上海交通大学学报

上海交通大学学报 >

2023 , Vol. 57 >Issue 6: 719 - 727

DOI: https://doi.org/10.16183/j.cnki.jsjtu.2022.014

航空航天

高精度WCNS格式加权策略改进与数值验证

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  • 上海交通大学 航空航天学院,上海 200240
杨 强(1995-),硕士生,从事飞行器设计研究.

收稿日期: 2022-01-17

  修回日期: 2022-06-14

  录用日期: 2022-07-12

  网络出版日期: 2022-09-16

基金资助

国家自然科学基金(92052101)

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Improvement and Numerical Verification of Weighting Strategy for High Precision WCNS Scheme

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  • School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China

Received date: 2022-01-17

  Revised date: 2022-06-14

  Accepted date: 2022-07-12

  Online published: 2022-09-16

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摘要

为了揭示复杂的流动机理,国内外提出了一系列高阶精度格式,其中加权非线性紧致格式(WCNS)具有良好的激波捕捉能力,已广泛用于复杂流动数值模拟,然而在模拟小尺度流动时分辨率不足、耗散偏大.在WCNS的框架下,借鉴基于目标本质无振荡(TENO)格式的加权策略,将间断检测和模板加权的新方法引入WCNS构造中,发展了一种7阶精度的WCNS7-T格式,通过一维激波管问题和二维黎曼问题等开展算例测试,并与传统的WCNS7-Z格式计算结果进行对比来验证新格式的改善性能.数值实验表明,WCNS7-T格式更好地抑制了间断附近的数值振荡,在提高分辨率和激波捕捉能力的同时也进一步降低了耗散.

关键词： 可压缩流动; 高精度格式; 激波间断; 非线性加权

本文引用格式

杨强, 李伟鹏 . 高精度WCNS格式加权策略改进与数值验证[J]. 上海交通大学学报, 2023 , 57(6) : 719 -727 . DOI: 10.16183/j.cnki.jsjtu.2022.014

Abstract

In order to reveal the complex flow mechanism, a series of high-order precision schemes have been proposed at home and abroad, of which, the weighted compact nonlinear scheme (WCNS) has a good shock capture ability and has been widely used in the numerical simulation of complex flows. However, it has insufficient resolution and large dissipation in the simulation of small-scale flows. In the framework of the WCNS, by using the weighting strategy of the targeted essentially non-oscillatory (TENO) scheme for reference, this paper introduces the new methods of discontinuity detection and template weighting into the construction of the WCNS scheme, and develops a WCNS7-T scheme with a 7-order accuracy. Example tests are conducted through one-dimensional shock tube problem and two-dimensional Riemann problem. By comparing with the traditional WCNS7-Z scheme, the improved performance of the new scheme is verified. The numerical experiments show that the WCNS7-T scheme can better suppress the numerical oscillation near the discontinuity, improve the resolution and shock capture ability, and further reduce the dissipation.

Key words： compressible flow; high precision scheme; shock discontinuity; nonlinear weighting

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