高精度中心-WENO混合格式在可压缩各向同性湍流大涡模拟中的应用

李震; 琚亚平; 张楚华

doi:10.7652/xjtuxb201701005

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高精度中心-WENO混合格式在可压缩各向同性湍流大涡模拟中的应用

更新时间：2025-07-09

- 高精度中心-WENO混合格式在可压缩各向同性湍流大涡模拟中的应用
- High Accuracy Central-WENO Scheme for Large Eddy Simulations of Compressible Isotropic Turbulence
- 西安交通大学学报 2017年51卷第1期页码：25-30
- 作者机构：
  
  西安交通大学能源与动力工程学院,西安,710049
- 作者简介：
- 基金信息：
  
  : 2016-06-22。作者简介: 李震(1990—),男,博士生;琚亚平(通信作者),女,副教授。基金项目: 国家重点基础研究发展规化资助项目(2016YFB0200901);国家自然科学基金资助项目(51406148);教育部重大科技基础设施培育计划资助项目
- DOI：10.7652/xjtuxb201701005
  中图分类号： O35
- 网络首发：2017-01-10，
  
  纸质出版：2017
- 稿件说明：
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李震, 琚亚平, 张楚华. 高精度中心-WENO混合格式在可压缩各向同性湍流大涡模拟中的应用[J]. 西安交通大学学报, 2017,51(1):25-30.

High Accuracy Central-WENO Scheme for Large Eddy Simulations of Compressible Isotropic Turbulence[J]. 2017, 51(1): 25-30.
李震, 琚亚平, 张楚华. 高精度中心-WENO混合格式在可压缩各向同性湍流大涡模拟中的应用[J]. 西安交通大学学报, 2017,51(1):25-30. DOI： 10.7652/xjtuxb201701005.

High Accuracy Central-WENO Scheme for Large Eddy Simulations of Compressible Isotropic Turbulence[J]. 2017, 51(1): 25-30. DOI： 10.7652/xjtuxb201701005.

摘要

为提高可压缩湍流大涡模拟的格式精度和分辨率

通过引入当地压力脉动的感应因子和格式加权函数的取值界限

发展了一种数值耗散自适应可控的近似6阶中心-WENO(加权本质无振荡)混合格式

采用傅里叶法对离散格式数学特性进行了理论分析

并对一维激波/密度脉动干涉问题和三维可压缩各向同性湍流大涡模拟问题进行了计算。结果表明:近似6阶中心-WENO混合格式相比于5阶-WENO格式具有更小的耗散误差

且对激波和物理脉动均具有较高的分辨率; 基于所发展的中心-WENO混合格式的大涡模拟计算结果与已有的直接数值模拟结果符合较好

且能够成功捕捉-5/3幂律能谱特性曲线; 该格式标定了适合于可压缩流动大涡模拟的格式加权函数界限数值

为流体机械内部可压缩湍流的高精度大涡模拟研究奠定了算法基础。

Abstract

Aiming at high accuracy and high resolution computation for large eddy simulation of compressible turbulence

a qusi-6th order central-WENO(weighted essentially non-oscillatory)hybrid scheme with adaptively controlled numerical dissipation is developed by introducing a local pressure gradient sensor and the upper and lower bounds of the weighting function. The mathematical characteristics of the developed hybrid scheme are theoretically analyzed with Fourier method. The 1D shock/density wave interaction problem and the 3D large eddy simulation of compressible isotropic turbulence are numerically analyzed to verify the validity and effectiveness of the scheme. The results show that the quasi-6th order central-WENO hybrid scheme has lower numerical dissipative error than the 5th order WENO scheme and can hold the high resolution for both the discontinuities and physical fluctuations in the flow fields. The decay curves of the turbulent statistics obtained by large eddy simulation with the central-WENO hybrid scheme coincide well with the available direct numerical simulation

and the -5/3 power law of the theoretical energy spectrum is successfully captured. The specific bounds of the weighting function applicable to the large eddy simulation of compressible flow are calibrated. This work lays a solid algorithm foundation for high accuracy large eddy simulation of compressible turbulence in fluid machinery.

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