比与分析。分析表明:两种改进格式耗散有不同程度的降低。数值实验表明:改进格式具有更优越的激波捕捉性能,对小尺度流场结构具有更高的分辨率。
针对精确模拟含激波等复杂流动结构的流场对高精度格式的低耗散低色散要求,基于5阶有限差分WENO-Z格式,提出一种模板重组技术。在计算WENO非线性权时,引入一个由3点模板重新组合的4点模板,优化原格式中各模板的权重分配,进而提出了两种改进WENO-Z格式。采用近似色散关系分析方法对改进前后格式色散与耗散特性进行了对比与分析。分析表明:两种改进格式耗散有不同程度的降低。数值实验表明:改进格式具有更优越的激波捕捉性能,对小尺度流场结构具有更高的分辨率。
基金项目：
国家科技重大专项资助项目(J2019-Ⅲ-0010-0054)；国家自然科学基金资助项目(12172372)
国家科技重大专项资助项目(J2019-Ⅲ-0010-0054)；国家自然科学基金资助项目(12172372)
Weight-optimized WENO-Z schemes with reorganized stencil
CHAI Delin
Key Laboratory of Icing and Anti/De-Icing, China Aerodynamics Research and Development Center, Mianyang 621000, China,chaidelin@cardc.cn
WANG Qiang
Key Laboratory of Icing and Anti/De-Icing, China Aerodynamics Research and Development Center, Mianyang 621000, China;
State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, China
YI Xian
Key Laboratory of Icing and Anti/De-Icing, China Aerodynamics Research and Development Center, Mianyang 621000, China;
State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, China
LIU Yu
Key Laboratory of Icing and Anti/De-Icing, China Aerodynamics Research and Development Center, Mianyang 621000, China
Key Laboratory of Icing and Anti/De-Icing, China Aerodynamics Research and Development Center, Mianyang 621000, China,chaidelin@cardc.cn
WANG Qiang
Key Laboratory of Icing and Anti/De-Icing, China Aerodynamics Research and Development Center, Mianyang 621000, China;
State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, China
YI Xian
Key Laboratory of Icing and Anti/De-Icing, China Aerodynamics Research and Development Center, Mianyang 621000, China;
State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, China
LIU Yu
Key Laboratory of Icing and Anti/De-Icing, China Aerodynamics Research and Development Center, Mianyang 621000, China
Abstract：
For developing high-order scheme with low dissipation and low dispersion to accurately simulate the flow field with complex structures such as shock wave, a method of stencil reorganization was proposed based on the fifth-order finite difference WENO-Z scheme. A four-point central stencil recombined by three-point stencils is introduced in the calculation of WENO nonlinear weight in order to optimize the weight allocation of each template in the original format, and two improved WENO-Z schemes were proposed. The dispersion and dissipation properties of the schemes were compared and analyzed via the approximate dispersion relation analysis, which shows that the dissipation of the two improved schemes decreases at different extent. The numerical experiments show that the improved schemes have better shock capture property and higher resolution for small-scale flow structures.
For developing high-order scheme with low dissipation and low dispersion to accurately simulate the flow field with complex structures such as shock wave, a method of stencil reorganization was proposed based on the fifth-order finite difference WENO-Z scheme. A four-point central stencil recombined by three-point stencils is introduced in the calculation of WENO nonlinear weight in order to optimize the weight allocation of each template in the original format, and two improved WENO-Z schemes were proposed. The dispersion and dissipation properties of the schemes were compared and analyzed via the approximate dispersion relation analysis, which shows that the dissipation of the two improved schemes decreases at different extent. The numerical experiments show that the improved schemes have better shock capture property and higher resolution for small-scale flow structures.
收稿日期：
2021-10-10
2021-10-10
