北京航空航天大学学报 ›› 2017, Vol. 43 ›› Issue (8): 1602-1609.doi: 10.13700/j.bh.1001-5965.2016.0623

• 论文 • 上一篇    下一篇

适于可压缩多尺度流动的紧致型激波捕捉格式

李彦苏, 阎超, 于剑   

  1. 北京航空航天大学航空科学与工程学院, 北京 100083
  • 收稿日期:2016-07-27 修回日期:2016-11-11 出版日期:2017-08-20 发布日期:2016-12-12
  • 通讯作者: 阎超 E-mail:yanchao@buaa.edu.cn
  • 作者简介:李彦苏,女,博士研究生。主要研究方向:计算流体力学;阎超,男,博士,教授,博士生导师。主要研究方向:计算流体力学;于剑,男,博士,讲师,硕士生导师。主要研究方向:计算流体力学。
  • 基金资助:
    国家自然科学基金(11402016)

Compact shock capturing scheme for compressible multiscale flow

LI Yansu, YAN Chao, YU Jian   

  1. School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
  • Received:2016-07-27 Revised:2016-11-11 Online:2017-08-20 Published:2016-12-12
  • Supported by:
    National Natural Science Foundation of China (11402016)

摘要: 针对可压缩多尺度流动数值模拟特点,研究一种五阶高分辨率紧致型激波捕捉格式——紧致重构加权基本无振荡(CRWENO)格式。该格式利用非线性权系数将低阶紧致格式加权组合以达到高阶精度。在光滑区域蜕化成具有高分辨率的五阶线性紧致格式,在间断附近则能保持计算稳定无振荡。对CRWENO格式、目前广泛使用的加权基本无振荡(WENO)格式及两格式对应的线性格式(即五阶线性迎风格式和五阶紧致格式)进行数值性能研究,评估非线性权系数对格式耗散及频谱特性的影响。使用一维、二维、三维典型算例进行数值试验,探讨线性/非线性、紧致/非紧致格式在可压缩多尺度流动模拟中的优势和不足。结果表明,CRWENO格式在强压缩性流场模拟中能够稳定地捕捉激波,其紧致特性则改善了非线性格式普遍存在的耗散过大、分辨率较差的问题,使其能够清晰捕捉多尺度流动结构。因此,该格式在可压缩多尺度流动模拟中具有较大优势。

关键词: 紧致格式, 加权基本无振荡(WENO)格式, 激波捕捉, 数值耗散, 频谱特性, 可压缩多尺度流动

Abstract: Aimed at compressible multiscale flow simulations, a fifth-order high-resolution compact shock capturing scheme, compact-reconstruction weighted essentially non-oscillatory (CRWENO), is studied. Nonlinear weights are used to combine lower-order compact schemes to approximate a higher-order compact scheme. The scheme becomes the fifth-order linear compact scheme in smooth regions, while preserves computational stability across discontinuities. Numerical properties were analyzed for CRWENO and weighted essentially non-oscillatory (WENO) which is widely used these days, as well as the linear schemes that they correspond to, i.e. the fifth-order upwind linear scheme and the fifth-order compact scheme. The impacts of nonlinear weights on dissipation and spectral properties are evaluated. The advancements and drawbacks of linear/nonlinear and compact/explicit schemes in compressible multiscale flow simulations are discussed by performing 1D, 2D and 3D typical numerical tests. It can be concluded that CRWENO scheme can obtain non-oscillatory results near strong discontinuous regions. Its compact characteristic improves the problems of over-dissipation and low resolution exiting in nonlinear schemes and makes it clearly resolve multiscale flow structures. In a word, CRWENO is a proper candidate for compressible multiscale flow simulations.

Key words: compact scheme, weighted essentially non-oscillatory (WENO) scheme, shock capturing, numerical dissipation, spectral property, compressible multiscale flow

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