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A priori tests of large eddy simulation of the compressible plane mixing layer

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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.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Bert Vreman, Bernard Geurts & Hans Kuerten

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  1. Bert Vreman
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  2. Bernard Geurts
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  3. Hans Kuerten
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Vreman, B., Geurts, B. & Kuerten, H. A priori tests of large eddy simulation of the compressible plane mixing layer. J Eng Math 29, 299–327 (1995). https://doi.org/10.1007/BF00042759

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  • DOI: https://doi.org/10.1007/BF00042759

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