### Abstract

Three important aspects for the assessment of the possibilities of Large Eddy Simulation (LES) of compressible flow are investigated. In particular the magnitude of all subgrid-terms, the role of the discretization errors and the correlation of the turbulent stress tensor with several subgrid-models are studied. The basis of the investigation is a Direct Numerical Simulation (DNS) of the two- and three-dimensional compressible mixing layer, using a finite volume method on a sufficiently fine grid. With respect to the first aspect, the exact filtered Navier-Stokes equations are derived and all terms are classified according to their order of magnitude. It is found that the pressure dilatation subgrid-term in the filtered energy equation, which is usually neglected in the modelling-practice, is as large as e.g. the pressure velocity subgrid-term, which in general is modelled. The second aspect yields the result that second- and fourth-order accurate spatial discretization methods give rise to discretization errors which are larger than the corresponding subgrid-terms, if the ratio between the filter width and the grid-spacing is close to one. Even if an exact representation for the subgrid-scale contributions is assumed, LES performed on a (considerably) coarser grid than required for a DNS, is accurate only if this ratio is sufficiently larger than one. Finally the well-known turbulent stress tensor is investigated in more detail. A priori tests of subgrid-models for this tensor yield poor correlations for Smagorinsky's model, which is purely dissipative, while the non-eddy viscosity models considered here correlate considerably better.

Original language | English |
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Pages (from-to) | 299-327 |

Number of pages | 29 |

Journal | Journal of engineering mathematics |

Volume | 29 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1995 |

### Keywords

- METIS-140928
- IR-92563

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## Cite this

Vreman, A. W., Geurts, B. J., & Kuerten, J. G. M. (1995). A priori tests of large Eddy simulation of the compressible plane mixing layer.

*Journal of engineering mathematics*,*29*(4), 299-327. https://doi.org/10.1007/BF00042759