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Study of numerical errors in direct numerical simulation and large eddy simulation

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Abstract

By comparing the energy spectrum and total kinetic energy, the effects of numerical errors (which arise from aliasing and discretization errors), subgrid-scale (SGS) models, and their interactions on direct numerical simulation (DNS) and large eddy simulation (LES) are investigated. The decaying isotropic turbulence is chosen as the test case. To simulate complex geometries, both the spectral method and Padé compact difference schemes are studied. The truncated Navier-Stokes (TNS) equation model with Padé discrete filter is adopted as the SGS model. It is found that the discretization error plays a key role in DNS. Low order difference schemes may be unsuitable. However, for LES, it is found that the SGS model can represent the effect of small scales to large scales and dump the numerical errors. Therefore, reasonable results can also be obtained with a low order discretization scheme.

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Authors and Affiliations

  1. Research Center for Advanced Power-Strain Technology, Hunan University, Changsha, 410082, P. R. China

    Xiao-long Yang  (杨小龙)

  2. School of Aerospace Engineering, Tsinghua University, Beijing, 100084, P. R. China

    Song Fu  (符松)

Authors
  1. Xiao-long Yang  (杨小龙)
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  2. Song Fu  (符松)
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Corresponding author

Correspondence to Xiao-long Yang  (杨小龙).

Additional information

Communicated by ZHOU Zhe-wei

Project supported by the National Natural Science Foundation of China (No. 10502029) and the Scientific Research Foundation for Returned Overseas Chinese Scholars of Ministry of Education of China

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Yang, Xl., Fu, S. Study of numerical errors in direct numerical simulation and large eddy simulation. Appl. Math. Mech.-Engl. Ed. 29, 871–880 (2008). https://doi.org/10.1007/s10483-008-0705-x

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  • DOI: https://doi.org/10.1007/s10483-008-0705-x

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Chinese Library Classification

2000 Mathematics Subject Classification

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